Convert a decimal number to a portion using our calculator by entering a decimal value below. The calculator shows all the job-related in the solution so you deserve to view each action.

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Reduce the fractivity by finding the greatest common aspect. The biggest prevalent aspect of 75 and 100 is 25
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## How to Convert a Decimal to a Fraction

Decimal and fractional numbers both recurrent a number that is not an also integer or a number that is not a totality number. Eexceptionally decimal number have the right to be converted to a fraction in simply three basic steps.

Keep in mind that the process of converting a repeating decimal is various.

### Step One: Create the Starting Fraction

The first step in transcreating a decimal to a portion is producing a beginning fractivity through the decimal as the peak number and also 1 as the bottom number. For example, to transform .75 to a fraction, begin by making a portion with .75 as the numerator and also 1 as the denominator.

.75 = .751

### Step Two: Multiply by Ten

The next action is to multiply the numerator and also the denominator by 10 to get rid of the decimal area. Continue multiplying both by 10 until the numerator is a whole number. Continuing the example from above, let’s convert .751 to 75100

.751 = (.75 × 10)(1 × 10) = 7.5107.510 = (7.5 × 10)(10 × 10) = 75100

### Step Three: Reduce the Fraction

The last step in converting a decimal to a fraction is to reduce or simplify the fraction. To mitigate, discover the greatest prevalent element for the numerator and denominator. Then, divide both the numerator and the denominator by the greatest widespread factor. To finish the example over, we understand that the greatest widespread element of 75 and 100 is 25. So, let’s divide the numerator and denominator by 25 to settle the reduced fractivity.

75100 = (75 ÷ 25)(100 ÷ 25)75100 = 34

Here’s a tip: use our fractivity simplifier to conveniently minimize your fraction.

For negative numbers, rerelocate the negative symbol from the starting decimal, then follow the procedures above. After converting to fraction create, add the negative sign ago.

## How to Convert a Repeating Decimal to a Fraction

Repeating decimal numbers need a slightly different procedure to convert to a portion. A repeating decimal is a decimal number that proceeds infinitely, such as 1.1787878.

These numbers are usually expressed in a rounded create, such as .788, or with an over-bar like this: 1.178.

### Step One: Create an Equation

The first action in transdeveloping a repeating decimal is to create an algebraic equation to represent the decimal.

For example, let’s convert the decimal 1.178 into a fraction. Start by producing an equation to assign the expression 1.1787878 to x.

x = 1.1787878

### Step Two: Multiply by 10 Until the Repeating Decimal is on the Left

The second step is to continue multiplying both sides of the equation by 10 till the repeating number is on the left side of the decimal suggest.

If tright here are multiple repeating numbers that repeat in a pattern, then multiply by 10 until the repeating pattern is on the left side of the decimal suggest.

Continuing the instance above, let’s multiply both sides of the equation by 10 till the repeating “78” part of the decimal is on the left side of the decimal point.

x = 1.178787810 × x = 10 × 1.178787810x = 11.78787810 × 10x = 10 × 11.787878100x = 117.8787810 × 100x = 10 × 117.878781000x = 1178.78

### Tip Three: Multiply by 10 Until the Repeating Decimal is on the Right

The 3rd step is to develop a brand-new equation for x and multiply until the repeating decimal percentage is to the appropriate of the decimal point

Building on our example, multiply both sides of the equation by 10 till the repeating “78” part of the decimal is on the appropriate side of the decimal suggest.

x = 1.178787810 × x = 10 × 1.178787810x = 11.78

### Tip Four: Combine the Equations

The next action is to integrate the equations and also relocate both x variables to the left and both decimal worths to the right.

Let’s incorporate the equations and settle.

1000x – 10x = 1178.78 – 11.78990x = 1167990x990 = 1167990x = 1167990

## Decimal to Fractivity Conversion Table

An different strategy to transform a decimal to a portion is to use a convariation table such as this one. See the fractivity equivalents for some common decimal worths listed below. The table allows you to conveniently view the corresponding fraction for a decimal number.

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Table showing the convariation for decimal numbers to widespread fractionsDecimal ValueFractivity Value
0.06251/16
0.083331/12
0.11/10
0.1111/9
0.1251/8
0.16661/6
0.21/5
0.2222/9
0.251/4
0.3331/3
0.3753/8
0.42/5
0.4444/9
0.51/2
0.5555/9
0.63/5
0.6255/8
0.6662/3
0.753/4
0.7777/9
0.84/5
0.83335/6
0.8757/8
0.8888/9

See more fraction decimal equivalents.