Playing with Digits

We start writing numbers from 1, 2, 3 … and so on. There are nine 1-digit numbers.

Find out how many numbers have two digits, three digits, four digits, and five digits.

Komal observes that when she adds up digits of certain numbers the sum is the samedifferent.

For Example: Adding the digits of the number 68 will be samedifferent as adding the digits of 176 or 545.

Figure it Out 4

1. Digit sum 14.

a. Write other numbers whose digits add up to 14.

Some numbers whose digits add up to 14 are:

Instruction

b. What is the smallest number whose digit sum is 14?

The smallest number whose digit sum is 14 = .

c. What is the largest 5-digit whose digit sum is 14?

The largest 5 digit number containing 0 whose digit sum is 14 = .

The largest 5 digit number not containing 0 whose digit sum is 14 = .

d. How big a number can you form having the digit sum of 14? Can you make an even bigger number?

A very big number having the digit sum 14 can be made.

Ex: 95000000000000.

YesNo, we can make even bigger number e.g. 9500000000000000000000

2. Find out the digit sums of all the numbers from 40 to 70. Share your observations with the class.

3. Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you see a pattern? Will this pattern continue?

If we take numbers in reverse order, sum of digits will remain same.

YesNo, we observe a pattern.

i. e. (first number + 1) × 3 = digit sum.

After writing numbers from 1 to 100, Dinesh wondered how many times he would have written the digit ‘7’!

Among the numbers 1–100, how many times will the digit ‘7’ occur? times

Among the numbers 1–1000, how many times will the digit ‘7’ occur? times