CBSE Class 7 Mathematics Large Numbers Around Us Assignment Set 01

Short Answer Questions

Question 1. Answer the following about numbers near one lakh.
(i) Write the largest 5-digit number and the smallest 6-digit number, and state how they are related.
(ii) A town had a population of 82,400 in a survey. How much less than one lakh is this figure?
Answer:
(i) Largest 5-digit number: 99,999; smallest 6-digit number: 1,00,000.
They are next-door neighbours: 99,999 + 1 = 1,00,000, which is one lakh.
(ii) 1,00,000 − 82,400 = 17,600. The figure is 17,600 less than one lakh.
In simple words: 99,999 and 1,00,000 differ by 1, and 82,400 is 17,600 short of a lakh.

Teacher's Note:
1. Adding 1 to the largest number of one length gives the smallest of the next.
2. Subtract to find 'how much less'.

Question 2. Write each of these numbers in words using the Indian place value system.
(i) 6,07,045
(ii) 40,90,300
Answer:
Read the digits in the groups made by the Indian commas.
(i) 6,07,045 = Six lakh seven thousand forty-five.
(ii) 40,90,300 = Forty lakh ninety thousand three hundred.
In simple words: Read each comma group with its name: lakh, thousand, then the rest.

Teacher's Note:
1. A leading 0 in a group is not read.
2. Say 'lakh' after the lakhs group and 'thousand' after the thousands group.

Question 3. Write the number for each name below in the Indian place value system, placing the commas correctly.
(i) Three lakh sixty thousand nine hundred four
(ii) Twenty-five lakh eight thousand sixty
Answer:
Put each part in its own place; commas come after the hundreds and then after every two digits.
(i) Three lakh sixty thousand nine hundred four = 3,60,904.
(ii) Twenty-five lakh eight thousand sixty = 25,08,060.
In simple words: Fill the lakh, thousand and hundreds groups, using zeroes for missing places.

Teacher's Note:
1. 'Eight thousand' fills the thousands group as 08.
2. Check by reading your number back.

Question 4. In the Land of Tens, one calculator has only a +1000 button and another has only a +100 button.
(i) How many times must the +1000 button be pressed to show 47,000? How many times to show one lakh?
(ii) How many times must the +100 button be pressed to show 7,900?
Answer:
Each press adds a fixed amount, so divide the number by the button value.
(i) 47,000 ÷ 1000 = 47 presses; 1,00,000 ÷ 1000 = 100 presses. So one lakh is a hundred thousands.
(ii) 7,900 ÷ 100 = 79 presses.
In simple words: Divide the number by the button value to get the number of presses.

Teacher's Note:
1. Dividing by 1000 removes three zeroes.
2. 100 thousands make one lakh.

Question 5. Copy and complete: 1 lakh is 1 followed by ____ zeroes, 1 million by ____ zeroes, 1 crore by ____ zeroes and 1 arab by ____ zeroes. Also write how many lakhs make one crore.
Answer:
1 lakh is 1 followed by 5 zeroes: 1,00,000.
1 million is 1 followed by 6 zeroes: 1,000,000, the same as ten lakh.
1 crore is 1 followed by 7 zeroes: 1,00,00,000.
1 arab is 1 followed by 9 zeroes; it is the same as one billion.
100 lakhs make one crore.
In simple words: Lakh 5, million 6, crore 7, arab 9 zeroes; 100 lakh = 1 crore.

Teacher's Note:
1. Write each number with commas, then count zeroes.
2. Lakh to crore adds two zeroes, that is ×100.

Question 6. The number of books in a district library is 7,48,629. Write its nearest thousand, nearest ten thousand and nearest lakh.
Answer:
Look at the part just after the place you are rounding to.
Nearest thousand: 7,49,000, because 629 is more than 500.
Nearest ten thousand: 7,50,000, because 8,629 is more than 5,000.
Nearest lakh: 7,00,000, because 48,629 is less than 50,000.
In simple words: Round up when the leftover part is at least half, otherwise round down.

Teacher's Note:
1. Different places can round in different directions.
2. Halfway marks: 500, 5,000, 50,000.

Question 7. Use the regrouping shortcut to calculate these products quickly, showing your steps.
(i) 48 × 25
(ii) 2 × 3875 × 50
Answer:
(i) 25 = \( \frac{100}{4} \), so 48 × 25 = \( \frac{48}{4} \) × 100 = 12 × 100 = 1200.
(ii) Regroup: 2 × 3875 × 50 = 3875 × (2 × 50) = 3875 × 100 = 3,87,500.
In simple words: Turn 25 into 100 ÷ 4, and pair 2 with 50 to make 100.

Teacher's Note:
1. Look for pairs that make 10, 100 or 1000.
2. The order of multiplying can be changed.

Question 8. A bus can seat 50 passengers. How many passengers can 2,000 such buses carry altogether? Write the answer in figures and in words.
Answer:
Passengers = 2000 × 50 = 1,00,000.
In words: one lakh. So 2,000 buses carry exactly one lakh passengers.
In simple words: 2000 × 50 = 1,00,000, which is one lakh.

Teacher's Note:
1. 2 × 5 = 10, then add the zeroes.
2. Count five zeroes for a lakh.

Question 9. A calculator has the buttons +1, +10, +100, +1000, +10000 and +100000, and it wants to be used as little as possible. Write the expression for 6,05,240 that uses the smallest number of clicks, and state that number of clicks.
Answer:
Make each digit with its own place value button.
6,05,240 = (6 × 1,00,000) + (5 × 1000) + (2 × 100) + (4 × 10).
Number of clicks = 6 + 5 + 2 + 4 = 17, the sum of the digits.
In simple words: Use each place’s own button; the clicks add up to the sum of the digits.

Teacher's Note:
1. Zero digits need no clicks.
2. Least clicks = sum of the digits.

Question 10. The number 408070605 is written without commas.
(i) Insert commas in the Indian system and write its number name.
(ii) Insert commas in the American (International) system and write its number name.
Answer:
(i) Indian system (3 digits, then groups of 2): 40,80,70,605, read as forty crore eighty lakh seventy thousand six hundred five.
(ii) American system (groups of 3): 408,070,605, read as four hundred eight million seventy thousand six hundred five.
In simple words: Same number, different commas and names in the two systems.

Teacher's Note:
1. Always place commas from the right.
2. Indian: 3-2-2; American: 3-3-3.

Question 11. Fill in each blank with <, > or =, and give a one-line reason for each.
(i) 80 lakh ____ 8 million
(ii) 25 crore ____ 2 billion
(iii) 1500 thousand ____ 1 million
Answer:
(i) 80 lakh = 8 million, because both are 80,00,000.
(ii) 25 crore < 2 billion, because 25 crore is 25,00,00,000 while 2 billion is 2,00,00,00,000.
(iii) 1500 thousand > 1 million, because 1500 thousand is 15,00,000 and 1 million is only 10,00,000.
In simple words: Write both sides in Indian figures, then compare.

Teacher's Note:
1. 1 million = 10 lakh; 1 billion = 100 crore.
2. Convert to one system before comparing.

Question 12. Roxie says the sum 3,87,450 + 4,26,780 is near 8,00,000 and more than it. Estu says it is near 9,00,000 and less than it. Whose estimate is closer? Support your answer with the exact sum.
Answer:
Exact sum: 3,87,450 + 4,26,780 = 8,14,230.
It is more than 8,00,000 and less than 9,00,000, so both statements are true.
It is only 14,230 away from 8,00,000 but 85,770 away from 9,00,000, so Roxie’s estimate is closer.
In simple words: The sum 8,14,230 is much nearer to 8,00,000, so Roxie is closer.

Teacher's Note:
1. Both can be 'right' while one is closer.
2. Find the distance from each estimate.

Question 13. Explain, with one example each, a situation in which it is sensible to round a number up and a situation in which it is sensible to round a number down. Also name one situation where only the exact number will do.
Answer:
Round up: a school with 732 students and staff orders 750 sweets, so that nobody is left out.
Round down: a shopkeeper says an item priced ₹470 costs about ₹450, which still gives a fair idea of the price.
Exact number needed: when depositing or withdrawing money in a bank, as even one rupee matters.
In simple words: Round up when you must not fall short, round down for a rough idea, and use exact numbers for money, marks and votes.

Teacher's Note:
1. Any sensible example is accepted.
2. Say why the rounding suits the situation.

Question 14. Calculate these products quickly by regrouping, and write the method you used.
(i) 96 × 125
(ii) 4 × 25 × 125 × 8
Answer:
(i) 125 = \( \frac{1000}{8} \), so 96 × 125 = \( \frac{96}{8} \) × 1000 = 12 × 1000 = 12,000.
(ii) Make friendly pairs: (4 × 25) × (125 × 8) = 100 × 1000 = 1,00,000.
In simple words: Turn 125 into 1000 ÷ 8, and pair numbers that make 100 and 1000.

Teacher's Note:
1. 4 × 25 = 100 and 8 × 125 = 1000 are worth remembering.
2. Write the method, not just the answer.

Question 15. Without multiplying every possible pair, explain how many digits the product can have when
(i) a 2-digit number is multiplied by a 2-digit number,
(ii) a 3-digit number is multiplied by a 3-digit number.
Answer:
We only need to check the smallest and the largest possible products.
(i) Smallest: 10 × 10 = 100 (3 digits); largest: 99 × 99 = 9801 (4 digits). So the product has 3 or 4 digits.
(ii) Smallest: 100 × 100 = 10,000 (5 digits); largest: 999 × 999 = 9,98,001 (6 digits). So the product has 5 or 6 digits.
In simple words: Check the smallest and largest products; every other product lies between them.

Teacher's Note:
1. Rule: m + n − 1 or m + n digits.
2. The extreme cases settle the question.

Question 16. If 1 lakh people stand shoulder to shoulder in a line, the line stretches about 38 km. About how many people would be needed to make a line 190 km long? Show your reasoning.
Answer:
1 lakh people make a line about 38 km long.
190 ÷ 38 = 5, so the new line is 5 times as long.
People needed ≈ 5 × 1 lakh = 5,00,000 (5 lakh).
In simple words: A line 5 times longer needs 5 times as many people.

Teacher's Note:
1. Find 'how many times', then scale up.
2. Check: 38 × 5 = 190.

Question 17. A newspaper headline said, “About 2 crore people visited the state fair.” The organisers’ exact count was 1,96,84,573.
(i) Write the exact count in words in the Indian system.
(ii) Has the headline rounded the figure up or down? By how much?
(iii) Round the exact count to the nearest lakh.
Answer:
(i) One crore ninety-six lakh eighty-four thousand five hundred seventy-three.
(ii) 2,00,00,000 is more than the exact count, so it has been rounded up, by 2,00,00,000 − 1,96,84,573 = 3,15,427.
(iii) The number is between 1,96,00,000 and 1,97,00,000, and 84,573 is more than 50,000, so it rounds to 1,97,00,000.
In simple words: The headline rounded up by 3,15,427; to the nearest lakh the count is 1,97,00,000.

Teacher's Note:
1. Rounded value bigger than actual means rounding up.
2. Subtract to find by how much.

Question 18. Find a number, other than 30,00,000 itself, whose nearest thousand, nearest ten thousand and nearest lakh are all equal to 30,00,000. Write the number and justify each of the three roundings.
Answer:
One such number is 29,99,800 (others, such as 29,99,700 or 30,00,250, also work).
Nearest thousand: it lies between 29,99,000 and 30,00,000; 800 is more than 500, so it rounds to 30,00,000.
Nearest ten thousand: it lies between 29,90,000 and 30,00,000; it is only 200 away from 30,00,000 but 9,800 away from 29,90,000.
Nearest lakh: it lies between 29,00,000 and 30,00,000 and is far closer to 30,00,000.
So all three roundings give 30,00,000.
In simple words: Pick a number within 500 of 30,00,000; it rounds to 30,00,000 in all three ways.

Teacher's Note:
1. The nearest thousand is the strictest test.
2. Any number from 29,99,500 to 30,00,499 works.

Question 19. The approximate number of litres of water a large river pushes into the sea every second can be found from 2400 × 75,000.
(i) Find the product by regrouping the factors.
(ii) Read the answer in the Indian system and in the American system.
Answer:
(i) 2400 × 75,000 = (2400 × 75) × 1000 = 1,80,000 × 1000 = 18,00,00,000.
(ii) Indian: 18,00,00,000 is eighteen crore. American: 180,000,000 is one hundred eighty million.
In simple words: The product is 18 crore litres, which is 180 million litres.

Teacher's Note:
1. 24 × 75 = 1800; then add the zeroes.
2. 1 crore = 10 million, so 18 crore = 180 million.

Question 20. The distance from the Earth to the Moon is about 3,84,400 km. Roxie wonders whether she could cover this distance in 10 years by travelling 120 km every day. Work in stages (take 1 year = 365 days) and give your conclusion.
Answer:
Distance in one year = 120 × 365 = 43,800 km.
Distance in ten years = 43,800 × 10 = 4,38,000 km.
This is more than 3,84,400 km, so yes, Roxie could cover the Earth–Moon distance within 10 years.
In fact 43,800 × 8 = 3,50,400 and 43,800 × 9 = 3,94,200, so she would need a little less than 9 years.
In simple words: At 120 km a day she covers 4,38,000 km in 10 years, more than the Moon’s distance.

Teacher's Note:
1. Work in stages: a year first, then ten years.
2. Compare the final result with 3,84,400.