Decimal to Fraction to Percentage Converter

Convert a decimal to its simplest fraction and equivalent percentage by entering the decimal value; the calculator returns both forms. For example, 0.75 becomes 3/4 and 75%.

Formula

A decimal can be written as a fraction by expressing its digits over a power of 10, then reducing the numerator and denominator by their greatest common divisor. A decimal becomes a percentage by multiplying it by 100 and adding the percent sign.

• Fraction: If a decimal has n digits after the decimal point, write it over 10ⁿ, then simplify. For example, 0.75 = 75/100 = 3/4.
• Percentage: p = 100d, where d is the decimal number (unitless) and p is the percentage value, expressed in percentage points.

The calculator’s fraction output is the decimal value itself, so it is exact when the entered decimal is finite. The percentage output is rounded to two decimal places. A decimal input may be negative; its fraction and percentage retain the same sign.

Worked Example

Using the default input, d = 0.75:

1. Write 0.75 as 75/100 because it has two digits after the decimal point.
2. Divide the numerator and denominator by 25: 75/100 = 3/4.
3. Multiply the decimal by 100: 0.75 × 100 = 75.

The result is 3/4 and 75%. The percentage rounded to two decimal places is 75.00% if displayed with trailing zeroes; the calculator may display it as 75 depending on its number formatting.

How the Conversion Works

A decimal is a way of writing a number using place value. Each position to the right of the decimal point represents a fraction with a denominator that is a power of 10: tenths, hundredths, thousandths, and so on. That makes finite decimals straightforward to turn into fractions.

For example, 0.6 means six tenths, or 6/10. Dividing both terms by 2 gives 3/5. Likewise, 0.125 means 125/1000; dividing both terms by 125 gives 1/8.

Percent means “per hundred.” Multiplying a decimal by 100 changes its scale from a value per one to a value per hundred. Thus, 0.6 is 60%, and 1.25 is 125%. A percentage greater than 100% is valid: it describes an amount greater than the reference whole.

Steps for Converting by Hand

1. Count the decimal places. Use that count to choose a power of 10 for the fraction’s denominator.
2. Remove the decimal point from the numerator. Keep any leading or trailing digits needed to preserve the value. For instance, 0.04 is 4/100, not 4/10.
3. Simplify the fraction. Divide the numerator and denominator by their greatest common divisor until they have no common factor greater than 1.
4. Find the percentage. Multiply the original decimal by 100 and write the percent sign.
5. Check the result. Divide the fraction’s numerator by its denominator; the result should match the original decimal. Divide the percentage by 100 to check it too.

For a negative decimal such as -0.2, the fraction is -1/5 and the percentage is -20%. The sign belongs to the value, not the denominator in the usual presentation.

Examples and When to Use Each Form

• 0.4: 4/10 simplifies to 2/5; the percentage is 40%.
• 0.08: 8/100 simplifies to 2/25; the percentage is 8%.
• 0.125: 125/1000 simplifies to 1/8; the percentage is 12.5%.
• 1.6: 16/10 simplifies to 8/5, or 1 3/5; the percentage is 160%.

Fractions are useful when an exact ratio matters, such as dividing a quantity into equal parts. Percentages are often easier for comparing proportions because they share a denominator of 100. Decimals are convenient for calculations and measurements. These are different notations for the same value, not different amounts.

Repeating Decimals, Rounding, and Common Mistakes

The method of placing a finite decimal over a power of 10 applies directly to decimals that end. A repeating decimal, such as 0.333…, does not have a final decimal place. It can still be represented exactly as a fraction: 0.333… = 1/3. To convert a repeating decimal, use algebra or a suitable fraction-conversion method rather than treating a few displayed digits as exact.

• Do not confuse decimal places with significant figures. In 0.007, there are three decimal places, so it is 7/1000 and 0.7%.
• Do not multiply by 100 when making the fraction. Multiplication by 100 is for the percentage conversion; the fraction comes from place value.
• Keep the percent sign. The number 25 is not the same written value as 25%; 25% equals 0.25.
• Round only when needed. Rounding a percentage for display can make it slightly less exact. Retain more digits when precision is important.

A calculator can express a decimal as a quotient, but it may not automatically reduce the fraction or display it in mixed-number form. For a very long decimal, a rounded input is only an approximation, so its fraction describes the rounded value rather than necessarily the original number.

Frequently Asked Questions

How do I convert a decimal to a fraction?
Write the decimal’s digits over 10, 100, 1,000, or another power of 10 according to the number of decimal places. Then divide the numerator and denominator by their greatest common divisor.

How do I convert a decimal to a percentage?
Multiply the decimal by 100 and add the percent sign. For example, 0.35 × 100 = 35%, while 1.2 × 100 = 120%.

What is 0.75 as a fraction and percentage?
As a fraction, 0.75 = 75/100 = 3/4. As a percentage, it is 75%.

Can a percentage be more than 100%?
Yes. A value such as 1.4 corresponds to 140%, meaning 1.4 times the reference amount, or 40% more than that amount.

How do I turn a repeating decimal into a fraction?
Use an equation to eliminate the repeating digits. For example, let x = 0.333…; then 10x = 3.333…, so 10x − x = 3, giving 9x = 3 and x = 1/3.

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in d | Decimal | - | 0.75 | 0
out f | Fraction value | - | d | 0
out p | Percentage | % | d * 100 | 2