Class 7 Maths Ganita Prakash Part 1 Chapter 1 MCQs – Large Numbers Around Us

The largest five-digit number is 99,999. Adding 1 gives the next number.
99,999 + 1 = 1,00,000
This number has six digits and is called one lakh. Every other six-digit number is larger.

Number of days = 100 × 365 = 36,500
Number of varieties = 36,500 × 3 = 1,09,500
This is 9,500 more than one lakh. The calculation assumes a new variety each time and ignores leap years.

In 12,78,830, the digit 7 is in the ten-thousands place.
Value of 7 = 7 × 10,000 = 70,000
The neighbouring digit 8 to its right represents 8,000, so these two digits together represent 78,000.

Increase = later population − earlier population
= 1,06,000 − 75,000
= 31,000
The first 25,000 takes 75,000 up to one lakh, and another 6,000 takes it to 1,06,000. Together these give an increase of 31,000.

Fifty lakh = 50,00,000, five thousand = 5,000, and fifty = 50.
50,00,000 + 5,000 + 50 = 50,05,050
The zeroes keep the unused places in position, so five thousand does not become fifty thousand.

Each press adds 1,000. One lakh is 1,00,000.
Number of presses = 1,00,000 ÷ 1,000 = 100
Checking by multiplication, 100 × 1,000 = 1,00,000. Thus, one lakh contains one hundred thousands.

Each of the 582 presses contributes 100.
Displayed number = 582 × 100 = 58,200
Multiplying by 100 makes each digit represent a value one hundred times as large. The result is fifty-eight thousand two hundred.

In (3 × 1,000) + (20 × 100) + 72, the three parts are 3,000, 2,000 and 72.
3,000 + 2,000 + 72 = 5,072
A number can have different correct decompositions. Here, twenty hundreds replace two thousands without changing the total.

40,629 = (4 × 10,000) + (6 × 100) + (2 × 10) + 9
Fewest presses = 4 + 6 + 2 + 9 = 21
Using ten smaller presses instead of one larger press would increase the count, so the place-value decomposition uses the fewest presses.

92,100 = (9 × 10,000) + (21 × 100)
Number of presses = 9 + 21 = 30
A tenth +10,000 press would go beyond 92,100. Using fewer than nine large presses would require many more +100 presses.

One crore = 1,00,00,000 = 10,000,000
One million = 1,000,000
Number of millions = 10,000,000 ÷ 1,000,000 = 10
The Indian and International systems give different names and comma groupings to the same quantity.

In the International system, digits are grouped in threes from the right.
246 | 813 | 579
So the number is 246,813,579. These groups represent millions, thousands and ones; the Indian system instead groups the digits as 24,68,13,579.

One billion = 1,000,000,000 and one lakh = 100,000.
Number of lakhs = 1,000,000,000 ÷ 100,000 = 10,000
This also agrees with one billion being 100 crores and each crore being 100 lakhs.

5 million = 50 lakhs
500 lakhs > 50 lakhs
Therefore, 500 lakhs is greater than 5 million. In fact, 500 lakhs equals 50 million, which is ten times 5 million.

One crore = 1,00,00,000; one lakh = 1,00,000; one thousand = 1,000.
1,00,00,000 + 1,00,000 + 1,000 + 10 = 1,01,01,010
Each part occupies its own place-value group, including the zeroes in the unused places.

14 packs contain 14 × 50 = 700 sweets, which are too few.
15 packs contain 15 × 50 = 750 sweets.
So 750 is the smallest available quantity that covers 732 people, with 18 sweets left over.

A telephone number identifies a particular connection. Changing even one digit can lead to a different connection or no connection at all. A rounded population, height or distance may still give a useful estimate, but rounding a telephone number changes its identity.

The neighbouring multiples of one lakh are 3,87,00,000 and 3,88,00,000.
Distance from the lower value = 69,957
Distance from the higher value = 30,043
The higher value is nearer, so the rounded number is 3,88,00,000.

4,63,128 + 4,19,682 = 8,82,810
9,00,000 − 8,82,810 = 17,190
8,82,810 − 8,00,000 = 82,810
Since 17,190 is the smaller distance, 9,00,000 is the closer estimate, although the exact sum is below it.

Increase = 31,15,431 − 25,38,473 = 5,76,958
This is 23,042 below 6,00,000 and 76,958 above 5,00,000.
It is closer to 6,00,000, so the population increased by approximately 6 lakh.

Since 25 = 100 ÷ 4, I can divide 824 by 4 and multiply by 100.
824 × 25 = (824 ÷ 4) × 100
= 206 × 100
= 20,600
This regrouping makes the multiplication easier.

Eight groups of 125 make 1,000. Since 72 = 9 × 8, the factors can be grouped conveniently.
72 × 125 = 9 × (8 × 125)
= 9 × 1,000
= 9,000

I can group factors that give round numbers.
125 × 40 × 8 × 25 = (125 × 8) × (40 × 25)
= 1,000 × 1,000
= 10,00,000
Changing the order and grouping of factors does not change their product.

The smallest product is 100 × 100 = 10,000, which has five digits. Every product is less than 1,000 × 1,000 = 10,00,000.
Therefore, the product has five or six digits. For example, 999 × 999 = 9,98,001 has six digits.

The smallest product is 10,000,000 × 100 = 1,000,000,000, with ten digits. Both factors are below 100,000,000 and 1,000 respectively.
Their product is therefore below 100,000,000,000, the smallest twelve-digit number. So it can have ten or eleven digits.

One lakh buses means 1,00,000 buses.
Total capacity = 1,00,000 × 50 = 50,00,000 people
50,00,000 is 50 lakh, or half a crore. The capacity is found by multiplying the number of buses by the capacity of one bus.

Total mass = 1,00,000 × 5 g = 5,00,000 g
Since 1,000 g = 1 kg,
5,00,000 ÷ 1,000 = 500 kg
The conversion to kilograms is necessary because the individual sheet mass was given in grams.

A multiple of 5 must end in 0 or 5. Putting 0 last lets all the remaining digits appear in descending order.
The number is 9876543210.
Any other arrangement first differs at a position with a smaller digit, so it is smaller.

Numbers 1–9 contribute 9 digits, and 10–99 contribute 90 × 2 = 180 digits.
1,000 − 189 = 811 digits remain.
270 three-digit numbers contribute 810 digits and end at 369. The next digit is the first digit of 370, which is 3.

To make the largest number, the leftmost digits must be as large as possible. The inserted 1 should follow 4 and 2 but come before 0.
This gives 421019.
Inserting it earlier replaces a larger early digit; inserting it later leaves 0 in the third place.

One lakh is equal to 1 followed by five zeroes, which is 1,00,000. It is the smallest six-digit number in the Indian place value system and is widely used in counting large quantities in India and neighboring countries.

The Indian number system is used in South Asian countries like Nepal and Bangladesh. The United States uses the International or American number system which groups digits in threes from the right using million and billion.

In the Indian place value system, 15,75,000 is read as fifteen lakh seventy five thousand. The commas separate the digits as per the 2-2-3 pattern used in the Indian system of numbering.

One crore is equal to 1 followed by seven zeroes, written as 1,00,00,000 in the Indian number system. It is one hundred times a lakh and is a common large number in Indian usage.

The Ahmedabad cricket stadium has a seating capacity of more than one lakh. This example is used to illustrate how large numbers can still represent physically small spaces.

3,00,600 is written in the Indian number system as three lakh six hundred. The placement of commas helps identify place values like thousands and lakhs for easier reading and understanding.

Since one hundred is 100 and one lakh is 1,00,000, we divide 1,00,000 by 100 to get 1000. Therefore, 1000 hundreds make up one lakh in the Indian number system.

The smallest 6-digit number is 1,00,000. This number comes after the largest 5-digit number which is 99,999. This is the first point where the digit count moves from five to six.

999 is the largest 3-digit number. It is one less than the smallest 4-digit number which is 1000. This fact is useful when identifying digit limits in place value systems.

Dividing 10,50,00,000 by 700 gives an estimate of the weight of an adult blue whale in kilograms. This example helps illustrate large numbers in context of real-world facts.

To reach 1,00,000 using the +1000 button, we must press it 1000 times because 1000 × 1000 = 1,00,000. This helps students relate operations to quantity and number value.

In the American number system, 1,00,00,000 is written as 10,000,000 and called ten million. This comparison helps students understand different international systems of naming and grouping large numbers.

When rounding 6,72,85,183 to the nearest crore, we get 7,00,00,000. This is done by checking the digit in the ten lakh place to decide whether to round up or down.

The exact sum of 4,63,128 and 4,19,682 is 8,83,128. The chapter uses this to illustrate estimation techniques and to understand rounding of large numbers in addition.

Creative Chitti’s calculator uses +10 thirty two times and then +1 once to form 321. This highlights different ways to construct numbers using breakdowns into simpler components.

1,00,00,00,000 is called one arab in the Indian number system. It is equal to 100 crores. This helps students understand very large numbers used in Indian administrative and business contexts.

A billion has nine zeroes and is written as 1,000,000,000 in the American number system. This number is commonly used in global statistics and finance contexts.

The population increased from 75,000 in 2011 to 1,06,000 in 2024. The difference is 31,000. This data is used to help students work with real-world large number comparisons.

The distance between Earth and Sun is estimated by calculating 2100 × 70,000 = 1,47,00,000 km, which is approximately 14 crore km. This shows how multiplication of large numbers provides real-world insights.

One lakh people standing shoulder to shoulder would stretch about 38 kilometers. This visualization helps in understanding the scale of large numbers through real-life analogies.