CBSE Class 7 Mathematics Large Numbers Around Us MCQs Set 11

Answer: (c) 1,00,000

Explanation:
1. The largest 5-digit number is 99,999.
2. Adding 1 to it gives 1,00,000, which has six digits.
3. So the smallest 6-digit number is 1,00,000 (one lakh).

Teacher's Note:
1. The smallest number with one more digit is always the largest number with fewer digits plus 1.
2. Count the digits of each option to check.

Answer: (d) 7

Explanation:
1. One crore = 100 lakh = 1,00,00,000.
2. Count the zeroes after 1: there are 7.
3. (One lakh has 5 zeroes and one arab has 9.)

Teacher's Note:
1. Lakh 5, crore 7, arab 9: each step adds two zeroes.
2. Write the number with commas, then count.

Answer: (b) Five lakh four thousand eighty five

Explanation:
1. Read the groups made by the commas: 5 | 04 | 085.
2. 5 lakh, 04 thousand and 085.
3. So it is five lakh four thousand eighty five.

Teacher's Note:
1. Each comma tells you where a new name begins.
2. A 0 in front of a group is not read.

Answer: (a) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. 1,00,000 is one lakh (r) and 10,00,000 is ten lakh (s).
2. 1,00,00,000 is one crore (p) and 1,00,00,00,000 is one arab, that is a hundred crore (q).
3. So the match is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. Each number in Column I is ten or a hundred times the one before it.
2. Count zeroes: 5 lakh, 7 crore, 9 arab.

Answer: (b) 3-2-2-2

Explanation:
1. The first comma comes after three digits from the right (thousands).
2. After that a comma comes after every two digits (lakhs, crores).
3. This gives the 3-2-2-2 pattern. The 3-3-3 pattern is the American system.

Teacher's Note:
1. Example: 9,87,65,01,234 has groups 9 | 87 | 65 | 01 | 234 from the left.
2. Always start counting from the right.

Answer: (d) ten lakh

Explanation:
1. One million is 1 followed by six zeroes: 1,000,000.
2. In Indian commas this is 10,00,000, which is ten lakh.
3. One crore is ten million, so it is much bigger.

Teacher's Note:
1. 1 million = 10 lakh; 10 million = 1 crore.
2. Rewrite the number with Indian commas to read its Indian name.

Answer: (a) 76,000

Explanation:
1. 76,068 lies between 76,000 and 77,000.
2. The hundreds digit is 0, which is less than 5, so we round down.
3. The answer is 76,000.

Teacher's Note:
1. To round to thousands, look at the hundreds digit.
2. 5 or more rounds up; less than 5 rounds down.

Answer: (c) dividing it by 2 and then multiplying by 10

Explanation:
1. 5 = 10 ÷ 2.
2. So multiplying by 5 is the same as halving the number and then multiplying by 10.
3. Example: 116 × 5 = 58 × 10 = 580. The answer is divide by 2 and then multiply by 10.

Teacher's Note:
1. Halving and adding a zero is easy to do mentally.
2. Test any option on a small number like 4.

Answer: (d) 300

Explanation:
1. 25 = 100 ÷ 4.
2. So 25 × 12 = \( \frac{12}{4} \) × 100 = 3 × 100.
3. The value is 300.

Teacher's Note:
1. Multiplying by 25 = dividing by 4 and multiplying by 100.
2. Check: 25 × 4 = 100, so 25 × 12 = 3 × 100.

Answer: (c) 11 times

Explanation:
1. Divide the two heights: 450 ÷ 40 = 11.25.
2. So the waterfall is about 11 times as high as the building.
3. (The Statue of Unity, 180 m, is only about 4 times as high.)

Teacher's Note:
1. 'How many times' means divide.
2. Round the result to the nearest whole number.

Answer: (c) Both Statement I and Statement II are true

Explanation:
1. One lakh = 1,00,000, that is 1 followed by five zeroes, so Statement I is true.
2. One arab = 1,00,00,00,000 = 100 crore, so Statement II is true.
3. So both statements are true.

Teacher's Note:
1. A lakh is 100 thousand, a crore is 100 lakh, an arab is 100 crore.
2. Check each statement on its own.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The census figure is 76,068, and people often just say 'about 75,000'. So A is true.
2. R is also true: often only the size of a quantity matters.
3. R is exactly why the rounded figure is used, so R explains A.

Teacher's Note:
1. Approximate values are used when an idea of size is enough.
2. Exact values are kept for things like money, marks and votes.

Answer: (b) 976

Explanation:
1. Each press adds 100.
2. 97,600 ÷ 100 = 976.
3. So the button must be pressed 976 times.

Teacher's Note:
1. Number of presses = number ÷ button value.
2. Dividing by 100 removes two zeroes.

Answer: (b) the sum of the digits of the number

Explanation:
1. The fewest clicks come from making each digit with its own place value button.
2. So each digit d needs d clicks, and the total is the sum of the digits.
3. Example: 56,354 needs 5 + 6 + 3 + 5 + 4 = 23 clicks.

Teacher's Note:
1. The least-click way is just the place value expansion.
2. Try it on a small number to check.

Answer: (a) 10,20,30,040

Explanation:
1. Ten crore = 10,00,00,000.
2. Put 20 in the lakhs group, 30 in the thousands group and 040 in the last group.
3. So the number is 10,20,30,040.

Teacher's Note:
1. Fill the groups crore | lakh | thousand | hundreds one at a time.
2. A missing part becomes zeroes, never a skipped group.

Answer: (a) Only Statement I is correct

Explanation:
1. 500 lakh = 5,00,00,000 = 50 million, which is more than 5 million. Statement I is correct.
2. 640 crore = 6,40,00,00,000 = 6.4 billion, which is less than 60 billion. Statement II is wrong.
3. So only Statement I is correct.

Teacher's Note:
1. 10 lakh = 1 million and 100 crore = 1 billion.
2. Change both sides into the same system before comparing.

Answer: (d) 5,47,00,000

Explanation:
1. The number lies between 5,46,00,000 and 5,47,00,000.
2. Look at the ten thousands digit: it is 7, which is 5 or more, so round up.
3. The nearest lakh is 5,47,00,000.

Teacher's Note:
1. For the nearest lakh, check the ten thousands digit.
2. The answer must end in five zeroes.

Answer: (b) Surat

Explanation:
1. Surat grew from about 24 lakh to about 45 lakh, nearly twice as many.
2. Chennai and Kanpur grew only a little, and Kolkata’s population actually fell.
3. So the answer is Surat.

Teacher's Note:
1. Round to lakhs first: 24 lakh to 45 lakh.
2. Doubling means the new value is about 2 times the old one.

Answer: (c) 7 times

Explanation:
1. From the graph, Mumbai has about 124 lakh people and Patna about 17 lakh.
2. 124 ÷ 17 is a little more than 7.
3. So Mumbai’s population is about 7 times that of Patna.

Teacher's Note:
1. Read the values at the top of the bars.
2. Check: 17 × 7 = 119, close to 124.

Answer: (d) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. 5 = 10 ÷ 2 (r) and 25 = 100 ÷ 4 (s).
2. 125 = 1000 ÷ 8 (p) and 50 = 100 ÷ 2 (q).
3. So the match is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. Write each multiplier as a round number divided by a small number.
2. Check: 8 × 125 = 1000.

Answer: (c) A is true, but R is false.

Explanation:
1. 1000 × 10 = 10,000, a 5-digit product. So A is true.
2. An m-digit number times an n-digit number has m + n − 1 or m + n digits, not always m + n. So R is false.
3. So A is true but R is false.

Teacher's Note:
1. The word 'always' in R makes it false.
2. Test with the smallest numbers, like 1000 × 10.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. One crore = 1,00,00,000, so A is true.
2. One lakh = 1,00,000 = 100 thousand, so R is true.
3. A crore has seven zeroes because it is 100 × 1,00,000 (a hundred lakhs). R talks about lakhs and thousands, so it does not explain A.

Teacher's Note:
1. Both can be true and still not linked.
2. Ask: does R give the reason for A?

Answer: (d) A is false, but R is true.

Explanation:
1. ₹450 is less than the actual ₹470, so this is rounding down, not up. A is false.
2. R correctly states the meaning of rounding down. R is true.
3. So A is false but R is true.

Teacher's Note:
1. Rounded value bigger than actual: rounding up. Smaller: rounding down.
2. Compare 450 with 470.

Answer: (c) Both statements are correct

Explanation:
1. Check I: 9300 × 150 = 13,95,000. Correct.
2. Check II: 1,50,000 × 700 = 10,50,00,000. Correct.
3. So both statements are correct.

Teacher's Note:
1. Check a division by multiplying back.
2. Count the zeroes carefully.

Answer: (b) 38 km

Explanation:
1. In one day: 12,000 ÷ 13 ≈ 923 km.
2. In one hour: 923 ÷ 24 ≈ 38 km.
3. So the bird flies about 38 km in an hour.

Teacher's Note:
1. Work in two stages: per day, then per hour.
2. 1 day = 24 hours.

Answer: (d) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

Explanation:
1. Nearest thousand: hundreds digit 6, so 4,57,84,000 (r). Nearest lakh: ten thousands digit 8, so 4,58,00,000 (p).
2. Nearest ten lakh: lakhs digit 7, so 4,60,00,000 (s). Nearest crore: ten lakhs digit 5, so 5,00,00,000 (q).
3. So the match is (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q).

Teacher's Note:
1. Look at the digit just to the right of the place you round to.
2. 5 or more means round up.

Answer: (a) Only Statement I is correct

Explanation:
1. 1,00,000 × 5 g = 5,00,000 g = 500 kg, so Statement I is correct.
2. Nobody can lift 500 kg at one time, so Statement II is wrong.
3. So only Statement I is correct.

Teacher's Note:
1. 1000 g = 1 kg.
2. Compare the answer with something familiar, like your own weight.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. 1,00,000 × 50 = 50,00,000, that is 50 lakh seats. So R is true.
2. 50 lakh is far less than 1,24,42,373, so the buses cannot carry everyone. A is true.
3. R gives the exact reason for A, so R explains A.

Teacher's Note:
1. A lakh buses sounds huge, but the city is bigger.
2. Compare 50 lakh with about 124 lakh.

Answer: (c) A is true, but R is false.

Explanation:
1. 100 × 365 × 10 = 3,65,000 km, which is less than the Moon’s distance of 3,84,400 km. So A is true.
2. The Moon is about 3,84,400 km away, not 38,44,000 km. So R is false.
3. So A is true but R is false.

Teacher's Note:
1. Look carefully at the commas in R: it is ten times too big.
2. Work in stages: per year, then for 10 years.

Answer: (a) 465

Explanation:
1. Use as many +10,000 clicks as possible: 40,36,200 = (403 × 10,000) + (62 × 100).
2. Clicks = 403 + 62 = 465.
3. Using one fewer +10,000 click would need 100 extra +100 clicks, which is more.

Teacher's Note:
1. Use the bigger button as much as you can.
2. Check: 40,30,000 + 6,200 = 40,36,200.