RBSE Solutions Class 6 Maths Chapter 1 Know the Numbers More Ques

Pg. No. 4

Question 1. In the following group of numbers; Circle the greatest number and put (x) on the smallest number.
(i) 4536, 4892, 4370, 4452
(ii) 15623, 15073, 15189, 15800
(iii) 25286, 25245, 25270, 25210
(iv) 6895, 23787, 24569, 24659
(v) 4685, 4444, 3847, 9071
Answer:
(i) For the numbers 4536, 4892, 4370, 4452:
Greatest number is 4892.
Smallest number is 4370.

(ii) For the numbers 15623, 15073, 15189, 15800:
Greatest number is 15800.
Smallest number is 15073.

(iii) For the numbers 25286, 25245, 25270, 25210:
Greatest number is 25286.
Smallest number is 25210.

(iv) For the numbers 6895, 23787, 24569, 24659:
Greatest number is 24659.
Smallest number is 6895.

(v) For the numbers 4685, 4444, 3847, 9071:
Greatest number is 9071.
Smallest number is 3847.
In simple words: To find the greatest number, look for the one with the most digits or the largest first digit. To find the smallest, look for the one with the fewest digits or the smallest first digit.

🎯 Exam Tip: When comparing numbers, always start from the leftmost digit. If digits are equal, move to the next digit to the right until you find a difference.

Question 2. Complete the following table :
Answer: The table showing place values for numbers is completed below. The greatest number in the original list from the table is 98,453 (circled) and the smallest number is 12,345 (crossed).

In simple words: This table shows how to write numbers in words and in an expanded form, breaking them down by their place value, like tens, hundreds, and thousands.
🎯 Exam Tip: Always practice writing numbers in both standard and expanded forms to clearly understand their place value, which is crucial for larger number operations.

Pg. No. 6

Question 1. Write the number names for the following digits.
(i) 5,005
(ii) 5,438
(iii) 38,400
(iv) 65,740
(v) 89,324
(vi) 20,05,002
(vii) 85,00,801
(viii) 7,07,007
Answer:
(i) Five thousand five
(ii) Five thousand four hundred thirty eight
(iii) Thirty eight thousand four hundred
(iv) Sixty five thousand seven hundred forty
(v) Eighty nine thousand three hundred twenty four
(vi) Twenty lakh five thousand two
(vii) Eighty five lakh eight hundred one
(viii) Seven lakh seven thousand seven
In simple words: To write a number in words, read it from left to right, saying the place value for each group of digits, like "thousand" or "lakh".

🎯 Exam Tip: Pay close attention to zeroes within a number, as they often determine if a place value is mentioned or skipped when writing out the name.

Question 2. Keeping the place value of number six at the same place and jumbling the digits of number 6350947; the smallest number shall be:
(i) 6975430
(ii) 6043579
(iii) 6034579
(iv) 6034759
Answer: (iii) 6034579
In simple words: To make the smallest number while keeping '6' in its place, arrange the other digits (0, 3, 4, 5, 7, 9) in increasing order.

🎯 Exam Tip: When forming the smallest number, place the smallest digits in the higher place value positions (leftmost) and remember that zero cannot be the very first digit unless it's a special case like a decimal.

Question 3. The largest five digit number using digits 7, 8 and 9 is :
(i) 98978
(ii) 99897
(iii) 99987
(iv) 98799
Answer: (iii) 99987
In simple words: To create the largest five-digit number using only the digits 7, 8, and 9, you should use the largest digit, 9, as many times as possible in the most significant places.

🎯 Exam Tip: To form the largest possible number from a given set of digits, arrange them in descending order from left to right, repeating the largest digits if fewer digits are provided than required places.

Pg. No. 5

Question. Discuss with your friends and write the numbers in descending order.
Answer: The provided table gives numbers and their details. To write them in descending order, we compare them from largest to smallest. The numbers are 99,99,999; 40,50,607; 32,05,004; 10,00,000; 98,76,543.
The numbers in descending order are:
\( 99,99,999 > 98,76,543 > 57,68,423 > 40,50,607 > 32,05,004 > 10,00,000 \)

In simple words: We organized these large numbers from the biggest to the smallest. This helps us see which number is much larger than the others, based on their place values.
🎯 Exam Tip: To correctly order large numbers, ensure you compare them digit by digit from left to right, focusing on their place values, especially for numbers with different numbers of digits.

Pg. No. 7

Question 1. Complete the following table :
Answer: The table of numbers and their expanded forms is completed below. It helps us understand the value of each digit in a number.

In simple words: This table breaks down large numbers to show what value each digit has. It helps in understanding the Indian number system clearly.
🎯 Exam Tip: When filling out a place value table for large numbers, it's helpful to first mentally group the digits according to the Indian (or International) system, usually in sets of two or three from the right.

Question. Write the numbers given in the table in ascending and descending order.
Answer: The numbers given in the table are 7,65,43,201; 1,00,00,000; 9,09,09,009; 6,50,41,300. We will write them in ascending (smallest to largest) and descending (largest to smallest) order.
Writing the numbers in ascending order:
\( 1,00,00,000 < 4,35,01,076 < 4,53,10,670 < 6,50,41,300 < 7,65,43,201 < 9,09,09,009 \)

Writing the numbers in descending order:
\( 9,09,09,009 > 7,65,43,201 > 6,50,41,300 > 4,53,10,670 > 4,35,01,076 > 1,00,00,000 \)
In simple words: Ascending order means arranging numbers from the smallest to the biggest. Descending order means arranging them from the biggest to the smallest.

🎯 Exam Tip: To correctly order large numbers, always compare the number of digits first. If the number of digits is the same, compare the leftmost digit, then move right if they are equal.

Pg. No. 15

Question 1. Take various kinds of things in your hand (wheat, corn, soyabean, pebbles etc.) and ask your friend to estimate the number. Now count it.
Answer: This is an activity designed to help understand estimation. For example, if you estimate a handful of wheat grains to be 100, then count them to be 95, you learn how close your estimate was. It helps to develop a sense of quantity.
In simple words: Pick some small things, guess how many there are, and then count them to see how accurate your guess was.

🎯 Exam Tip: When estimating, try to use a smaller, known quantity as a reference (e.g., "this pile looks like three of my smaller groups of ten").

Question 2. Divide into groups of 4 in your class and estimate their weights and fill it in the following :

Now weight the children on weighing machines and find out
1. How many of your guessed the correct weight ?
2. How many of you guessed the weight close to the actual weight ?
3. How many of you guessed the weight not close to the actual weight ?
Answer: This is a practical activity. An example of a completed table with estimated and actual weights, along with answers to the follow-up questions, is provided below:

1. Following children guessed the correct weight: Vikas, Rahul, Neel, Roli, Sonal, Babita, and Seema.
2. Six students estimated a weight nearest to their actual weight.
3. Three students estimated a weight far from their actual weight.
In simple words: This activity helps us learn how to guess weights. We guess, then measure, and see how close our guesses are.
🎯 Exam Tip: For estimation tasks, it's good to have a mental reference point, like knowing the average weight of common objects, to make more accurate guesses.

Question 3. Discuss with your friends and guess following :
1. Estimated distance of the school from your house is ..................m/km.
Answer:
1. The estimated distance of the school from your house can vary for each student. For example, it might be around 500 meters or 2 kilometers, depending on where you live. This is a personal estimation activity.
In simple words: This question asks you to guess how far your school is from your home, using meters or kilometers.

🎯 Exam Tip: When estimating distances, consider using known landmarks or the time it takes to walk/travel to gauge the distance more accurately.

Pg. No. 1-2

Question 1. Think about the situations, where we use numbers.
Answer: We use numbers in our daily lives for many things. For example, we use them to count students, chairs, tables, doors, windows, and fans in a room. We also use numbers for money, time, and addresses.
In simple words: We use numbers every day for counting things around us and for important information like time or money.

🎯 Exam Tip: When asked for examples, try to list a variety of situations to show a broad understanding of the concept.

Question 2. Ramesh and Afsana formed a four digit number using digit 3, 5, 7, 8. Using these numbers, you also form different numbers. Ask your friend to arrange them in ascending and descending order.
Answer: Using the digits 3, 5, 7, 8, we can form many different four-digit numbers. For instance, some numbers are 3578, 3758, 3785, 3587, 3857, 3875, and so on. If we use all possible permutations and include digits like 5378, 5387, 5837, 5873, 5738, 5783, 7358, 7385, 7538, 7583, 7835, 7853, 8357, 8375, 8735, 8753, 8537, 8573, the complete list will be quite long.

Numbers in ascending order (smallest to largest) are:
3578, 3587, 3758, 3785, 3857, 3875, 5378, 5387, 5738, 5783, 5837, 5873, 7358, 7385, 7538, 7583, 7835, 7853, 8357, 8375, 8537, 8573, 8735, 8753.

Numbers in descending order (largest to smallest) are:
8753, 8735, 8573, 8537, 8375, 8357, 7853, 7835, 7583, 7538, 7385, 7358, 5873, 5837, 5783, 5738, 5387, 5378, 3875, 3857, 3785, 3758, 3587, 3578.
In simple words: We take the given digits and make all possible four-digit numbers. Then we put them in order from the smallest to the biggest, and from the biggest to the smallest.

🎯 Exam Tip: To ensure you don't miss any numbers when forming combinations, list them systematically or think about how many options there are for each digit place.

Question 3. Which is the smallest number among the numbers you made?
Answer: The smallest number formed using the digits 3, 5, 7, and 8 is 3578. When forming the smallest number, the smallest digits should be placed in the highest value positions.
In simple words: The smallest number we can make using 3, 5, 7, and 8 is 3578.

🎯 Exam Tip: Always place the smallest digit in the leftmost position (highest place value) to form the smallest possible number from a given set of digits.

Question 4. Form a five digit number using 4, 5, 2, 6 and 3. You also form more numbers of 5-digit using these digits and write in following table.
Answer: Using the digits 4, 5, 2, 6, and 3, several five-digit numbers can be formed. These numbers can then be written in words, as shown in the table below.

In simple words: We used the digits 4, 5, 2, 6, and 3 to make different five-digit numbers and then wrote down what each number is called.
🎯 Exam Tip: When forming numbers from a given set of digits, try to arrange them in various combinations to explore all possibilities and understand how digit placement affects the number's value.

Question 5. Among the numbers 64532 and 64352 which is greater? How?
Answer: To find which number is greater between 64532 and 64352, we compare them from left to right, digit by digit:
For both numbers, the ten thousands digit is 6, and the thousands digit is 4. These are the same.
When we look at the hundreds place, 64532 has a 5, and 64352 has a 3. Since 5 is greater than 3, the number 64532 is greater than 64352.
\[ 64532 \]
\[ 60000 = 60000 \]
\[ 4000 = 4000 \]
\[ 500 > 300 \]
\[ 64352 \]
Thus, number 64532 is greater than 64352.
In simple words: We compare the numbers from left to right. The first place where they are different tells us which number is bigger. Here, the hundreds digit in 64532 is bigger than in 64352, so 64532 is the greater number.

🎯 Exam Tip: Always compare numbers by starting from the leftmost digit and moving to the right. The first digit that is different determines which number is larger or smaller.

Question 2. Compare the numbers 56432 and 56342 from left to right and see which is the bigger number.
Answer: To compare 56432 and 56342, we look at their digits from left to right.
- Both numbers have 5 in the ten thousands place: \( 5 = 5 \)
- Both numbers have 6 in the thousands place: \( 6 = 6 \)
- In the hundreds place, 56432 has a 4, and 56342 has a 3. Since \( 4 > 3 \), the number 56432 is greater.
Therefore, 56432 is greater than 56342.

In simple words: When comparing 56432 and 56342, the first two digits are the same. But in the hundreds place, 4 is bigger than 3, so 56432 is the larger number.
🎯 Exam Tip: When numbers have the same count of digits, start comparing from the leftmost digit. The first digit that differs will tell you which number is greater.

Pg. No. 5

Question 1. Take six digits of your choice and form different numbers and compare them.
Answer: Let's choose six digits: 7, 4, 8, 3, 5, 9. We can form various numbers using these digits, for example:
345789, 754398, 987543, 839547, 495378, 589374.

Now, let's compare these numbers and arrange them in descending order:
\( 987543 > 839547 > 754398 > 589374 > 495378 > 345789 \)
In simple words: We picked six numbers and made different large numbers from them. Then we put them in order from the biggest to the smallest.

🎯 Exam Tip: To get diverse numbers from a set of digits, try changing the order of digits to create both the largest and smallest possible numbers, as well as several in between.

Question 2. Complete the following table -
Answer: The table showing place values for various numbers in the Indian system is completed below. This helps in understanding large numbers and how to write them in words.

In simple words: This table shows how to write numbers by breaking them into their place values (like lakhs and thousands) and then writing their full name.
🎯 Exam Tip: When filling out a table like this, remember to correctly group digits according to the Indian number system's place values to avoid errors in naming them.

Question 3. Write the given numbers is table, in ascending order.
Answer: The numbers provided in the table are 7,00,295; 9,99,999; 1,00,000; 5,67,890; 6,04,307; 4,72,280; 3,52,027; 2,43,596. We will arrange these in ascending order, from the smallest to the largest. Remember, 1,00,000 is one lakh.
Writing the numbers in ascending order:
\( 1,00,000 < 2,43,596 < 3,52,027 < 4,72,280 < 5,67,890 < 6,04,307 < 7,00,295 < 9,99,999 \)
In simple words: We take all the numbers from the table and line them up from the smallest one to the biggest one.

🎯 Exam Tip: Always double-check the number of digits in each number first, as numbers with fewer digits are usually smaller than those with more (e.g., a 5-digit number is smaller than a 6-digit number).

Question 5. How do you read 10,00,000?
Answer: The number 10,00,000 is read as Ten Lakh. In the Indian number system, one lakh is equal to one hundred thousand.
In simple words: 10,00,000 is called "Ten Lakh".

🎯 Exam Tip: Remember the grouping of digits in the Indian number system (3, 2, 2, ...) to correctly read large numbers. For example, 1,00,000 is one lakh, and 10,00,000 is ten lakh.

Question 6. How we read number 15,40,400?
Answer: The number 15,40,400 is read as Fifteen Lakh Forty Thousand Four Hundred. This follows the Indian number system where numbers are grouped into lakhs and thousands.
In simple words: 15,40,400 is read as "Fifteen Lakh Forty Thousand Four Hundred".

🎯 Exam Tip: Practice reading numbers aloud to get comfortable with the Indian number system's place values (crores, lakhs, thousands, hundreds, tens, ones).

Think

Pg. No. 9

Question 1. How many lakhs is equal to one million?
Answer: Ten lakhs are equal to one million. The Indian number system uses 'lakhs' and 'crores', while the International system uses 'millions' and 'billions'. One million is 1,000,000, and one lakh is 1,00,000.
In simple words: One million is the same as ten lakhs.

🎯 Exam Tip: Knowing the conversion between Indian and International number systems is key. Remember that 1 Million \( = 10 \text{ Lakh} \) and 1 Crore \( = 10 \text{ Million} \).

Question 2. How many millions is equal to one crore
Answer: Ten million is equal to one crore. In the Indian number system, one crore is written as 1,00,00,000. In the International system, ten million is written as 10,000,000.
In simple words: One crore is the same as ten million.

🎯 Exam Tip: A useful way to remember conversions is to write out both numbers with their zeroes: 1,00,00,000 (Indian) and 10,000,000 (International) to see they are equivalent.

Question 3. Write five large numbers in Indian and International system.
Answer: Here are five large numbers written in both the Indian and International number systems:

In simple words: This table shows the same large numbers written in two different ways: one way uses lakhs and crores (Indian system), and the other uses millions (International system).
🎯 Exam Tip: Pay close attention to the placement of commas in each system. The Indian system groups digits after the first three into twos, while the International system groups them into threes.

Pg. No. 12-13

Question 1. Detail of one month's purchase from Khichdi Kirana Store is as follows :

(1) Can you find out the total weight of things sold by Khichdi Kirana store last month? (excluding the weight of soapcake).
(2) What is the total weight of soap cake in kilogram sold last month?
(3) How many amount of money did Kirana Store get by selling sugar and tea?
(4) How much amount did Kirana store get by selling salt and chilli?
Answer:
(1) Total weight of things sold by Khichdi Kirana store (excluding soap cake) is calculated by adding the weights of all other items:
Weight of Gur \( = 325 \text{ kg} \)
Weight of Sugar \( = 3837 \text{ kg} \)
Weight of Rice basmati \( = 906 \text{ kg} \)
Weight of Seeng dana \( = 164 \text{ kg} \)
Weight of Pure ghee \( = 500 \text{ kg} \)
Weight of Tuar dal \( = 1369 \text{ kg} \)
Weight of Tea leaves \( = 188 \text{ kg} \)
Weight of Salt \( = 234 \text{ kg} \)
Weight of Chilli powder \( = 93 \text{ kg} \)
Weight of Coriander powder \( = 147 \text{ kg} \)
Weight of Turmeric powder \( = 189 \text{ kg} \)
Weight of Chana Dal \( = 3273 \text{ kg} \)
Total weight \( = 325 + 3837 + 906 + 164 + 500 + 1369 + 188 + 234 + 93 + 147 + 189 + 3273 \text{ kg} \)
Total weight \( = 11,225 \text{ kg} \)

(2) Total weight of soap cake sold last month in kilograms:
Weight of one bar soap \( = 75 \text{ gm} \)
Soap bars bought \( = 13048 \text{ pieces} \)
Total weight of soap bar \( = 13048 \times 75 \text{ gm} \)
Total weight of soap bar \( = 978600 \text{ gm} \)
To convert grams to kilograms, we divide by 1000:
Total weight of soap bar \( = \frac{978600}{1000} \text{ kg} \)
Total weight of soap bar \( = 978.6 \text{ kg} \)

(3) Amount of money Kirana Store got by selling sugar and tea:

(4) Amount of money Kirana Store got by selling salt and chilli:

In simple words: The shopkeeper calculated the total weight of items sold by adding up each product's weight. For soap, total weight was found by multiplying pieces by weight per piece and converting to kilograms. The money earned from sugar, tea, salt, and chilli was calculated by multiplying their weights by their respective prices.🎯 Exam Tip: Always pay attention to the units (kg, gm, pieces) and convert them correctly when performing calculations. Ensure all items are included as specified in the question.

Question 1. Detail of one month's purchase from Khichdi Kirana Store is as follows :
(1) Can you find out the total weight of things sold by khichdi kirana store last month? (excluding the weight of soapcake).
(2) What is the total weight of soap cake in kilogram sold last month?
(3) How much amount of money did Kirana Store get by selling sugar and tea?
(4) How much amount did Kirana store get by selling salt and chilli?
Answer:
(1) Here are some of the items and their weights:
Tuar dal: 1369 kg
Tea leaves: 188 kg
Salt: 234 kg
Chilli powder: 93 kg
Coriander powder: 147 kg
Turmeric powder: 189 kg
Chana Dal: 3273 kg
The total weight of things sold by the store (excluding soap cake) was \( 11,225 \) kg. This total includes all listed items and potentially others not specified in the individual breakdown.
(2) The weight of one soap bar is \( 75 \) gm. The store bought \( 13,048 \) pieces of soap.
To find the total weight of soap bars, we multiply the number of pieces by the weight of each bar:
Total weight of soap bars \( = 13,048 \times 75 \) gm \( = 978,600 \) gm.
To convert grams to kilograms, we divide by \( 1000 \) (since \( 1000 \) gm \( = 1 \) kg):
Total weight of soap bars \( = \frac { 978,600 }{ 1000 } \) kg \( = 978.6 \) kg.
So, the total weight of soap cake sold last month was \( 978.6 \) kg.
(3) To find the money earned from selling sugar and tea, we calculate the earnings from each item and add them up:
For Sugar: Weight \( = 3837 \) kg, Rate \( = \) Rs. \( 35 \) per kg.
Amount from Sugar \( = 3837 \times 35 = \) Rs. \( 1,34,295 \).
For Tea leaves: Weight \( = 188 \) kg, Rate \( = \) Rs. \( 175 \) per kg.
Amount from Tea leaves \( = 188 \times 175 = \) Rs. \( 32,900 \).
Total amount from Sugar and Tea \( = 1,34,295 + 32,900 = \) Rs. \( 1,67,195 \).
The store earned Rs. \( 1,67,195 \) from selling sugar and tea.
(4) To find the money earned from selling salt and chilli, we calculate the earnings from each item and add them up:
For Salt: Weight \( = 234 \) kg, Rate \( = \) Rs. \( 7 \) per kg.
Amount from Salt \( = 234 \times 7 = \) Rs. \( 1,638 \).
For Chilli powder: Weight \( = 93 \) kg, Rate \( = \) Rs. \( 180 \) per kg.
Amount from Chilli powder \( = 93 \times 180 = \) Rs. \( 16,740 \).
Total amount from Salt and Chilli \( = 1,638 + 16,740 = \) Rs. \( 18,378 \).
The store earned Rs. \( 18,378 \) from selling salt and chilli.
In simple words: We calculated the total weight of various items, then the weight of soap. After that, we found out how much money the store earned from sugar and tea, and then from salt and chilli, by multiplying weights by their prices. Each step helps us understand the store's sales.
🎯 Exam Tip: When dealing with multiple parts in a problem, break it down into smaller, manageable steps. Pay attention to units, converting them when necessary (like grams to kilograms), and ensure all calculations are accurate to avoid errors.

Complete The Following Table -

Question 1. Think about the situations where we use a rounded-off number and when we need an exact number.
Answer: We use rounded-off numbers for general estimations, like when talking about distances, speeds, or time without needing precise details. For example, saying a journey will take "about 2 hours" is a rounded-off number. However, we always need exact numbers for things like calculating rent, paying bills, or receiving salaries. These situations require precise figures to avoid errors.
In simple words: We round numbers for quick estimates but need exact numbers for important things like money or measurements that must be precise.
🎯 Exam Tip: Distinguishing between estimation and exact calculation is crucial in real-life applications. Understanding when to use which helps in making practical decisions.

Question 2. Rounding numbers to the nearest tens.
(i) Which flag is closer to 10?
(ii) Which flag is closer to 20 ?
Answer:
(i) Flag 13 is closer to 10. (The distance from 13 to 10 is 3 units, while from 13 to 20 is 7 units).
(ii) Flag 17 is closer to 20. (The distance from 17 to 20 is 3 units, while from 17 to 10 is 7 units).
Here is the number line showing the flags and their positions:

In simple words: Look at the number line. The flag at 13 is closer to 10 than to 20. The flag at 17 is closer to 20 than to 10. This helps us understand which 'ten' a number is nearest to.
🎯 Exam Tip: When rounding, always check the digit in the place value to the right of the rounding place. If it's 5 or more, round up; if it's less than 5, round down. Visualizing on a number line can help confirm your choice.

Question 3. How do we round off the numbers written on the number line ?
Answer: We round numbers to the nearest tens by looking at the unit digit. If the unit digit is 5 or more, we round up the tens digit. If it is less than 5, we keep the tens digit as it is.
(i) For the numbers 54 and 66:
For 54:
The unit digit is 4, which is less than 5. So, the tens digit remains 5 (representing 50). The rounded value is 50.
For 66:
The unit digit is 6, which is greater than 5. So, we round up the tens digit from 6 to 7 (representing 70). The rounded value is 70.

(ii) For the numbers 278 and 283:
For 278:
The unit digit is 8, which is greater than 5. So, we round up the tens digit from 7 to 8 (representing 280). The rounded value is 280.
For 283:
The unit digit is 3, which is less than 5. So, the tens digit remains 8 (representing 280). The rounded value is 280.

In simple words: To round a number to the nearest ten, check the last digit. If it's 5 or more, the tens digit goes up. If it's less than 5, the tens digit stays the same. The numbers 54 and 283 round down, while 66 and 278 round up.
🎯 Exam Tip: Always identify the 'rounding place' first (here, the tens place) and then look one digit to the right (the units place). This simple rule is key to correct rounding.

Question 4. Are 278 and 283 both rounded off to 280? Why?
Answer: Yes, both 278 and 283 round off to 280 when rounded to the nearest ten. For 278, the unit digit is 8, which is 5 or greater, so we round up the tens digit (7 becomes 8). For 283, the unit digit is 3, which is less than 5, so the tens digit (8) stays the same. In both cases, the number rounds to 280 because their nearest multiple of ten is 280. When rounding 78 to the nearest ten, it becomes 80, and rounding 83 to the nearest ten also becomes 80.
In simple words: Yes, both numbers become 280 when rounded to the closest ten. This happens because 278 is closer to 280 than 270, and 283 is also closer to 280 than 290.
🎯 Exam Tip: Remember that rounding to the nearest ten means finding the multiple of ten that is closest to the given number. Numbers ending in 5 are typically rounded up.

Question 5. Learn these:
\( 9 + 1 = 10 \)
\( 99 + 1 = 100 \)
\( 999 + 1 = \)
\( 9,999 + 1 = \)
\( 99,999 + 1 = \)
\( 9,99,999 + 1 = \)
\( 99,99,999 + 1 = 1,00,00,000 \)

\( 10 \times 10 = 100 \)
\( 100 \times 10 = 1,000 \)
\( 1,000 \times 10 = 10,000 \)
\( 10,000 \times 10 = 1,00,000 \)
\( 1,00,000 \times 10 = 10,00,000 \)
\( 10,00,000 \times 10 = 1,00,00,000 \)
Answer: Here are the completed patterns, showing how numbers grow with addition and multiplication:
\( 9 + 1 = 10 \)
\( 99 + 1 = 100 \)
\( 999 + 1 = 1,000 \)
\( 9,999 + 1 = 10,000 \)
\( 99,999 + 1 = 1,00,000 \)
\( 9,99,999 + 1 = 10,00,000 \)
\( 99,99,999 + 1 = 1,00,00,000 \)

\( 10 \times 10 = 100 \)
\( 100 \times 10 = 1,000 \)
\( 1,000 \times 10 = 10,000 \)
\( 10,000 \times 10 = 1,00,000 \)
\( 1,00,000 \times 10 = 10,00,000 \)
\( 10,00,000 \times 10 = 1,00,00,000 \)
In simple words: These patterns demonstrate how adding one to a sequence of nines creates a power of ten, and how multiplying by ten consistently adds a zero, increasing the number's magnitude.
🎯 Exam Tip: Recognize that these patterns highlight the concept of place value in our decimal system. Each '9' turning to '0' and carrying over, or each multiplication by 10, shifts digits to the left, increasing their value.

Question 1. Identify the pattern.
\( 0 \times 9 + 1 = 1 \)
\( 1 \times 9 + 2 = 11 \)
\( 12 \times 9 + 3 = 111 \)
\( 123 \times 9 + 4 = 1111 \)
\( 1234 \times 9 + 5 = \)

\( 9 \times 9 + 7 = 88 \)
\( 98 \times 9 + 6 = 888 \)
\( 987 \times 9 + 5 = 8888 \)
\( 9876 \times 9 + 4 = 88888 \)
\( 98765 \times 9 + \dots = \)

Answer: Here are the completed patterns, showing how numbers follow predictable rules:
**First Pattern:**
\( 0 \times 9 + 1 = 1 \)
\( 1 \times 9 + 2 = 11 \)
\( 12 \times 9 + 3 = 111 \)
\( 123 \times 9 + 4 = 1111 \)
\( 1234 \times 9 + 5 = 11111 \)
\( 12345 \times 9 + 6 = 111111 \)
\( 123456 \times 9 + 7 = 1111111 \)
\( 1234567 \times 9 + 8 = 11111111 \)

**Second Pattern:**
\( 9 \times 9 + 7 = 88 \)
\( 98 \times 9 + 6 = 888 \)
\( 987 \times 9 + 5 = 8888 \)
\( 9876 \times 9 + 4 = 88888 \)
\( 98765 \times 9 + 3 = 888888 \)
\( 987654 \times 9 + 2 = 8888888 \)
\( 9876543 \times 9 + 1 = 88888888 \)
In simple words: These are number patterns where the numbers on the left side grow in a special way, and multiplying them by 9 and adding a certain number always gives a result with repeating ones or eights. Looking closely helps you guess the next line.
🎯 Exam Tip: When identifying patterns, carefully observe how each part of the equation changes from one line to the next. Look for changes in the digits being multiplied, the number added, and the resulting digits to predict the next steps.