Decimal Calculator

Our free decimal calculator handles two core tasks: decimal arithmetic (add, subtract, multiply, divide) with detailed step-by-step breakdowns, and bidirectional conversion between decimals, fractions, and percentages. It detects repeating decimals like 0.333... and converts them to exact fractions like 1/3.

star 4.8
auto_awesome AI
New
Result
4.25
As Fraction
17/4
As Percent
425%
Mixed Number
4 1/4
format_list_numbered Step-by-Step
    Quick:

    How to Use This Calculator

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    Choose Mode

    Select Arithmetic for +, -, x, / on decimals, or Conversion to switch between decimals, fractions, and percents.

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    Enter Values

    Type your decimal numbers and choose an operation, or enter a value to convert.

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    Calculate

    Press Calculate to see the result with a step-by-step explanation.

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    View Steps

    Review the detailed breakdown to understand each step of the calculation.

    The Formula

    Convert a decimal to a fraction by expressing it over a power of 10, then simplifying with GCD. For repeating decimals, use algebra: let x = 0.333..., then 10x = 3.333..., so 9x = 3, x = 1/3. Multiply by 100 for percent.

    decimal = numerator / denominator; percent = decimal x 100

    lightbulb Variables Explained

    • decimal The decimal value
    • numerator Top of the fraction
    • denominator Bottom of the fraction
    • percent Percentage equivalent

    tips_and_updates Pro Tips

    1

    To convert a decimal to a fraction, count the decimal places and put the number over 10^n, then simplify.

    2

    A repeating decimal like 0.333... equals 1/3. Enter the repeating pattern in conversion mode.

    3

    Percent is simply the decimal multiplied by 100.

    4

    When dividing decimals, move the decimal point to make the divisor a whole number.

    5

    Line up decimal points when adding or subtracting decimals.

    6

    Use this calculator alongside the fraction calculator for cross-verification.

    Decimal Calculator - Arithmetic & Conversion Tool

    Perform decimal arithmetic and convert between decimals, fractions, and percentages instantly. Our free online decimal calculator shows step-by-step solutions for every operation.

    Decimal Arithmetic Operations

    Add, subtract, multiply, and divide decimals with ease. The calculator shows each step including decimal alignment for addition/subtraction, place-value counting for multiplication, and long-division technique for division.

    Decimal to Fraction Conversion

    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.

    Fraction to Decimal Conversion

    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.

    Decimal to Percent and Percent to 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 Decimals

    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.

    Rounding Decimals

    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.

    Frequently Asked Questions

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    Data sourced from trusted institutions

    All formulas verified against official standards.