CBSE Class 6 Mathematics Revision Worksheet Set 05

Choose the correct option in Q. 1, 2 and 3

Q.1 In 698382 the digit which has the greatest place value is ___________
(a) 6
(b) 5
(c) 8
(d) 9
Answer: (a) 6
The place value of each digit in 698382 from left to right is:
6 has place value \(6 \times 100000 = 600000\)
9 has place value \(9 \times 10000 = 90000\)
8 has place value \(8 \times 1000 = 8000\)
3 has place value \(3 \times 100 = 300\)
8 has place value \(8 \times 10 = 80\)
2 has place value \(2 \times 1 = 2\)
Comparing the place values, 600000 is the greatest, which belongs to the digit 6.
In simple words: The digit farthest to the left in a whole number always has the greatest place value.

Exam Tip: Always look at the leftmost digit and its position to determine the greatest place value without calculating all values.

Q.2 987653 _______ 9873521
(a) >
(b) \(\geq$
(c) =
(d) <
Answer: (d) <
Number of digits in 987653 = 6 digits
Number of digits in 9873521 = 7 digits
Since a 7-digit number is always greater than a 6-digit number, 987653 is less than 9873521.
In simple words: A number with fewer digits is always smaller than a number with more digits.

Exam Tip: First count the total digits in both numbers. The number with more digits is always larger.

Q.3 The difference between the largest three digit number and the largest three digit number with distinct digits is
(a) 10
(b) 0
(c) 12
(d) 13
Answer: (b) 0
Largest three-digit number = 999
Largest three-digit number with distinct digits = 987
Wait, let us re-read carefully: The largest three digit number is 999. The largest three digit number with distinct digits is also 987, but let us check if the question implies something else or if it is 999 and 999? No, distinct digits means all digits are different. Largest 3-digit number is 999. Largest 3-digit number with distinct digits is 987. Wait, let us check standard options. If the question meant largest 3-digit number with distinct digits compared to itself, or if there is a typo in the question. Let us compute \(999 - 999 = 0\). If the question meant "largest 3-digit number" and "largest 3-digit number with distinct digits", the difference is \(999 - 987 = 12\), which is option (c). Let us verify option (c): 12.
Largest 3-digit number = 999
Largest 3-digit number with distinct digits = 987
Difference = \(999 - 987 = 12\)
Therefore, the correct option is (c).
In simple words: Subtract the largest 3-digit number having all different digits (987) from the general largest 3-digit number (999) to get 12.

Exam Tip: "Distinct digits" means no digit can be repeated. For the largest 3-digit number with distinct digits, use 9, 8, and 7 in descending order.

Q.4 Find the place value of the digit 5 in each case.
(a) 5982346
(b) 9452784
(c) 92469523
(d) 230597628
Answer:
(a) In 5982346, 5 is at the ten-lakhs (millions) place.
Place value of 5 = \( 5 \times 1000000 = 5000000$
(b) In 9452784, 5 is at the thousands place.
Place value of 5 = \( 5 \times 1000 = 5000$
(c) In 92469523, 5 is at the hundreds place.
Place value of 5 = \( 5 \times 100 = 500$
(d) In 230597628, 5 is at the lakhs place.
Place value of 5 = \( 5 \times 100000 = 500000$
In simple words: Multiply the digit 5 by the value of its position (like 10, 100, 1000) to find its place value.

Exam Tip: Write the digit and replace all digits to its right with zeros to quickly find the place value.

Q.5 Find the greatest and the smallest numbers in each of the following cases.
(a) 134506, 763084, 270895, 270983
(b) 173689, 923176, 368921, 126837
Answer:
(a) Given numbers: 134506, 763084, 270895, 270983
Comparing the leftmost digits (lakhs place): 1, 7, 2, 2.
The greatest is 763084.
Comparing the two numbers starting with 2 (270895 and 270983): at the hundreds place, 9 is greater than 8, so 270983 > 270895.
The smallest is 134506.
Greatest number = 763084, Smallest number = 134506.

(b) Given numbers: 173689, 923176, 368921, 126837
Comparing the leftmost digits (lakhs place): 1, 9, 3, 1.
The greatest is 923176.
Comparing the two numbers starting with 1 (173689 and 126837): at the ten-thousands place, 7 > 2, so 173689 > 126837.
The smallest is 126837.
Greatest number = 923176, Smallest number = 126837.
In simple words: Compare digits from left to right. The number with the larger digit at the earliest place is greater.

Exam Tip: When numbers have the same number of digits, always compare starting from the highest place value (leftmost digit).

Q.6 Rewrite the following numbers in ascending order:
(a) 177048, 999999, 10000000, 305006
(b) 237045, 823765, 62113, 99999
Answer:
(a) Counting digits:
177048 (6 digits)
999999 (6 digits)
10000000 (8 digits)
305006 (6 digits)
Comparing the 6-digit numbers (177048, 999999, 305006) by their first digit: 1 < 3 < 9.
So order for 6-digit numbers is: 177048, 305006, 999999.
The 8-digit number 10000000 is the largest.
Ascending order: 177048, 305006, 999999, 10000000.

(b) Counting digits:
237045 (6 digits)
823765 (6 digits)
62113 (5 digits)
99999 (5 digits)
Comparing the 5-digit numbers (62113, 99999): 62113 < 99999.
Comparing the 6-digit numbers (237045, 823765): 237045 < 823765.
Ascending order: 62113, 99999, 237045, 823765.
In simple words: Ascending order means arranging numbers from the smallest to the largest.

Exam Tip: Group numbers by digit count first. Fewer digits always come first in ascending order.

Q.7 Rewrite the following numbers in the descending order
(a) 57681, 421357, 12350, 355601
(b) 6800, 6008, 86000, 80006
Answer:
(a) Given numbers: 57681 (5 digits), 421357 (6 digits), 12350 (5 digits), 355601 (6 digits).
6-digit numbers are 421357 and 355601. Since 421357 > 355601, 421357 comes first.
5-digit numbers are 57681 and 12350. Since 57681 > 12350, 57681 comes before 12350.
Descending order: 421357, 355601, 57681, 12350.

(b) Given numbers: 6800 (4 digits), 6008 (4 digits), 86000 (5 digits), 80006 (5 digits).
5-digit numbers are 86000 and 80006. Since 86000 > 80006, 86000 comes first, followed by 80006.
4-digit numbers are 6800 and 6008. Since 6800 > 6008, 6800 comes next, followed by 6008.
Descending order: 86000, 80006, 6800, 6008.
In simple words: Descending order means arranging numbers from the largest to the smallest.

Exam Tip: Start with the largest number of digits, and arrange numbers from highest to lowest value.

Q.8 In each case, use all the digits only once to make the smallest possible 6 digit number
(a) 4, 1, 7, 3, 5, 2
(b) 5, 1, 6, 3, 8, 9
Answer:
(a) Given digits: 4, 1, 7, 3, 5, 2
To form the smallest 6-digit number, arrange the digits in ascending order from left to right.
Ascending order of digits: 1, 2, 3, 4, 5, 7.
Smallest 6-digit number = 123457.

(b) Given digits: 5, 1, 6, 3, 8, 9
Arranging the digits in ascending order: 1, 3, 5, 6, 8, 9.
Smallest 6-digit number = 135689.
In simple words: To make the smallest number, put the smallest digit first, then the next larger digit, and so on.

Exam Tip: If 0 is present among the digits, remember it cannot be placed at the extreme left (ten-thousands or lakhs place). Place the next smallest non-zero digit first, followed immediately by 0.

Q.9 Write the smallest and the greatest 7 digit numbers by using the following digits (repetition allowed)
(a) 4, 7, 3, 2, 6, 5
(b) 3, 6, 9, 7, 0, 4
Answer:
(a) Given digits: 4, 7, 3, 2, 6, 5 (6 digits given, need to form a 7-digit number by repeating one digit).
Smallest digit is 2. To make the smallest 7-digit number, repeat the smallest digit (2) extra times.
Smallest 7-digit number = 2234567.
Greatest digit is 7. To make the greatest 7-digit number, repeat the greatest digit (7) extra times.
Greatest 7-digit number = 7765432.

(b) Given digits: 3, 6, 9, 7, 0, 4 (6 digits given, need to form a 7-digit number).
Smallest digit is 0, but 0 cannot be at the leftmost place. The smallest non-zero digit is 3. Repeat 0 to make the smallest number.
Smallest 7-digit number = 3004679.
Greatest digit is 9. Repeat 9 to make the greatest number.
Greatest 7-digit number = 9976430.
In simple words: To form the smallest number with repetition, repeat the smallest digit. To form the greatest number, repeat the largest digit.

Exam Tip: When forming the smallest number with a zero, place the smallest non-zero digit first, then put zeros as many times as needed.

Q.10 Find the sum of the place values of digits 3 and 7 in the number 90, 30, 678.
Answer:
Given number = 90,30,678
Position of digit 3 is at the thousands place.
Place value of 3 = \( 3 \times 1000 = 3000$
Position of digit 7 is at the tens place.
Place value of 7 = \( 7 \times 10 = 70$
Sum of the place values = \( 3000 + 70 = 3070$
In simple words: Find the place value of 3 (3000) and 7 (70), then add them together to get 3070.

Exam Tip: Identify each digit's position carefully before calculating its place value and adding them.