Decimal to Fraction Calculator

Decimal to fraction calculator at a glance#

How do you convert a decimal to a fraction?#

To convert a decimal to a fraction, write the digits after the decimal point over 10, 100, or 1,000, depending on the number of digits, then simplify. For instance, if you have 0.625 with three decimal places, it's written as 625/1000. By dividing both the top and bottom by 125, you get 5/8. When you input a decimal into the calculator above, it returns the fraction in its simplest form and as a mixed number if the decimal exceeds 1.

What is 10.625 as a fraction?#

When represented as a mixed number, 10.625 is 10 5/8, or as an improper fraction, it's 85/8. The whole number remains 10, while the 0.625 is converted to 5/8.

How do you turn a repeating decimal into a fraction?#

To convert a repeating decimal into a fraction using the calculator, place the repeating digits inside parentheses: enter 2.(6) for 2.666..., and you'll get the result 2 2/3. If you're doing it manually, multiply by 10 to shift one repeating block, then subtract the original number so the repeating section cancels out and solve from there. The steps are further down this page.

How decimal place value becomes a fraction#

Every digit after a decimal point has a specific place value. The first digit represents tenths, the second represents hundredths, and the third represents thousandths, as explained by the OpenStax Prealgebra 2e textbook. A decimal is a fraction in disguise: 0.625 reads as six hundred twenty-five thousandths, which is 625/1000.

This page uses 10.625 as its main example. It consists of a whole number part, 10, and a decimal part, 0.625, with its last digit located in the thousandths place.

How to convert a decimal to a fraction#

OpenStax provides four steps that are applicable to any decimal that terminates.

1. Begin by examining the whole number part. If it's 0, the resulting fraction is proper. If it's not, the result is a mixed number. For 10.625, write the 10 first.
2. Determine the place value of the last digit. The 5 in 10.625 is in the thousandths place.
3. Place the digits following the decimal point over that place value: 625/1000.
4. Simplify. The greatest common factor of 625 and 1000 is 125, so 625/1000 simplifies to 5/8, and 10.625 becomes 10 5/8.

The GCF calculator is useful for finding the greatest common factor for step 4, and the simplifying fractions calculator reduces a fraction in a single step. Alternatively, you can simplify gradually. 625/1000 divided by 5 results in 125/200, then 25/40, and finally 5/8. Using the GCF achieves this in one division.

Mixed numbers and improper fractions#

The calculator displays results as mixed numbers. However, certain homework problems and recipes require improper fractions. To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator: 10 × 8 + 5 = 85. Therefore, 10 5/8 converts to 85/8. Similarly, 2.25 as a mixed number is 2 1/4, which is 9/4 when written as an improper fraction. The mixed number calculator handles conversions in both directions.

Negative decimals#

Handle negative decimals by working with them as positive numbers first, then placing the minus sign in front. For example, −1.25 is −1 1/4, or −5/4, and −0.4 becomes −4/10, which simplifies to −2/5. The calculator accepts negative inputs directly, so you can type negative decimals as they are.

Repeating decimals#

A repeating decimal continues indefinitely, making it impossible to express it accurately over 10, 100, or 1,000. The solution involves a small algebraic trick, the same method detailed in OpenStax Contemporary Mathematics exercises on repeating decimals.

Consider 2.666..., where 6 repeats.

• Define the number as x, so x = 2.666...
• With one digit repeating, multiply by 10: 10x = 26.666...
• Subtract the first equation from the second. The repeating parts cancel out: 9x = 24.
• Solve: x = 24/9, which simplifies to 8/3, or 2 2/3.

If two digits repeat, multiply by 100 and subtract to find 99x, continuing similarly for longer sequences. If a single digit repeats, placing it over 9 offers a shortcut: 0.777... becomes 7/9, making 1.777... equal to 1 7/9.

The calculator can perform these operations if you indicate the repeating section with parentheses. For example, type 2.(6) to get 2 2/3, 1.(7) to obtain 1 7/9 or 0.1(6) for 1/6. If you enter 2.66666 instead, the calculator interprets it as a finite decimal and returns 2 33333/50000, which is correct for the exact input but may not match your intended number.

Decimal inches to fractions#

In the United States, tape measures and rulers typically show measurements in fractions of an inch, often divided down to sixteenths. However, when dealing with plans, calipers, and spreadsheets, measurements often appear as decimals. Many of these decimals are exact eighths like 10.625, 11.375, or 16.875, making them easy to convert into tidy fractions such as 10 5/8, 11 3/8, and 16 7/8.

When a decimal isn't an exact sixteenth, rounding to the nearest mark is necessary, something this calculator doesn't do. It gives you the exact fraction, meaning 0.3 inch becomes 3/10. To find the nearest sixteenth, multiply by 16 and round: 0.3 × 16 results in 4.8, which rounds to 5, so the nearest mark is 5/16 inch (0.3125 inch, or approximately 0.79 cm).

Common conversions#

The first table provides a list of every sixteenth of an inch alongside its decimal equivalent and length in centimeters. The second table translates commonly referenced decimals into their simplest-form fractions.

To reverse the process from a fraction back to a decimal, use the fraction to decimal calculator.

Sources#

• OpenStax, Prealgebra 2e, section 5.1: Decimals
• OpenStax, Contemporary Mathematics, section 3.4: Rational Numbers

Frequently asked questions#

What is 2.25 as an improper fraction?#

The number 2.25 is expressed as 2 1/4 when represented as a mixed number. By multiplying 2 by 4 and adding 1, you get 9, resulting in the improper fraction 9/4.

What is −0.4 as a fraction?#

The value −0.4 is equivalent to −4/10, and dividing both the numerator and denominator by 2 simplifies it to −2/5.

What is 0.01625 as a fraction?#

With five decimal places, 0.01625 translates to 1625/100000. The greatest common factor (GCF) of 1625 and 100000 is 125, reducing it to 13/800.

How do you write 45.3 as a fraction?#

The number 45.3 is represented as 45 3/10 because 3 is in the tenths place. As an improper fraction, it's 453/10. Since 3 and 10 have no common factor, it cannot be simplified further.

What is 1.28571 as a fraction?#

When typed precisely, 1.28571 becomes 1 28571/100000. If it represents a rounded version of 1.285714285714..., equating to 9/7, type 1.(285714) to have the calculator return 1 2/7.

Can every decimal be written as a fraction?#

Decimals that are terminating or repeating can be expressed as fractions. Numbers that neither end nor repeat, such as pi, cannot be written as a fraction of two whole numbers. According to OpenStax Contemporary Mathematics, such numbers are not rational numbers.