What is the 15th digit after the decimal point of 1/27? Step by Step

Step by step

The question

Question: What is the 15th digit after the decimal point of 1/27?

1 Find the block

10 divided by 27 is 0, and 10 is left.

digit 1 = 10 ÷ 27 = 0, 10 left

We divide 1 by 27 the long way.

Each time we bring down a 0.

1 ÷ 27: bring down a 0 each time

100 divided by 27 is 3, and 19 is left.

digit 2 = 100 ÷ 27 = 3, 19 left

190 divided by 27 is 7, and 1 is left.

1 left: that is where we started.

So the digits repeat from here.

digit 3 = 190 ÷ 27 = 7, 1 left

So 1/27 is 0 point 0 3 7, and the same 3 digits again and again.

127 = 0.037 037 …

The block is 3 long.

length = 3

2 Divide

The block comes again and again.

So we divide by its length.

What is left over tells us the place in the block.

n ÷ (length of the block): what is left = the place in the block

3 times 5 is 15.

So 5 full blocks take us to the 15th digit.

15 minus 15 is 0 more.

15 ÷ 3 = 3 × 5 = 15, 15 − 15 = 0

3 Count into the block

Nothing is left over.

So the 15th is the end of a block: the last one, 7.

15th digit = nothing left: the last in the block = 7

4 Check

Let's check by counting on.

A block ends at the 12th digit.

Then we count on: 0, 3, 7.

The 15th is 7.

So it is right!

12th = 7 (end of a block), 13th = 0, 14th = 3, 15th = 7 ✓

Let's look back.

First: find the block.

Then: divide.

Then: count into the block.

Last: check.

Answer