Terminating Decimal to Fraction Calculator
Convert terminating decimals (like 0.25, 0.375, or 0.8) to fractions in simplest form. Understand the steps and the math behind it.
Simplest Form
Decimal Fraction
Simplest Fraction
Step-by-Step Solution
Visual Representation
What is a Terminating Decimal?
A terminating decimal is a decimal that has a finite number of digits (e.g., 0.25, 0.5, 0.875). This is in contrast to a repeating decimal, which continues indefinitely with a recurring pattern (e.g., 0.333...).
Converting Terminating Decimals
How to convert a terminating decimal to a fraction step-by-step:
- Count the number of decimal places in your terminating decimal (let’s call this n).
- Write the digits (without the decimal point) as the numerator.
- Write 10n (e.g. 10, 100, 1000) as the denominator.
- Find the greatest common divisor (GCD) of the numerator and denominator.
- Simplify the fraction by dividing both numerator and denominator by the GCD.
Example: 0.375
Example: Convert 0.375 to a fraction 1) Identify digits after decimal: 3 digits -> denominator is 10^3 = 1000 2) Form fraction: 375 / 1000 3) Find GCD(375, 1000) = 125 4) Divide numerator and denominator by 125: (375÷125) / (1000÷125) = 3 / 8 Result: 0.375 = 3/8
Decimal to Fraction
General decimal to fraction conversion.
Repeating Decimals
Convert repeating decimals to fractions.
Mixed Decimals
Convert mixed numbers and decimals.
Frequently Asked Questions
Common questions about terminating decimals
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01 What is the difference between terminating and repeating decimals?
A terminating decimal comes to a complete stop after a certain number of decimal places (like 0.75). A repeating decimal goes on forever with a repeating pattern (like 0.333...).
02 What is the place value method?
The place value method involves counting the number of digits after the decimal point and placing the number over 10 raised to that power (10, 100, 1000, etc.).
03 Why do we use powers of 10 in the denominator?
Because our number system is base-10. Each place value after the decimal point represents a fraction with a denominator of a power of 10 (tenths, hundredths, thousandths).
04 How do you simplify the fraction?
Find the Greatest Common Divisor (GCD) of the numerator and the denominator, then divide both numbers by it to get the fraction in its simplest form.
05 Can all terminating decimals be written as fractions?
Yes, all terminating decimals are rational numbers and can therefore be written exactly as a fraction of two integers.