Large Numbers Around Us: questions with answers

Counting up from 9,999, the next number is 10,000. It is the first number to need 5 digits, and it is written as 1 followed by 4 zeroes. The largest number with one digit fewer is 9,999, which is 1 less than the answer, not the answer itself.

In figures, one crore is 1,00,00,000. The leading 1 is a digit too, so the total number of digits is 7 + 1 = 8.

In one year, the bus travels 100 × 365 = 36,500 km. In one year, it travels 36,500 × 1 = 36,500 km. The difference is 36,500 − 25,000 = 11,500 km, so it travels 11,500 km more than 25,000 km.

The number of buses has to be turned into a number of people first: 1,00,000 times 50 is 50,00,000. The count of buses on its own says nothing about how many people fit.

Counting from the right, the first group holds three digits and every group after that holds two, giving 27,56,340. Three-digit groups all the way, 2,756,340, is the international pattern and marks different places.

10,00,000 has more places, and a number with more places is larger whatever its leading digit is. 9,99,999 starts with a bigger digit but reaches only up to lakhs.

Each press of the +1000 button adds 1,000. So divide 97,600 by 1,000. It is not a whole number, so no number of presses lands on it. The 100 button does reach it in 976 presses.

The parts already given come to 4072, leaving 1000 to be made with the +100 button, so the blank is 10. It is not a digit copied out of 5072.

100 crore is 1,00,00,00,000 and 1 billion is 1,00,00,00,000, so the correct sign is =. A hundred crore make one billion, so a crore count has to be divided by a hundred before it can be set against a billion count.

5 lakh is 5,00,000 and 5 million is 50,00,000, so the correct sign is <. The units differ, so the two leading numbers cannot be compared directly.

Each level is decided by everything below it: 6,72,85,000 | 6,73,00,000 | 7,00,00,000. Blanking the lower digits gives 6,72,85,000 | 6,72,00,000 | 6,00,00,000, and looking only at the digit sitting in each place gives 6,72,86,000 | 6,72,00,000 | 7,00,00,000; both go wrong at some level.

Both 3,76,905 and 3,58,442 lie between 3,00,000 and 4,00,000. Their sum is therefore more than 6,00,000 and less than 8,00,000. The exact sum is 7,35,347. It is greater than 7,00,000, so the narrower interval does not contain it. Adding only the lakh parts gives 6,00,000, not the exact sum.

1768 x 50 = 88,400, so the factor 2 was left out. Multiply 88,400 by 2 to get 1,76,800. Multiplying by 1 would leave the incorrect result unchanged.

4 x 25 = 100, so the product is 379 x 100 = 37,900. Every factor has to appear in the end: leaving one out gives 9,475.

The smallest such product is 10 × 100 = 1,000, which has 4 digits. The largest is 99 × 999 = 98,901, which has 5 digits. Every such product lies between these two, and both digit counts are possible. So the product can have 4 or 5 digits. Adding the digit counts gives only the largest possible digit count.