Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 1 Numbers Exercise 1.6

Question 1. Try to open my locked suitcase which has the biggest 5 digit odd number as the password comprising the digits 7, 5, 4, 3 and 8. Find the password.
Answer: To find the biggest 5-digit odd number using the digits 7, 5, 4, 3, and 8, we first arrange the digits in descending order to make the largest number: 8, 7, 5, 4, 3. This gives us 87543. Since the last digit (3) is an odd number, the number 87543 is already the biggest 5-digit odd number that can be formed using these digits. This number is unique because arranging the digits from largest to smallest naturally results in an odd number ending in 3. Therefore, the password for the locked suitcase is 87543.
In simple words: To make the biggest number, put the digits from largest to smallest. Since the last digit (3) is odd, the number 87543 is the biggest odd number you can make with those digits.

🎯 Exam Tip: To create the largest number, arrange digits in descending order. To make it odd, the last digit must be odd; if the largest number created isn't odd, swap the last digit with the smallest available odd digit.

Question 2. As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.

Answer: We need to arrange the populations in order from smallest to largest (ascending) and from largest to smallest (descending). Comparing the given populations:
Rajasthan: 68,548,437
Tamil Nadu: 72,147,030
Madhya Pradesh: 72,626,809
West Bengal: 91,276,115

Ascending Order: 68,548,437 < 72,147,030 < 72,626,809 < 91,276,115
Descending Order: 91,276,115 > 72,626,809 > 72,147,030 > 68,548,437
In simple words: First, list all the numbers from the smallest to the biggest. This is ascending order. Then, list them from the biggest to the smallest. This is descending order.

🎯 Exam Tip: When comparing large numbers, always start by comparing the digits from the leftmost place value. If the leftmost digits are the same, move to the next digit to the right.

Question 3. Study the following table and answer the questions.

(i) How many tigers were there in 2011?
(ii) How many tigers were less in 2008 than in 1990?
(iii) Did the number of tigers increase or decrease between 2011 and 2014? If yes, by how much?
Answer:
(i) From the table, we can see that in the year 2011, there were 1706 tigers.
(ii) To find out how many fewer tigers were there in 2008 compared to 1990, we subtract the number of tigers in 2008 from the number in 1990.
Number of tigers in 1990 = 3500
Number of tigers in 2008 = 1400
Difference = \( 3500 - 1400 = 2100 \)
So, there were 2100 fewer tigers in 2008 than in 1990.
(iii) To see if the number of tigers increased or decreased between 2011 and 2014, we compare the numbers for those years.
Number of tigers in 2011 = 1706
Number of tigers in 2014 = 2226
Since 2226 is greater than 1706, the number of tigers increased.
To find out by how much, we subtract the number in 2011 from the number in 2014.
Increase = \( 2226 - 1706 = 520 \)
The number of tigers increased by 520 between 2011 and 2014. These conservation efforts are crucial for wildlife.
In simple words: Look at the table carefully. For part (i), find the tigers in 2011. For part (ii), subtract tigers in 2008 from those in 1990. For part (iii), compare tigers in 2011 and 2014; if the later number is bigger, it's an increase, then subtract to find out by how much.

🎯 Exam Tip: Always double-check the year and corresponding data points when reading from a table to avoid simple errors. Pay attention to keywords like "increase," "decrease," "how many less," or "how many more."

Question 4. Mullaikodi has 25 bags of apples. In each bag, there are 9 apples. She shares them equally amongst her 6 friends. How many apples does each get? Are there any apples left over?
Answer: First, we need to find the total number of apples Mullaikodi has.
Number of apple bags = 25
Apples in each bag = 9
Total number of apples = \( 25 \times 9 = 225 \) apples.

Next, she shares these apples equally among her 6 friends.
Apples shared among 6 friends = \( 225 \div 6 \)
When we divide 225 by 6:
\( 225 \div 6 = 37 \) with a remainder of 3.
This means each of her 6 friends gets 37 apples, and there are 3 apples left over. Sharing equally ensures fairness, which is important in many real-life situations.
In simple words: Multiply the bags by apples per bag to get the total apples. Then, divide the total apples by the number of friends. The answer is how many each friend gets, and any leftover is the remainder.

🎯 Exam Tip: For division problems, remember that the quotient is the number each person gets, and the remainder is what is left over and cannot be shared equally.

Question 5. Poultry has produced 15472 eggs and fits 30 eggs in a tray. How many trays do they need?
Answer: To find out how many trays are needed, we need to divide the total number of eggs by the number of eggs that fit in one tray.
Total number of eggs produced = 15472
Number of eggs that fit in one tray = 30

Number of trays required = \( 15472 \div 30 \)
When we perform the division:
\( 15472 \div 30 = 515 \) with a remainder of 22.
This means 515 trays will be completely filled. However, there are 22 eggs remaining. Since these remaining eggs also need to be placed in trays, one additional tray is needed for them, even if it's not completely full.
So, total trays needed = \( 515 + 1 = 516 \) trays. This ensures all eggs are packaged properly.
In simple words: Divide the total eggs by how many fit in one tray. If there are any eggs left over, you need one extra tray for them.

🎯 Exam Tip: In real-world "how many containers are needed" problems, if there's a remainder after division, you usually need one extra container for the remaining items, even if it's not full.

Question 6. Read the table and answer the following questions.

(i) Write the Canopus star's diameter in words, in the Indian and the International System.
(ii) Write the sum of the place values of 5 in Sirius star's diameter in the Indian System.
(iii) Eight hundred sixty four million seven hundred thirty. Write in Indian System.
(iv) Write the diameter in words of Arcturus star in the International System.
(v) Write the difference of the diameters of Canopus and Arcturus stars in the Indian and the International Systems.
Answer:
(i) Canopus star's diameter is 25,941,900 miles.
Indian System: Two crores fifty-nine lakh forty-one thousand nine hundred.
International System: Twenty-five million nine hundred forty-one thousand nine hundred.

(ii) Sirius star's diameter is 1,556,500 miles.
The digit 5 appears in three places:
- At the Lakhs place (hundred thousands place in International System): 5,00,000
- At the Ten Thousands place (ten thousands place in International System): 50,000
- At the Hundreds place (hundreds place in International System): 500
Sum of place values of 5 = \( 5,00,000 + 50,000 + 500 = 5,50,500 \). Understanding place values helps us work with large numbers.

(iii) The number "Eight hundred sixty four million seven hundred thirty" is written as 864,000,730 in the International System.
In the Indian System, this number is written as 86,40,00,730.
Indian System words: Eighty-six crore forty lakh seven hundred thirty.

(iv) Arcturus star's diameter is 19,888,800 miles.
International System: Nineteen million eight hundred eighty-eight thousand eight hundred.

(v) Canopus diameter = 25,941,900 miles.
Arcturus diameter = 19,888,800 miles.
Difference = \( 25,941,900 - 19,888,800 = 6,053,100 \).

Indian System: Sixty lakh fifty-three thousand one hundred.
International System: Six million fifty-three thousand one hundred. Comparing these systems helps in understanding global number representation.
In simple words: For (i), write the Canopus number using Indian and International number words. For (ii), find all the '5's in the Sirius number and add up their values. For (iii), convert the big number given in words to the Indian number system. For (iv), write the Arcturus number using International number words. For (v), subtract Arcturus's diameter from Canopus's and then write this new number in both Indian and International words.

🎯 Exam Tip: Remember the grouping of digits for Indian (3, 2, 2) and International (3, 3, 3) number systems when writing large numbers in words or placing commas.

Question 7. Anbu asks Arivu Selvi to guess a five-digit odd number. He gives the following hints. The digit in the 1000s place is less than 5. The digit in the 100s place is greater than 6. The digit in the 10s place is 8. What is Arivu Selvi's answer? Does she give more than one answer?
Answer: Let the five-digit number be ABCDE.
The hints are:
1. The digit in the 1000s place (B) is less than 5. So, B can be 0, 1, 2, 3, or 4.
2. The digit in the 100s place (C) is greater than 6. So, C can be 7, 8, or 9.
3. The digit in the 10s place (D) is 8.
4. The number must be odd, so the digit in the units place (E) must be an odd number (1, 3, 5, 7, 9).
5. The first digit (A) cannot be 0, as it's a five-digit number.

Yes, Arivu Selvi can give more than one answer because there are multiple options for digits A, B, C, and E.

One possible answer, following all rules, is 54781.
(Here, A=5, B=4 (<5), C=7 (>6), D=8, E=1 (odd)).

Some other possible numbers that fit all the rules are:
- 13983 (A=1, B=3 (<5), C=9 (>6), D=8, E=3 (odd))
- 21785 (A=2, B=1 (<5), C=7 (>6), D=8, E=5 (odd))
- 94887 (A=9, B=4 (<5), C=8 (>6), D=8, E=7 (odd))
- 32989 (A=3, B=2 (<5), C=9 (>6), D=8, E=9 (odd))
These examples show the flexibility in choosing digits for the unconstrained positions, leading to many possible correct answers.
In simple words: Yes, there can be many answers. We need to pick digits that fit all the given rules: the thousands digit is small, the hundreds digit is large, the tens digit is 8, and the last digit is odd.

🎯 Exam Tip: When forming numbers based on rules, list all possible digits for each place value. If a problem asks for "a number" or "more than one answer," provide examples that strictly follow all conditions, especially the first digit rule for multi-digit numbers.

Question 8. A Music concert is taking place in a stadium. A total of 7,689 chairs are to be put in rows of 90. (i) How many rows will there be? (ii) Will there be any chairs left over?
Answer: We need to divide the total number of chairs by the number of chairs in each row.
Total chairs = 7,689
Chairs in each row = 90

(i) To find how many full rows there will be, we perform the division:
\( 7689 \div 90 \)
We find that \( 7689 = 90 \times 85 + 39 \).
So, there will be 85 complete rows. If an incomplete row is also counted, then 86 rows would be needed, with the last row having 39 chairs. Usually, "how many rows" implies fully arranged rows.

(ii) Yes, there will be chairs left over.
From the division, the remainder is 39.
So, 39 chairs will be left over after making 85 full rows. This helps in planning seating arrangements efficiently.
In simple words: Divide the total chairs by 90 to see how many full rows you can make. The number before the remainder is the number of rows. The remainder is how many chairs are left.

🎯 Exam Tip: For division problems with remainders, clearly state both the quotient (number of full groups) and the remainder (what's left). Be careful with how the question asks to interpret partial groups or leftover items.

Question 9. Round off the seven-digit number 29,75,842 to the nearest lakhs and ten lakhs. Are they the same?
Answer: The given number is 29,75,842.

To round off to the nearest lakh (100,000):
We look at the digit in the ten thousands place, which is 7.
Since 7 is 5 or greater, we round up the lakhs digit. The lakhs digit is 9, so rounding it up makes it 10. This carries over to the next place value (ten lakhs).
So, 29,75,842 rounded to the nearest lakh is 30,00,000.

To round off to the nearest ten lakhs (1,000,000):
We look at the digit in the lakhs place, which is 9.
Since 9 is 5 or greater, we round up the ten lakhs digit. The ten lakhs digit is 2, so rounding it up makes it 3.
So, 29,75,842 rounded to the nearest ten lakhs is 30,00,000.

Yes, both rounded values are the same. In this case, rounding to both the nearest lakh and nearest ten lakhs yields the same result, 30,00,000, which highlights how rounding can sometimes align across different place values.
In simple words: To round to the nearest lakh, look at the number next to the lakh place; if it's 5 or more, add one to the lakh. To round to the nearest ten lakh, look at the number next to the ten lakh place; if it's 5 or more, add one to the ten lakh. In this example, both rounding methods give the same answer.

🎯 Exam Tip: When rounding, identify the target place value and then look at the digit immediately to its right. If that digit is 5 or more, round up; if it's less than 5, keep the target digit as it is.

Question 10. Find the 5 or 6 or 7 digit numbers from a newspaper or a magazine to get a rounded number to the nearest ten thousand.
Answer: This question asks to find examples of numbers from real sources and round them. Here are two examples of 5 or 6 digit numbers rounded to the nearest ten thousand:
(i) Let's take the number 14276.
To round 14276 to the nearest ten thousand, we look at the thousands digit, which is 4. Since 4 is less than 5, we round down.
So, \( 14276 \approx 10000 \).

(ii) Let's take the number 186945.
To round 186945 to the nearest ten thousand, we look at the thousands digit, which is 6. Since 6 is 5 or greater, we round up.
So, \( 186945 \approx 190000 \).

These examples show how rounding numbers to a specific place value can simplify them for estimation or general reporting, which is common in news.
In simple words: Find numbers that have 5, 6, or 7 digits. Then, to round them to the nearest ten thousand, check the thousands digit. If it's 5 or more, round up the ten thousand. If it's less than 5, keep the ten thousand as it is.

🎯 Exam Tip: Remember that "rounding down" means the digit in the target place value stays the same, and all digits to its right become zero. "Rounding up" means the digit in the target place value increases by one, and digits to its right become zero.