CBSE Class 6 Maths Advanced Knowing Our Numbers Short Answer Questions Set 01

Short Answer Questions

Question 1. 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.
(A) Maharashtra 96878627
(B) Andhra Pradesh 76210007
(C) Bihar 82998509
(D) Uttar Pradesh 166197921
Answer:
Uttar Pradesh has 9 digits and the others have 8 digits, so Uttar Pradesh is the greatest.
Among the 8-digit numbers compare from the left: 76210007 < 82998509 < 96878627.
Ascending: Andhra Pradesh, Bihar, Maharashtra, Uttar Pradesh.
Descending: Uttar Pradesh, Maharashtra, Bihar, Andhra Pradesh.
In simple words: Smallest to largest: Andhra Pradesh, Bihar, Maharashtra, Uttar Pradesh.

Teacher's Note:
1. Count digits first, then compare the leading digits.
2. Descending order is the exact reverse of ascending.

Question 2. Write the place value of each digit of number 560271
Answer:
560271 = 5,60,271. Digits from the left:
5 is in the lakh place: 500000.
6 is in the ten-thousands place: 60000.
0 is in the thousands place: 0.
2 is in the hundreds place: 200.
7 is in the tens place: 70.
1 is in the ones place: 1.
In simple words: Each digit is multiplied by the value of its place.

Teacher's Note:
1. The place value of 0 is always 0.
2. Check that the place values add to 560271.

Question 3. Find the difference between place value and face value of digit 6 in 298654
Answer:
In 298654 the digit 6 is in the hundreds place.
Place value = 600 and face value = 6.
Difference = 600 − 6 = 594.
In simple words: The difference is 594.

Teacher's Note:
1. Face value is the digit itself.
2. Locate the place by counting from the right.

Question 4. Find the product of place value of 8 and face value of 2 in 92486
Answer:
In 92486 the digit 8 is in the tens place, so its place value is 80.
The face value of 2 is 2.
Product = 80 × 2 = 160.
In simple words: The product is 160.

Teacher's Note:
1. Face value does not change with position.
2. Find the place of 8 by counting from the right.

Question 5. Write the following numbers in expanded notation. (a) 2,84,231 (b) 52,11,568 (c) 6,04,18,517 (d) 8,91,81,213
Answer:
(a) 2,00,000 + 80,000 + 4,000 + 200 + 30 + 1.
(b) 50,00,000 + 2,00,000 + 10,000 + 1,000 + 500 + 60 + 8.
(c) 6,00,00,000 + 4,00,000 + 10,000 + 8,000 + 500 + 10 + 7.
(d) 8,00,00,000 + 90,00,000 + 1,00,000 + 80,000 + 1,000 + 200 + 10 + 3.
In simple words: Write each non-zero digit with its place value and add.

Teacher's Note:
1. Skip the digits that are 0.
2. Add the parts back to check.

Question 6. Write the following numbers as numerals. (a) Sixty two lakh forty five thousand six hundred thirty five (b) Nine crore fifty eight lakh sixty one thousand eighty nine
Answer:
(a) 62 lakh = 62,00,000; 45 thousand = 45,000; 635. The number is 62,45,635.
(b) 9 crore = 9,00,00,000; 58 lakh = 58,00,000; 61 thousand = 61,000; 89. The number is 9,58,61,089.
In simple words: Fill each period: crore, lakh, thousand, ones.

Teacher's Note:
1. Remember the zero in the hundreds place of (b): eighty nine is 089.
2. Use Indian commas: 3 digits, then 2, 2, ...

Question 7. In 2001, the population of Tripura and Meghalaya were 3,199,203 and 2,318,822, respectively. Write the populations of these two states in words.
Answer:
Tripura: 3,199,203 = three million one hundred ninety-nine thousand two hundred three.
Meghalaya: 2,318,822 = two million three hundred eighteen thousand eight hundred twenty-two.
In simple words: The commas are in the International style, so use million and thousand.

Teacher's Note:
1. Read each group of three digits with its name.
2. Millions come before thousands.

Question 8. How many lakhs make five billions?
Answer:
5 billion = 5,000,000,000 = 500,00,00,000 in the Indian system.
1 lakh = 1,00,000.
5,000,000,000 ÷ 100,000 = 50000 lakhs.
In simple words: Five billion is 50,000 lakh.

Teacher's Note:
1. 1 billion = 1,000 million = 100 crore.
2. Divide by 1 lakh to change to lakhs.

Question 9. Estimate the product of 287 × 231 by rounding off the first number upwards and the second number downwards.
Answer:
Round 287 up to the next hundred: 300.
Round 231 down to the previous hundred: 200.
Estimated product = 300 × 200 = 60000.
In simple words: The estimate is 60000.

Teacher's Note:
1. Up means to the higher hundred; down means to the lower hundred.
2. Multiply 3 × 2 and add four zeros.

Question 10. Give a rough estimate and a closer estimate of 4,89,342 − 48,365.
Answer:
Rough estimate (round each number to its greatest place): 4,89,342 ≈ 5,00,000 and 48,365 ≈ 50,000. Rough estimate = 5,00,000 − 50,000 = 4,50,000.
Closer estimate (round both to the nearest ten thousand): 4,89,342 ≈ 4,90,000 and 48,365 ≈ 50,000. Closer estimate = 4,90,000 − 50,000 = 4,40,000.
In simple words: Rough 4,50,000 and closer 4,40,000.

Teacher's Note:
1. The more digits you keep, the closer the estimate.
2. The actual difference is 4,40,977.

Question 11. 12 drums of milk have 84 litres of milk in them. Find the capacity of one drum in millilitres.
Answer:
Capacity of one drum = 84 ÷ 12 = 7 litres.
1 litre = 1000 mL, so 7 L = 7 × 1000 = 7000 mL.
In simple words: Each drum holds 7000 mL.

Teacher's Note:
1. Divide first, then convert.
2. 1 L = 1000 mL.

Question 12. Radius of the Earth is 6400km and that of Mars is 4300000m. Whose radius is bigger and by how much?
Answer:
Convert Mars's radius to km: 4300000 m ÷ 1000 = 4300 km.
6400 km is greater than 4300 km, so the Earth's radius is bigger.
Difference = 6400 − 4300 = 2100 km.
In simple words: The Earth is bigger by 2100 km.

Teacher's Note:
1. Change both to the same unit before comparing.
2. 1 km = 1000 m.

Question 13. Write the equivalent Roman numeral of each of the following Hindu-Arabic numeral. (a) 46 (b) 90 (c) 120 (d) 150
Answer:
(a) 46 = 40 + 6 = XL + VI = XLVI.
(b) 90 = XC.
(c) 120 = 100 + 20 = CXX.
(d) 150 = 100 + 50 = CL.
In simple words: XLVI, XC, CXX and CL.

Teacher's Note:
1. Split into hundreds, tens and ones.
2. 40 is XL and 90 is XC.

Question 14. Write the equivalent Hindu Arabic numerals of the following Roman numerals. (a) XXII (b) CCX (c) DCC (d) LXIII
Answer:
(a) XXII = 10 + 10 + 1 + 1 = 22.
(b) CCX = 100 + 100 + 10 = 210.
(c) DCC = 500 + 100 + 100 = 700.
(d) LXIII = 50 + 10 + 1 + 1 + 1 = 63.
In simple words: 22, 210, 700 and 63.

Teacher's Note:
1. When symbols fall in descending order, add them.
2. Count repeated symbols carefully.

Question 15. Write the expanded form of the following: (a) 87609 (b) 900376
Answer:
(a) 87609 = 80000 + 7000 + 600 + 0 + 9, that is 8 × 10000 + 7 × 1000 + 6 × 100 + 0 × 10 + 9 × 1.
(b) 900376 = 900000 + 0 + 0 + 300 + 70 + 6, that is 9 × 100000 + 0 × 10000 + 0 × 1000 + 3 × 100 + 7 × 10 + 6 × 1.
In simple words: Write each digit times its place value.

Teacher's Note:
1. The zero digits contribute nothing.
2. Add the parts to check.

Question 16. Write the number 999999998 in the Indian system in numeral form and in words.
Answer:
Indian grouping (3 digits, then 2, 2, 2): 99,99,99,998.
In words: Ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-eight.
In simple words: 99,99,99,998 is ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-eight.

Teacher's Note:
1. Start commas from the right.
2. Name the periods: crore, lakh, thousand, ones.

Question 17. Estimate the following by rounding off each factor to nearest hundreds: (a) 730 + 998 (b) 673 − 458
Answer:
(a) 730 ≈ 700 and 998 ≈ 1000. Estimate = 700 + 1000 = 1700.
(b) 673 ≈ 700 and 458 ≈ 500. Estimate = 700 − 500 = 200.
In simple words: (a) about 1700 and (b) about 200.

Teacher's Note:
1. Compare with the actual: 1728 and 215.
2. Check the tens digit for each rounding.

Question 18. Estimate the following by rounding off each factor to nearest thousands: (a) 21397 + 27807 + 42505 (b) 28292 − 21496
Answer:
(a) 21397 ≈ 21000, 27807 ≈ 28000, 42505 ≈ 43000. Sum ≈ 21000 + 28000 + 43000 = 92000.
(b) 28292 ≈ 28000 and 21496 ≈ 21000. Difference ≈ 28000 − 21000 = 7000.
In simple words: (a) about 92000 and (b) about 7000.

Teacher's Note:
1. Look at the hundreds digit each time.
2. Actual answers: 91709 and 6796.

Question 19. Estimate the product of 183 × 153 by rounding off the first number upwards and the second number downwards.
Answer:
Round 183 up to the next hundred: 200.
Round 153 down to the previous hundred: 100.
Estimated product = 200 × 100 = 20000.
In simple words: The estimate is 20000.

Teacher's Note:
1. Up and down mean the next and the previous hundred.
2. The actual product is 27999, so this is only a rough estimate.

Question 20. Give a rough estimate and also a closer estimate of 4,89,342 − 48,365.
Answer:
Rough estimate: round to the greatest place: 5,00,000 − 50,000 = 4,50,000.
Closer estimate: round to the nearest ten thousand: 4,90,000 − 50,000 = 4,40,000.
In simple words: Rough 4,50,000 and closer 4,40,000.

Teacher's Note:
1. A smaller rounding place gives a closer estimate.
2. The actual difference is 4,40,977.

Question 21. India's population has been steadily increasing from 439 millions in 1961 to 1028 millions in 2001. Find the total increase in popular from 1961 to 2001. Write the increase in population in Indian System of Numeration, using commas suitably.
Answer:
Increase = 1028 − 439 = 589 million = 589,000,000.
In the Indian system this is 58,90,00,000 (58 crore 90 lakh), which is also 5890 lakh.
In simple words: The population increased by 58,90,00,000.

Teacher's Note:
1. 1 million = 10 lakh, so 589 million = 5890 lakh.
2. Re-group the commas: 3, then 2, 2, 2.

Question 22. In 2001, the populations of Tripura and Meghalaya were 3,199,203 and 2,318,822, respectively. Write the populations of these two states in words.
Answer:
Tripura: three million one hundred ninety-nine thousand two hundred three.
Meghalaya: two million three hundred eighteen thousand eight hundred twenty-two.
In simple words: Use million, thousand and ones for these International-style numbers.

Teacher's Note:
1. Each comma marks a new group.
2. Say the group number and then its name.

Question 23. Chinmay had Rs 610000. He gave Rs 87500 to Jyoti, Rs 126380 to Javed and Rs 350000 to John. How much money was left with him ?
Answer:
Total given = 87500 + 126380 + 350000 = 563880.
Money left = 610000 − 563880 = Rs. 46120.
In simple words: Rs. 46120 was left.

Teacher's Note:
1. Add all the gifts first.
2. Subtract the total from the money he had.

Question 24. A factory has a container filled with 35874 litres of cold drink. In how many bottles of 200 ml capacity each can it be filled ?
Answer:
35874 L = 35874 × 1000 mL = 35,874,000 mL.
Number of bottles = 35,874,000 ÷ 200 = 179370.
In simple words: 179370 bottles can be filled.

Teacher's Note:
1. Change litres to millilitres first.
2. Divide the total volume by the bottle size.

Question 25. A box contains 50 packets of biscuits each weighing 120g. How many such boxes can be loaded in a van which cannot carry beyond 900kg ?
Answer:
Weight of one box = 50 × 120 g = 6000 g = 6 kg.
900 kg ÷ 6 kg = 150 boxes.
In simple words: The van can carry 150 boxes.

Teacher's Note:
1. Convert grams to kilograms before dividing.
2. 1000 g = 1 kg.