Fraction to Decimal Calculator

Numerator:

Denominator:

Result:

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How to Convert a Fraction to a Decimal

There are several methods available to convert a fraction to a decimal representation. We will discuss each method in detail below.

Method 1: Using a Calculator

The simplest way to convert a fraction to a decimal is to divide the numerator by the denominator. By performing this division, you obtain the decimal value of the fraction.

numerator/denominator = numerator ÷ denominator(alert-passed)

For example, to convert the fraction 1/8 to a decimal, divide the numerator (1) by the denominator (8):

1/8 = 1 ÷ 8 = 0.125

Therefore, the decimal representation of 1/8 is 0.125.

You might also be interested in our fraction to percent calculator for similar conversions.

Method 2: Long Division

Another method to convert a fraction to a decimal is through long division. This involves dividing the numerator by the denominator using long division steps.

To start, identify the dividend (numerator) and the divisor (denominator). Place them in the long division format, adding decimal points and necessary zeros if the dividend is smaller than the divisor.

Then, perform the long division process to arrive at the decimal representation of the fraction.

Here’s a tip: use a long division calculator to solve this problem and see each step.

Method 3: Simplification

An alternative approach to converting a fraction to a decimal is by expressing the numerator as a fraction over 100. This method simplifies the process by aligning the fraction with the decimal system, which is based on powers of 10.

To employ this method, multiply the denominator by a factor that yields 100. Determine this factor by dividing 100 by the denominator. Then, multiply both the numerator and denominator by this factor.

Next, shift the decimal point two places to the left for both the numerator and denominator. This will simplify the fraction to a value out of 1. Since any fraction out of 1 is equal to its decimal value, the numerator becomes the final decimal representation.

For example, let's convert the fraction 1/16 to a decimal using this method:

Start by finding the multiple needed to multiply the denominator (16) to reach 100:

100 = 16 × 6.25

The multiple is 6.25.

Now, multiply the numerator (1) by the multiple (6.25):

1 × 6.25 = 6.25

Thus, the fraction 1/16 can also be represented as 6.25/100.

1/16 = 6.25/100

Move the decimal point two places to the left for both the numerator and denominator:

6.25/100 = 0.0625/1

The numerator (0.0625) is the resulting decimal.

Therefore, the decimal representation of 1/16 is 0.0625.
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Method 4: Conversion Chart

An additional approach to converting fractions to decimals is by utilizing a conversion chart. The chart provides the decimal values for common fractions, enabling a quick reference for conversion.

Fraction	Decimal
1/2	0.5
1/3	0.3333
2/3	0.6667
1/4	0.25
3/4	0.75
1/5	0.2
2/5	0.4
3/5	0.6
4/5	0.8
1/6	0.1667
5/6	0.8333
1/7	0.1429
2/7	0.2857
3/7	0.4286
4/7	0.5714
5/7	0.7143
6/7	0.8571
1/8	0.125
3/8	0.375
5/8	0.625
7/8	0.875
1/9	0.1111
2/9	0.2222
4/9	0.4444
5/9	0.5556
7/9	0.7778
8/9	0.8889
1/10	0.1
3/10	0.3
7/10	0.7
9/10	0.9
1/11	0.0909
2/11	0.1818
3/11	0.2727
4/11	0.3636
5/11	0.4545
6/11	0.5455
7/11	0.6364
8/11	0.7273
9/11	0.8182
10/11	0.9091
1/12	0.0833
5/12	0.4167
7/12	0.5833
11/12	0.9167
1/13	0.0769
2/13	0.1538
3/13	0.2308
4/13	0.3077
5/13	0.3846
6/13	0.4615
7/13	0.5385
8/13	0.6154
9/13	0.6923
10/13	0.7692
11/13	0.8462
12/13	0.9231
1/14	0.0714
3/14	0.2143
5/14	0.3571
9/14	0.6429
11/14	0.7857
13/14	0.9286
1/15	0.0667
2/15	0.1333
4/15	0.2667
7/15	0.4667
8/15	0.5333
11/15	0.7333
13/15	0.8667
14/15	0.9333
1/16	0.0625
3/16	0.1875
5/16	0.3125
7/16	0.4375
9/16	0.5625
11/16	0.6875
13/16	0.8125
15/16	0.9375
1/17	0.0588
2/17	0.1176
3/17	0.1765
4/17	0.2353
5/17	0.2941
6/17	0.3529
7/17	0.4118
8/17	0.4706
9/17	0.5294
10/17	0.5882
11/17	0.6471
12/17	0.7059
13/17	0.7647
14/17	0.8235
15/17	0.8824
16/17	0.9412
1/18	0.0556
5/18	0.2778
7/18	0.3889
11/18	0.6111
13/18	0.7222
17/18	0.9444
1/19	0.0526
2/19	0.1053
3/19	0.1579
4/19	0.2105
5/19	0.2632
6/19	0.3158
7/19	0.3684
8/19	0.4211
9/19	0.4737
10/19	0.5263
11/19	0.5789
12/19	0.6316
13/19	0.6842
14/19	0.7368
15/19	0.7895
16/19	0.8421
17/19	0.8947
18/19	0.9474
1/20	0.05
3/20	0.15
7/20	0.35
9/20	0.45
11/20	0.55
13/20	0.65
17/20	0.85
19/20	0.95

See our inch fraction calculator for a comprehensive inch fraction to decimal chart.

Converting Mixed Fractions to Decimals

The aforementioned methods are applicable to both proper and improper fractions but do not directly support mixed fractions. Mixed fractions consist of a whole number combined with a fraction.

To convert mixed fractions to decimals, begin by converting them to improper fractions. Multiply the whole number by the denominator and add the resulting product to the numerator. This creates a new fraction with the sum as the numerator and the original denominator.

Once the mixed fraction is transformed into an improper fraction, any of the previously mentioned methods can be employed to convert it to a decimal.

Frequently Asked Questions

Why do you divide a fraction to make it a decimal?

The division of a fraction represents a conversion to decimal form. Fractions and decimals represent the same quantity but in different formats. Dividing the numerator by the denominator yields the quotient, which is the decimal representation of the fraction.

When do you need to convert fractions to decimals?

Converting fractions to decimals becomes necessary in various situations. Decimals are often more convenient for calculations, comparisons, and measurements. Fields such as communication, sciences, and mathematical operations commonly rely on decimal representations.

Can every fraction be converted to a decimal?

All fractions can be converted to decimals. However, not all fractions yield terminating or finite decimals. Some fractions produce repeating decimals, where a digit or group of digits repeats infinitely, such as 1/3, which is equivalent to 0.3333...