What is the 20th digit after the decimal point of 5/11? Step by Step

Step by step

The question

Question: What is the 20th digit after the decimal point of 5/11?

1 Find the block

50 divided by 11 is 4, and 6 is left.

digit 1 = 50 ÷ 11 = 4, 6 left

We divide 5 by 11 the long way.

Each time we bring down a 0.

5 ÷ 11: bring down a 0 each time

60 divided by 11 is 5, and 5 is left.

5 left: that is where we started.

So the digits repeat from here.

digit 2 = 60 ÷ 11 = 5, 5 left

So 5/11 is 0 point 4 5, and the same 2 digits again and again.

511 = 0.45 45 …

The block is 2 long.

length = 2

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

2 times 10 is 20.

So 10 full blocks take us to the 20th digit.

20 minus 20 is 0 more.

20 ÷ 2 = 2 × 10 = 20, 20 − 20 = 0

3 Count into the block

Nothing is left over.

So the 20th is the end of a block: the last one, 5.

20th digit = nothing left: the last in the block = 5

4 Check

Let's check by counting on.

A block ends at the 18th digit.

Then we count on: 4, 5.

The 20th is 5.

So it is right!

18th = 5 (end of a block), 19th = 4, 20th = 5 ✓

Let's look back.

First: find the block.

Then: divide.

Then: count into the block.

Last: check.

Answer