Decimal to fraction - Repeating

If you have a repeating decimal it is the division of any number by `9` that makes it repeat.

i.e.   `1div9=1/9=0.111dot1`

`2div9=2/9=0.222dot2`

`3div9=3/9=0.333dot3`

 

I keep seeing nines everywhere doctor.

 

For repeating decimals think

	`0`	`*`	`1`	`1`	`1`	`1`	`1`	etc
			`darr`	`darr`	`darr`	`darr`	`darr`
			`1/9`	`1/90`	`1/900`	`1/9000`	`1/(90,000)`

Or

	`0`	`*`	`2`	`2`	`2`	`2`	`2`	etc
			`darr`	`darr`	`darr`	`darr`	`darr`
			`2/9`	`2/90`	`2/900`	`2/9000`	`2/(90,000)`

Or

	`0`	`*`	`3`	`3`	`3`	`3`	`3`	etc
			`darr`	`darr`	`darr`	`darr`	`darr`
			`3/9`	`3/90`	`3/900`	`3/9000`	`3/(90,000)`

 

 Find where it starts repeating and the number it repeats

Example 1

Convert `0.dot2` to a fraction

`0.dot2=0.222222` recurring.

Remember:

`0`	`*`	`2`	`2`	`2`	`2`
		`darr`
		`2/9`

Therefore

`0.dot2=2/9`

Now check on a calculator `2div9=0.22dot2`

 

Example 2

Convert `0.0dot2` to a fraction

`0.0dot2=0.0222222` recurring.

Remember:

`0`	`*`	`2`	`2`
		`darr`	`darr`
		`2/9`	`2/90`

Therefore

`0.0dot2=2/90=1/45`

Now check on a calculator `2div90=0.022dot2`

 

Example 3

Convert `0.000222dot2` to a fraction

`0.000dot2=0.000222222` recurring.

Remember:

`0`	`*`	`2`	`2`	`2`	`2`
		`darr`	`darr`	`darr`	`darr`
		`2/9`	`2/90`	`2/900`	`2/(9,000)`

Therefore

`0.dot2=2/(9,000)=1/(4,500)`

Now check on a calculator `2div9,000=0.00022dot2`

 

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