Question

How do you write 0.09 as a fraction?

Answer 1

`9/100`

Explanation:

Every place value after the decimal point can be expressed as a fraction with `10` to some power in the denominator.

The first place after the decimal point is called the "tenths place" If I had `0.9`, I would have `9` tenths, or as a fraction `9/10`.

The second place after the decimal is called the "hundredths place". The question above asks for `0.09`. This would be `9` hundredths, or as a fraction `9/100`.

Answer 2

`0.09 = 9/100`

Explanation:

I enjoy working with decimals because every one converts to a fraction that has a denominator of 10 or a power of 10.
Powers of 10 simply means adding more zeros.
`10, 100, 1000 ...`

After working with a few of these examples you will see a trend.
Every time you have another decimal place in a decimal number, then you will need that many zeros in the denominator to create a fraction from the given number.

So `0.09` will give us a whole number of 9 for the numerator and there are two decimal places. That indicates there will be two zeros in the denominator to give `1/100.`

`0.09 = 9/100`

Try also converting `0.1085` to a fraction.
Numerator is `1085` and there are four decimal places.
Denominator now needs four zeros to give `1/10000`

`0.1085 = 1085/10000` which simplifies to `217/2000`

What about decimal numbers greater than 1?

Convert `25.492` to a fraction.

The whole number is already `25`, the decimal part needs to be written as a fraction

Numerator is `492` and there are three decimal places.
Denominator now needs three zeros to give `1/1000`

`25.492 = 25 492/1000` which simplifies to `25 123/250`

Note that this can also be written as `25492/1000 = 6373/250`