## Introduction: Decimal to Fraction

This instructable is to instruct how to convert decimals to fractions. Although the easiest way is to type the decimal into a scientific calculator, hit =, the hit the fraction key, but not very many people carry a calculator in the back pocket. So.. Onwards Mathematicians!!!!

## Step 1: Converting Rational Decimals to Fractions

To convert a rational decimal number (rational number= number that can be written exactly as a fraction) one simply has to draw a vinculum or fraction bar, and for the denominator count the places held after the decimal point, then put that amount of zeros after a one. For the numerator, just put the numbers after the decimal point.

eg

0.13579 = 13579 / 100000

0.00520347 = 520347 / 100000000

eg

0.13579 = 13579 / 100000

0.00520347 = 520347 / 100000000

## Step 2: Converting Repeating Decimals to Fractions

Converting repeating decimals to fractions it a little bit harder than typing it in on a calculator because the calculator doesn't have an infinitely long screen. Still it can be done with relative ease if you just think it simple. Converting repeating decimals requires a little algebraic manipulation.

1. Let x equal your repeating decimal. Call this equation

2. Multiply both sides of your previous expressions by 10 . Call this equation

3.Subtract equation

4.Solve for x. eg, x=6/9

=2/3

5. But x is also equal to 0.66666..., therefore 0.666... is equal to 2/3.

NOTE: In harder repeating decimals such as decimals which repeat a string of number may need you to multiply by 100 or 1000 etc to allow the repeats behind the decimal point to cancel in the subraction

1. Let x equal your repeating decimal. Call this equation

**1**eg, x=0.6666666...2. Multiply both sides of your previous expressions by 10 . Call this equation

**2**eg, 10x=6.6666666...3.Subtract equation

**2**from equation**1**. eg, 9x=6 (see picture for clearer explanation)4.Solve for x. eg, x=6/9

=2/3

5. But x is also equal to 0.66666..., therefore 0.666... is equal to 2/3.

NOTE: In harder repeating decimals such as decimals which repeat a string of number may need you to multiply by 100 or 1000 etc to allow the repeats behind the decimal point to cancel in the subraction

## Step 3: Decimals Greater Than 1

For decimals greater than one, such as 1.0347, ignore the numbers in front of the decimal point and carry out the conversion as you would in the previous steps. When you obtain the fraction equivalent to the decimal without the whole numbers in front of the point, just write it down and then transpose the numbers in front of the point in front of the fraction. This give the answer in a mixed fraction form. See picture.

NOTE: In the picture below the the decimal digits after the point are the same and therefore the parts of a whole are the same, hence the same fractions. All that changes is the number of whole parts.

NOTE: In the picture below the the decimal digits after the point are the same and therefore the parts of a whole are the same, hence the same fractions. All that changes is the number of whole parts.

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