Decimal Calculator

Add, subtract, multiply, and divide decimals with ease.

The calculator shows each step, including:

• decimal alignment for addition/subtraction
• place-value counting for multiplication
• long-division technique for division

Convert any decimal to its simplest fraction form.

The tool expresses the decimal over a power of 10, then reduces using the GCD.

Repeating decimals like 0.333... are detected and converted to exact fractions like 1/3.

Enter any fraction and get its decimal equivalent instantly.

The calculator performs the division and identifies whether the result is a terminating or repeating decimal.

Multiply by 100 to go from decimal to percent, or divide by 100 for the reverse.

The calculator handles both directions with clear step-by-step explanations.

Repeating (recurring) decimals have a digit or block that repeats infinitely.

This calculator uses the algebraic method to convert them to exact fractions. For example, 0.142857142857... = 1/7.

Round results to any number of decimal places.

The calculator shows the rounding rule applied and the final value, useful for financial and scientific calculations.

A decimal number is a value written in the base-10 positional system, where each place is worth ten times the place to its right and digits after the decimal point represent tenths, hundredths, thousandths, and so on.

According to Encyclopaedia Britannica, this Hindu-Arabic decimal notation lets any real number be expressed compactly using ten symbols (0 through 9). The decimal point separates the whole-number part from the fractional part, so 12.34 means 12 + 3/10 + 4/100.

Wolfram MathWorld notes that every rational number has either a terminating or an eventually periodic (repeating) decimal expansion, which is why our calculator can convert cleanly between decimals and exact fractions.

To convert a terminating decimal to a fraction, write the digits after the decimal point over the matching power of 10, then simplify by dividing by the greatest common divisor (GCD).

For example, 0.375 becomes 375/1000; since GCD(375, 1000) = 125, it reduces to 3/8. Similarly, 0.6 = 6/10 = 3/5 and 0.05 = 5/100 = 1/20. Khan Academy teaches this count-the-places method as the standard approach.

For repeating decimals, an algebraic method is used instead: setting x equal to the decimal, multiplying by a power of 10, and subtracting to eliminate the repeat, as shown for 0.333... = 1/3.

A fraction in lowest terms produces a terminating decimal if and only if its denominator has no prime factors other than 2 and 5; otherwise the decimal repeats forever.

For example, 1/8 = 0.125 terminates because 8 = 2 x 2 x 2, and 1/20 = 0.05 terminates because 20 = 2 x 2 x 5. By contrast, 1/3 = 0.333... and 1/7 = 0.142857142857... repeat, since 3 and 7 introduce primes outside {2, 5}.

Wolfram MathWorld describes the length of the repeating block as the period of the decimal. Understanding this rule lets you predict a fraction's decimal behavior before dividing.

Decimals appear anywhere quantities fall between whole numbers, especially in money, measurement, and science.

Prices such as $4.99, interest rates like 3.75%, and metric measurements such as 2.54 centimeters per inch all rely on decimal arithmetic. Engineers and scientists use decimals to record precise readings, and the NIST Digital Library of Mathematical Functions (DLMF) expresses many constants, such as pi = 3.14159..., as non-terminating decimals.

Converting between decimals, fractions, and percentages is essential in cooking, finance, statistics, and construction, where a ratio calculator often complements this work when you need to scale proportions up or down. This calculator supports all of these tasks, letting you switch representations and round to the precision a given context requires.

The most frequent errors involve misplacing the decimal point.

• When adding or subtracting, always line up the decimal points; writing 1.5 + 0.75 without alignment can produce a wrong sum instead of the correct 2.25.
• When multiplying, count the total decimal places in both factors: 0.2 x 0.3 = 0.06, not 0.6.
• In division, remember to shift the decimal in both divisor and dividend equally, so 1.44 / 1.2 = 1.2.
• Another common slip is rounding too early, which compounds error; Khan Academy recommends rounding only the final answer.
• Finally, confusing 0.333... (exactly 1/3) with the truncated 0.333 (which is 333/1000) leads to small inaccuracies.