CBSE Class 6 Mathematics Knowing Our Numbers Worksheet Set 13

I. Fill in the blanks

Question 1. 1 gram = _______ mg
Answer: 1000 mg
In simple words: 1 gram is equal to 1000 milligrams.

Exam Tip: Remember standard metric conversions: milli means one-thousandth (\(\frac{1}{1000}\)), so 1 unit = 1000 milli-units.

Question 2. 1 l = _______ ml
Answer: 1000 ml
In simple words: 1 litre equals 1000 millilitres.

Exam Tip: Always multiply litres by 1000 to convert to millilitres.

Question 3. 1 kl = _______ ml
Answer: 1000000 ml
In simple words: 1 kilolitre is 1000 litres, and each litre is 1000 millilitres, giving 10,00,000 millilitres.

Exam Tip: \(1 \text{ kl} = 1000 \text{ l}\) and \(1 \text{ l} = 1000 \text{ ml}\), so \(1 \text{ kl} = 1000 \times 1000 \text{ ml} = 10,00,000 \text{ ml}\).

Question 4. 1 m = _______ cm
Answer: 100 cm
In simple words: 1 metre equals 100 centimetres.

Exam Tip: Centi means one-hundredth, so 1 metre contains 100 centimetres.

Question 5. 1 m = _______ mm
Answer: 1000 mm
In simple words: 1 metre equals 1000 millimetres.

Exam Tip: Since \(1 \text{ m} = 100 \text{ cm}\) and \(1 \text{ cm} = 10 \text{ mm}\), multiplying gives \(100 \times 10 = 1000 \text{ mm}\).

Question 6. 1 km = _______ cm
Answer: 100000 cm
In simple words: 1 kilometre is 100,000 centimetres.

Exam Tip: \(1 \text{ km} = 1000 \text{ m}\) and \(1 \text{ m} = 100 \text{ cm}\), so \(1000 \times 100 = 1,00,000 \text{ cm}\).

Question 7. 1 kg = _______ mg
Answer: 1000000 mg
In simple words: 1 kilogram is equal to 1,000,000 milligrams.

Exam Tip: \(1 \text{ kg} = 1000 \text{ g}\) and \(1 \text{ g} = 1000 \text{ mg}\), so \(1000 \times 1000 = 10,00,000 \text{ mg}\).

Question 8. 1 km = _______ mm
Answer: 1000000 mm
In simple words: 1 kilometre is equal to 1,000,000 millimetres.

Exam Tip: \(1 \text{ km} = 1000 \text{ m}\) and \(1 \text{ m} = 1000 \text{ mm}\), so \(1000 \times 1000 = 10,00,000 \text{ mm}\).

II.

Question 1. Find the sum of the greatest and the least number that can be written using the digits 5, 3, 9, 0, 1 each only once.
Answer:
Given digits: 5, 3, 9, 0, 1
Greatest 5-digit number formed by arranging digits in descending order (starting with the largest non-zero digit if needed, but here 9 is largest) = 95310
Least 5-digit number formed by arranging digits in ascending order. Note that a 5-digit number cannot start with 0, so the smallest non-zero digit is written first: 10359
Sum = \(95310 + 10359 = 105669\)
In simple words: Find the biggest and smallest numbers possible using all given digits without repeating them, then add them together.

Exam Tip: When forming the smallest number, remember that 0 cannot be placed at the extreme left (highest place value).

Question 2. Find the product of the greatest 5-digit number and the smallest 2-digit number.
Answer:
Greatest 5-digit number = 99999
Smallest 2-digit number = 10
Product = \(99999 \times 10 = 999990\)
In simple words: Multiply 99,999 by 10 to get the final product.

Exam Tip: Multiplying any integer by 10 simply appends a zero to the right of the number.

Question 3. Find the sum of the smallest 4-digit and the greatest 4-digit number.
Answer:
Smallest 4-digit number = 1000
Greatest 4-digit number = 9999
Sum = \(1000 + 9999 = 10999\)
In simple words: Add 1,000 and 9,999 together.

Exam Tip: The smallest 4-digit number is \(10^3\) (1 followed by three zeros) and the greatest is 4 nines.

Question 4. Find the difference between the largest 6-digit number and the smallest 5-digit number.
Answer:
Largest 6-digit number = 999999
Smallest 5-digit number = 10000
Difference = \(999999 - 10000 = 989999\)
In simple words: Subtract 10,000 from 9,99,999.

Question 5. The price of a water cooler is Rs 5496. A school bought 26 coolers. Find the total cost.
Answer:
Cost of 1 water cooler = Rs 5496
Number of coolers bought = 26
Total cost = \(5496 \times 26\)
\(5496 \times 20 = 109920\)
\(5496 \times 6 = 32976\)
Total cost = \(109920 + 32976 = 142896\)
Total cost = Rs 142896
In simple words: Multiply the price of one cooler by the total number of coolers purchased.

Exam Tip: Show multiplication steps clearly to avoid calculation errors in large numbers.

Question 6. To stitch a frock, 1 m 50 cm cloth is needed. Out of 30 m cloth, how many frocks can be stitched and how much cloth will remain?
Answer:
Cloth needed for 1 frock = 1 m 50 cm = 150 cm
Total cloth available = 30 m = \(30 \times 100 = 3000\) cm
Number of frocks = \(\frac{3000}{150} = \frac{300}{15} = 20\)
Remainder cloth = 0 cm
Number of frocks that can be stitched = 20 frocks
Remaining cloth = 0 m (or 0 cm)
In simple words: Convert both total cloth and cloth per frock into centimetres, then divide to find the number of frocks.

Exam Tip: Always convert all units into the smaller unit (centimetres) before performing division.

Question 7. A water can has 10 litres of water. In how many bottles of 500 ml can it be filled?
Answer:
Total water in can = 10 litres = \(10 \times 1000 = 10000\) ml
Capacity of one bottle = 500 ml
Number of bottles = \(\frac{10000}{500} = \frac{100}{5} = 20\)
Number of bottles required = 20
In simple words: Convert litres to millilitres and divide by 500 ml.

Exam Tip: 1 litre = 1000 ml is a fundamental conversion that must be memorized.

Question 8. The distance between the office and the house of an officer is 1 km 200 m. Everyday he walks both ways. Find the total distance walked by him in a week (5 days).
Answer:
Distance from house to office = 1 km 200 m = 1200 m
Distance walked in one day (both ways) = \(2 \times 1200 \text{ m} = 2400 \text{ m}\)
Number of working days in a week = 5 days
Total distance walked in 5 days = \(5 \times 2400 \text{ m} = 12000 \text{ m} = 12 \text{ km}\)
In simple words: Multiply the one-way distance by 2 for the round trip, then multiply by 5 days.

Exam Tip: "Both ways" means multiplying the single journey distance by 2.

Question 9. A student multiplied 5863 by 35 instead of multiplying by 53. By how much was his answer smaller than the correct answer?
Answer:
Difference in multipliers = \(53 - 35 = 18\)
Difference in answer = \(5863 \times (53 - 35)\)
\(= 5863 \times 18\)
\(5863 \times 10 = 58630\)
\(5863 \times 8 = 46904\)
Total difference = \(58630 + 46904 = 105534\)
In simple words: Instead of doing long multiplications separately, find the difference between 53 and 35, then multiply that difference by 5,863.

Exam Tip: Using the distributive property \(a \times b - a \times c = a \times (b - c)\) saves time and reduces calculation errors.

Question 10. Find a rough estimate (by rounding to the nearest 100) and a closer estimate (by rounding to the nearest 10).
Answer:
Let us solve each sub-part for both estimates:

1) 9856 + 2014 + 8539
Rounding to nearest 100:
\(9856 \rightarrow 9900\)
\(2014 \rightarrow 2000\)
\(8539 \rightarrow 8500\)
Estimated sum = \(9900 + 2000 + 8500 = 20400\)
Rounding to nearest 10:
\(9856 \rightarrow 9860\)
\(2014 \rightarrow 2010\)
\(8539 \rightarrow 8540\)
Estimated sum = \(9860 + 2010 + 8540 = 20410\)
In simple words: Round each number to the nearest 100 for a rough estimate, and to the nearest 10 for a closer estimate, then add them up.

Exam Tip: Check the digit in the tens place when rounding to the nearest 100, and the units place when rounding to the nearest 10.

2) 416 + 89 + 612
Rounding to nearest 100:
\(416 \rightarrow 400\)
\(89 \rightarrow 100\)
\(612 \rightarrow 600\)
Estimated sum = \(400 + 100 + 600 = 1100\)
Rounding to nearest 10:
\(416 \rightarrow 420\)
\(89 \rightarrow 90\)
\(612 \rightarrow 610\)
Estimated sum = \(420 + 90 + 610 = 1120\)
In simple words: Round each term and add them for both estimation levels.

Exam Tip: 89 rounds up to 100 when rounding to the nearest 100 because the tens digit is 8 (which is 5 or more).

3) 996 + 485 + 3961
Rounding to nearest 100:
\(996 \rightarrow 1000\)
\(485 \rightarrow 500\)
\(3961 \rightarrow 4000\)
Estimated sum = \(1000 + 500 + 4000 = 5500\)
Rounding to nearest 10:
\(996 \rightarrow 1000\)
\(485 \rightarrow 490\)
\(3961 \rightarrow 3960\)
Estimated sum = \(1000 + 490 + 3960 = 5450\)
In simple words: Round each number to hundreds and tens, then find the respective sums.

Exam Tip: Be careful with numbers like 996 that round up across place value boundaries.

4) 28164 - 1285
Rounding to nearest 100:
\(28164 \rightarrow 28200\)
\(1285 \rightarrow 1300\)
Estimated difference = \(28200 - 1300 = 26900\)
Rounding to nearest 10:
\(28164 \rightarrow 28160\)
\(1285 \rightarrow 1290\)
Estimated difference = \(28160 - 1290 = 26870\)
In simple words: Round both numbers, then subtract them.

Exam Tip: For subtraction, ensure you subtract the rounded subtrahend from the rounded minuend correctly.

5) 34217 - 7625
Rounding to nearest 100:
\(34217 \rightarrow 34200\)
\(7625 \rightarrow 7600\)
Estimated difference = \(34200 - 7600 = 26600\)
Rounding to nearest 10:
\(34217 \rightarrow 34220\)
\(7625 \rightarrow 7630\)
Estimated difference = \(34220 - 7630 = 26590\)
In simple words: Round each value to the specified place value and subtract.

Exam Tip: Check the digit in the place immediately to the right of the target rounding place.

6) 10062 - 1009
Rounding to nearest 100:
\(10062 \rightarrow 10100\)
\(1009 \rightarrow 1000\)
Estimated difference = \(10100 - 1000 = 9100\)
Rounding to nearest 10:
\(10062 \rightarrow 10060\)
\(1009 \rightarrow 1010\)
Estimated difference = \(10060 - 1010 = 9050\)
In simple words: Round the numbers to nearest 100 and nearest 10, then find the differences.

Exam Tip: 1009 rounded to the nearest 10 becomes 1010 because the units digit is 9.