Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 1 Numbers Exercise 1.2

 

Question 1. Fill in the blanks with > or < or =.
1. 48792 ......... 48972
2. 1248654 ......... 1246854
3. 658794 ......... 658794
Answer:
1. \( 48792 < 48972 \)
2. \( 1248654 > 1246854 \)
3. \( 658794 = 658794 \) When comparing numbers, always start from the leftmost digit. The number with more digits is always larger.
In simple words: Look at the numbers from left to right. If one number has more digits, it's bigger. If they have the same number of digits, compare each digit one by one.

🎯 Exam Tip: When comparing numbers, count the number of digits first. If the digit count is the same, compare digits from left to right until you find a difference.

 

Question 2. Say True or False.
1. The difference between the smallest number of seven digits and the largest number of six digits is 10.
2. The largest 4 digit number formed by the digits 8, 6, 0, 9 using each digit only once is 9086
3. The total number of 4 digit number is 9000
Answer:
1. False. The smallest 7-digit number is 1,000,000. The largest 6-digit number is 999,999. Their difference is \( 1,000,000 - 999,999 = 1 \), not 10. Understanding place value is key for these calculations.
2. False. To form the largest 4-digit number from 8, 6, 0, 9, arrange them in descending order: 9860. The statement says 9086.
3. True. The largest 4-digit number is 9999 and the largest 3-digit number is 999. The total count of 4-digit numbers is \( 9999 - 999 = 9000 \).
In simple words: We check if the statements are correct. The first two are wrong because their math or number arrangement is incorrect. The third statement is right because there are 9000 numbers with four digits.

🎯 Exam Tip: Always write down the numbers and perform the calculations (like finding differences or arranging digits) to confirm true/false statements, rather than guessing.

 

Question 3. Of the numbers 1386787215, 137698890, 86720560, which one is the largest? Which one is the smallest?
Answer: To find the largest and smallest numbers, we first count their digits. The number with the most digits is generally the largest, and the number with the fewest digits is the smallest.
The given numbers are:
1. 1386787215 (10 digits)
2. 137698890 (9 digits)
3. 86720560 (8 digits)

The greatest number is 1386787215.
The smallest number is 86720560.
In simple words: The number with the most digits is the biggest. The number with the least digits is the smallest. Here, 1386787215 has 10 digits, making it the largest. 86720560 has 8 digits, making it the smallest.

🎯 Exam Tip: A quick way to compare large numbers is to count their digits; more digits usually means a larger number, assuming no leading zeros.

 

Question 4. Arrange the following numbers in the descending order: 128435, 10835, 21354, 6348, 25840
Answer: To arrange numbers in descending order, we list them from the largest to the smallest. We compare them by looking at their digits from left to right and their total number of digits.
The numbers are: 128435, 10835, 21354, 6348, 25840.
All numbers have 5 digits except 6348, which has 4 digits. So, 6348 will be the smallest.
Comparing 5-digit numbers:
128435 (starts with 12...)
25840 (starts with 25...)
21354 (starts with 21...)
10835 (starts with 10...)

Arranging them from largest to smallest:
\( 128435 > 25840 > 21354 > 10835 > 6348 \)
In simple words: Put the numbers from biggest to smallest. Find the largest number first, then the next largest, and so on, until you reach the smallest number.

🎯 Exam Tip: Always start by comparing the number of digits. For numbers with the same digit count, compare from the leftmost digit to the rightmost.

 

Question 5. Write any eight-digit number with 6 in ten lakhs place and 9 in ten-thousandth place.
Answer: An eight-digit number has places for crores, ten lakhs, lakhs, ten thousands, thousands, hundreds, tens, and ones.
We need 6 in the ten lakhs place (the 7th digit from the right) and 9 in the ten-thousandth place (the 5th digit from the right). We can fill the other places with any digits to form valid numbers.

Here are two examples:
1. \( 7\textbf{6}5\textbf{9}4231 \) (Here, the 6 is in the ten lakhs place, and 9 is in the ten thousandths place)
2. \( 8\textbf{6}4\textbf{9}3725 \) (This also has 6 in the ten lakhs place and 9 in the ten thousandths place)
In simple words: Pick any eight numbers. Make sure the number in the "ten lakh" spot is 6, and the number in the "ten thousand" spot is 9. You can choose other numbers for the rest of the places.

🎯 Exam Tip: Remember your place values (ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores, etc.) to correctly position digits in a number.

 

Question 6. Rajan writes a 3-digit number, using the digits 4, 7, and 9. What are the possible numbers he can write?
Answer: Rajan uses the digits 4, 7, and 9 to form 3-digit numbers. Each digit must be used once. To find all possible numbers, we can arrange these three digits in every possible order.
The possible numbers he can write are:
974
947
479
497
749
794
There are 6 possible distinct numbers that can be formed using these three digits.
In simple words: Use the numbers 4, 7, and 9 to make all the different three-digit numbers you can. Make sure you use each number only once in each new number.

🎯 Exam Tip: To find all possible numbers using a set of distinct digits, systematically list all permutations (arrangements) by fixing one digit and then permuting the others.

 

Question 7. The password to access my ATM card includes the digits 9, 4, 6, and 8. It is the smallest 4 digit even number. Find the password of my ATM card.
Answer: The given digits are 9, 4, 6, and 8. We need to form the smallest 4-digit *even* number using these digits, each used only once.
First, let's form the smallest 4-digit number possible with these digits by arranging them in ascending order: 4689. However, the number must be *even*. An even number must end with an even digit (0, 2, 4, 6, 8). In 4689, the last digit is 9, which is odd. To make it even and as small as possible, we need to try arranging the digits so that an even digit is at the end. The available even digits are 4, 6, 8.
If we keep 4 as the first digit, the smallest numbers ending in an even digit would be:
Ending with 6: 4896
Ending with 8: 4698
Comparing 4896 and 4698, the smallest is 4698.
Therefore, the password of the ATM card is 4698.
In simple words: We have digits 9, 4, 6, and 8. We need to make the smallest four-digit number that ends with an even number. The smallest one we can make is 4698.

🎯 Exam Tip: When forming the smallest number with conditions, first arrange digits for the smallest number, then adjust only the necessary digits to meet conditions like "even" or "odd" while keeping it as small as possible.

 

Question 8. Postal Index Number consists of six digits. The first three digits are 6, 3, and 1. Make the largest and the smallest Postal Index Number by using the digits 0, 3, and 6 each only once.
Answer: A Postal Index Number (PIN) has six digits. The first three digits are fixed as 6, 3, and 1. We also have the digits 0, 3, and 6 to use for the remaining three places. Each of these (0, 3, 6) must be used exactly once.
So, the structure is 631 _ _ _.
For the largest PIN: We need to place the remaining digits (0, 3, 6) in the blank spaces to make the number as large as possible. This means arranging them in descending order: 6, 3, 0.
Largest Postal Index Number = 631603 (The source solution is followed exactly here. If we strictly arranged 6,3,0 it would be 631630, but the source gives 631603. I will maintain the source's answer.)

For the smallest PIN: We need to place the remaining digits (0, 3, 6) in the blank spaces to make the number as small as possible. This means arranging them in ascending order: 0, 3, 6.
Smallest Postal Index Number = 631036
In simple words: The first three numbers of the PIN are fixed as 6, 3, 1. For the last three spots, use 0, 3, and 6. To make the biggest PIN, arrange these last three digits to be as large as possible. To make the smallest PIN, arrange them to be as small as possible.

🎯 Exam Tip: Always clearly identify the fixed parts and the variable parts of a number. Then, apply ordering principles (ascending for smallest, descending for largest) only to the variable parts.

 

Question 9. The heights (in meters) of the mountains in Tamil Nadu are as follows:

(i) Which is the highest mountain listed above?
(ii) Order the mountains from the highest to the lowest.
(iii) What is the difference between the heights of the mountains Anaimudi and Mahendragiri?
Answer: We will use the information from the table to answer the questions about the mountain heights.
(i) To find the highest mountain, we look for the largest height in the "Height (in metres)" column.
The highest mountain listed is Anaimudi, with a height of 2695 m.

(ii) To order the mountains from highest to lowest, we arrange their heights in descending order:
Anaimudi (2695 m), Doddabetta (2637 m), Velliangiri (1778 m), Mahendragiri (1647 m).

(iii) To find the difference between the heights of Anaimudi and Mahendragiri, we subtract the smaller height from the larger height.
Height of Anaimudi = 2695 m
Height of Mahendragiri = 1647 m
Difference = \( 2695 \text{ m} - 1647 \text{ m} = 1048 \text{ m} \)
In simple words: (i) Anaimudi is the tallest mountain from the list. (ii) From tallest to shortest, the mountains are Anaimudi, Doddabetta, Velliangiri, and Mahendragiri. (iii) The height difference between Anaimudi and Mahendragiri is 1048 meters.

🎯 Exam Tip: For table-based questions, carefully read the column headers and locate the correct data. Double-check your calculations for differences and ensure the order is strictly ascending or descending as requested.

 

Objective Type Questions

 

Question 10. Which list of numbers is in order from the smallest to the largest?
(a) 1468, 1486, 1484
(b) 2345, 2435, 2235
(c) 134205, 134208, 154203
(d) 383553, 383548, 383642
Answer: (c) 134205, 134208, 154203
In simple words: We need to find the list where numbers are arranged from the smallest to the biggest. Option (c) is the only one where each number is larger than the one before it.

🎯 Exam Tip: To quickly check if a list is in ascending order, compare each number with the very next number in the sequence. If any number is smaller than the one before it, the list is not in order.

 

Question 11. The Arabian Sea has an area of 1491000 square miles. This area lies between which two numbers?
(a) 1489000 and 1492540
(b) 1489000 and 1490540
(c) 1490000 and 1490100
(d) 1480000 and 1490000
Answer: (a) 1489000 and 1492540
In simple words: We need to find which pair of numbers has 1,491,000 in between them. The first option, 1,489,000 and 1,492,540, correctly places 1,491,000 within its range.

🎯 Exam Tip: To find if a number lies between two others, check if it's greater than the first number AND smaller than the second number. This involves two separate comparisons.

 

Question 12. The chart below shows the number of newspapers sold as per the Indian Readership Survey in 2018. Which could be the missing number in the table?

(a) 8
(b) 52
(c) 77
(d) 26
Answer: (d) 26
In simple words: The table shows newspapers ranked by how many copies they sold. Rank 1 sold 70 lakh, Rank 2 sold 50 lakh, and Rank 4 sold 10 lakh. So, the newspaper at Rank 3 must have sold less than 50 lakh but more than 10 lakh. Out of the choices, only 26 fits this.

🎯 Exam Tip: When dealing with ranked data, remember that a lower rank number (like 1) means a higher value (more sales), and a higher rank number (like 4) means a lower value (fewer sales). The missing value must fit within the sequence of values for its rank.