# How do you write 0.09 as a fraction?

Nov 1, 2015

$\frac{9}{100}$

#### 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 $\frac{9}{10}$.

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 $\frac{9}{100}$.

Feb 6, 2017

$0.09 = \frac{9}{100}$

#### 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.
$10 , 100 , 1000 \ldots$

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 $\frac{1}{100.}$

$0.09 = \frac{9}{100}$

Try also converting $0.1085$ to a fraction.
Numerator is $1085$ and there are four decimal places.
Denominator now needs four zeros to give $\frac{1}{10000}$

$0.1085 = \frac{1085}{10000}$ which simplifies to $\frac{217}{2000}$

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 $\frac{1}{1000}$

$25.492 = 25 \frac{492}{1000}$ which simplifies to $25 \frac{123}{250}$

Note that this can also be written as $\frac{25492}{1000} = \frac{6373}{250}$