decimal to fraction

Decimal To Fraction Calculator

How to Convert a Decimal to a Fraction

Converting decimals to fractions is a fundamental skill in mathematics. By following a simple process, you can easily convert any decimal into its fractional equivalent. In this article, we will provide you with a step-by-step guide to master this conversion process.

Step One: Create the Starting Fraction

To begin the conversion, create a starting fraction with the decimal as the numerator and 1 as the denominator. This initial fraction represents the decimal value.

For example, let's convert the decimal 0.75 to a fraction. We create the starting fraction as follows:

0.75 = 0.75/1

Step Two: Multiply by Powers of Ten

Next, multiply both the numerator and the denominator by 10 to eliminate the decimal place. Repeat this process until the numerator becomes a whole number.

Continuing with our example, let's multiply the starting fraction by 10:

0.75/1 = (0.75 × 10)/(1 × 10) = 7.5/10

Since the numerator is still not a whole number, we continue:

7.5/10 = (7.5 × 10)/(10 × 10) = 75/100

Step Three: Reduce the Fraction

The final step is to reduce the fraction to its simplest form. Find the greatest common factor (GCF) of the numerator and the denominator. Divide both the numerator and the denominator by their GCF to simplify the fraction.

In our example, the GCF of 75 and 100 is 25. Dividing both numerator and denominator by 25 yields the simplified fraction:

75/100 = (75 ÷ 25)/(100 ÷ 25) = 3/4

Therefore, 0.75 as a fraction is 3/4.

Converting Repeating Decimals to Fractions

In addition to terminating decimals, there are repeating decimals that continue indefinitely. Converting repeating decimals to fractions requires a slightly different approach.

Step One: Create an Equation

Start by creating an algebraic equation to represent the repeating decimal. Assign the decimal value to a variable, let's say x.

For instance, to convert the repeating decimal 1.1787878, we create the equation:

x = 1.1787878

Step Two: Multiply by Powers of Ten

Multiply both sides of the equation by 10 until the repeating portion of the decimal is on the left side of the decimal point.

Continuing the example, let's multiply both sides by 10:

10x = 11.787878

Step Three: Multiply by Powers of Ten Again

Create a new equation for x and multiply both sides by 10 until the repeating portion is on the right side of the decimal point.

In our example, we continue multiplying by 10:

100x = 117.87878

Step Four: Combine the Equations

Combine the equations to eliminate the repeating portion. Subtract the equation obtained in Step Two from the equation obtained in Step Three.

Using our example:

100x - 10x = 117.87878 - 11.787878

Step Five: Solve for x

Solve the equation to find the value of x, which represents the repeating decimal.

Continuing the example:

90x = 106.090902

x = 106.090902 / 90

Simplifying further, we get:

x = 53.045451 / 45

The resulting fraction is 53.045451/45.

Converting Negative Decimals to Fractions

To convert a negative decimal to a fraction, follow these steps:

1. Remove the negative sign from the decimal.

2. Convert the positive decimal to a fraction using the methods described above.

3. Add the negative sign back to the resulting fraction.

For example, to convert -0.75 to a fraction:

1. Remove the negative sign: 0.75

2. Convert 0.75 to a fraction: 0.75 = 3/4

3. Add the negative sign back: -0.75 = -3/4

Decimal to Fraction Chart

If you need to quickly convert common decimal values to fractions, refer to the following chart:

Decimal Value Fraction Value
0.0625 1/16
0.08333 1/12
0.1 1/10
0.111 1/9
0.125 1/8
0.1666 1/6
0.2 1/5
0.222 2/9
0.25 1/4
0.333 1/3
0.375 3/8
0.4 2/5
0.444 4/9
0.5 1/2
0.555 5/9
0.6 3/5
0.625 5/8
0.666 2/3
0.75 3/4
0.777 7/9
0.8 4/5
0.8333 5/6
0.875 7/8
0.888 8/9
0.9 9/10
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Decimal Value	Fraction Value
0.0625	1/16
0.08333	1/12
0.1	1/10
0.111	1/9
0.125	1/8
0.1666	1/6
0.2	1/5
0.222	2/9
0.25	1/4
0.333	1/3
0.375	3/8
0.4	2/5
0.444	4/9
0.5	1/2
0.555	5/9
0.6	3/5
0.625	5/8
0.666	2/3
0.75	3/4
0.777	7/9
0.8	4/5
0.8333	5/6
0.875	7/8
0.888	8/9
0.9	9/10

Frequently Asked Questions

Q: When do you need to convert decimals to fractions?

A: Converting decimals to fractions can be helpful in various situations, such as simplifying calculations, making comparisons, or expressing quantities in a more appropriate format. Fractions are also compatible with traditional measuring systems, making them useful in fields like construction or recipes.

Q: What are the benefits of using fractions over decimals?

A: Fractions can be easier to understand, especially for those unfamiliar with decimal notation. They can provide greater precision in certain calculations and are compatible with traditional measurement systems. Fractions can also simplify calculations and convey information more clearly in specific contexts.

Q: How do you convert a decimal greater than 1 to a fraction?

A: To convert a decimal greater than 1 to a fraction, count the number of decimal places and write the decimal as a fraction with a denominator of 1 followed by the same number of zeros as the decimal places. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).

By following the steps outlined in this article, you can confidently convert decimals to fractions. Regular practice will enhance your skills in this fundamental mathematical process.