*Do you need to convert a decimal to a fraction or back the other way?*

This will explain how to convert:

Decimals to Fractions

**AND**

Fractions back to Decimals

**Signing Up**

## Step 1: The conversion

_{see the chart below}

To make it easier think of it this way:

the ones place is

**x/1**, place just to the right of the decimal is

**x/10**, the next place to the right is

**x/100**, etc...

For

**each place**the you move

**to the right**of the decimal

**add another**

*zero*(0) to the denominator.so 0.5 = 5/10, 0.006 = 6/1000, 0.0004 = 4/10000

## Step 2: What about a decimal with more than one numeral???

For example: If the decimal is 0.0023 you would go to the largest place (the 4

^{th}place in this case) and use that as your denominator (4

^{th}place= x/10000). The numerator is the numerals in the decimal(23 in this case). So for the decimal 0.0023, the fraction would be 23/10000.

## Step 3: Simplifying a Fraction

_{if you need help with the GCF see step 1 and 2 of this instructable by Phoenixsong.}

Ex: The GCD of 60/140 is 20. 60/2=3 and 140/20=7. The new simplified fraction is 3/7.

## Step 4: Fraction back to a decimal

*translated into english would by*

**a/b***a*divided by

*b*.

So to find the equation for converting two-thirds (2/3) into a decimal. You would take

**a**(2) and divide it by

**b**(3).

_{(If you don't know how to divide look at this instructable by TechnoGeek95.)}

2/3=0.66666...

## Step 5: Types of Decimals

This is called a

**repeating decimal**it goes on forever repeating the same digits over and over.

ex: 0.66666...., 0.123123123..., 0.104710471047...

to simplify this number you have two options.

1)put a line over the repeating digits

2)round the decimal off

Another type of decimal is a

**terminating decimal**.

A terminating decimal is a decimal that stops.

ex: 1/8 = 0.125, 1/50 =0.02, 1/32 = 0.03125

The third type of decimal is a

**irrational decimal**.

An irrational decimal is one that does not terminate or repeat.

ex: pi, the square root of 2, any other non-perfect square roots

To simplify this number you can:

1) Round it off to whatever place you choose.

All repeating fractions have (10

^{n-1) for the denominator, and the repeating part for the numerator, where n is the length of the repeating part.}Example:

0.12871287128712... = 1287/9999 = 13/101