## Introduction: Decimal to Fraction

*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

## Step 1: The Conversion

To convert a decimal to a fraction you need to know what each place in a decimal equals._{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???

If the decimal has more than one numeral in it it's still just as easy to turn into a fraction.

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

To simplify a fraction you first need to find the Greatest Common Factor (GCF) of both the numerator and the denominator. You then divide the numerator by the GCF and the denominator by the GCF. _{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

The fraction * a/b* translated into english would by

*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

2/3=0.66666...

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.

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## 4 Comments

I don't know if that would be "legal" wrt contest rules, or not?

Maybe one of the instructibles elders reading this could comment? I'm just a noob here really.

I would think it would be legal to make edits to your ible up until the deadline of the contest, but that's just a guess. As far as using my suggestions, I hereby give you permission to use whatever intellectual "stuff" I've given you, licence-free, and you don't have to a attribute it to me either.

Also I think maybe I just made that comment to show off a little bit, without the large amount of work of writing a whole instructible myself. That'd probably be the ethical way for me to show off my math smarts.

And of course, while I was trying to be smart the editor screwed up the formating. I was trying to write the denominator is (10

^{n}-1), not 10^{(n-1)}followed by a bunch of small superscripted text.;-)

Very nice instructable, but I can think of a way to make it nicer. You mention repeating decimals, but you don't tell us how to convert a repeating decimal to a fraction.

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

Think I should make an instructable converting decimals to percentages?Sure, if you can make is as well organized as this one (also note the first few of Kiteman's Laws ;-)

Very nice instructable, and useful too. Very well explained.