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Math & Conversions Decimal to Fraction Converter Decimal to Fraction Converter Convert any terminating decimal (e.g., 0.125, 3.4) into its simplest fractional form. Enter your decimal number below to get the results as a **simplified fraction**, an **improper fraction**, and a **mixed number**. Enter Decimal Number Convert to Fraction Conversion Results Simplified Fraction (Lowest Terms) Improper Fraction Mixed Number Step-by-Step Simplification The Three Steps to Converting Decimals to Fractions The key principle is that the place value of the last digit in the decimal determines the denominator (a power of ten) of the initial fraction. Determine Initial Fraction ($A/B$): Identify the place value of the last digit in the decimal. If the decimal is 0.7 (tenths place), the denominator is 10. Fraction: $\frac{7}{10}$ If the decimal is 0.75 (hundredths place), the denominator is 100. Fraction: $\frac{75}{100}$ If the decimal is 0.125 (thousandths place), the denominator is 1000. Fraction: $\frac{125}{1000}$ The whole number part is temporarily ignored or used to convert to an improper fraction later. Find the Greatest Common Divisor (GCD): The GCD is the largest number that divides evenly into both the numerator and the denominator. This is the crucial step for simplification. Simplify: Divide both the numerator and the denominator by the GCD to get the simplified fraction (lowest terms). Handling Decimals with a Whole Number For a number like $4.3$, treat the whole number (4) and the decimal part (0.3) separately. $0.3 = \frac{3}{10}$. The mixed number is $4\frac{3}{10}$. To find the improper fraction, convert the mixed number: $4\frac{3}{10} = \frac{(4 \times 10) + 3}{10} = \frac{43}{10}$. Converting Repeating Decimals This calculator primarily targets terminating decimals. Converting repeating decimals (like $0.\overline{6}$) requires a different algebraic technique: Let $x$ equal the repeating decimal (e.g., $x = 0.666...$). Multiply $x$ by $10^n$, where $n$ is the number of repeating digits (e.g., $10x = 6.666...$). Subtract the original equation from the new one ($10x - x = 6.666... - 0.666...$). Solve for $x$: $9x = 6$, so $x = \frac{6}{9}$, which simplifies to $\frac{2}{3}$. Frequently Asked Questions (FAQ) What is the fastest way to convert a decimal to a fraction? The fastest method is to identify the place value of the last digit. If $0.125$ ends in the thousandths place, the fraction is initially $125/1000$. If $0.8$ ends in the tenths place, the fraction is $8/10$. Then, simplify. How do you convert a decimal like 0.333... (repeating) to a fraction? For a simple repeating decimal like $0.\overline{3}$, the fraction is the repeating digit over 9. So $0.\overline{3} = 3/9$, which simplifies to $1/3$. For $0.\overline{12}$, the fraction is $12/99$. The rule is to use a denominator of 9s (one 9 for each repeating digit). How do I convert a decimal that includes a whole number (e.g., 5.4) to a fraction? For 5.4, the whole number (5) becomes the integer part of the mixed number. The decimal part (0.4) converts to a fraction ($4/10$), which simplifies to $2/5$. The result is $5 \frac{2}{5}$. What is the Greatest Common Divisor (GCD) in fraction conversion? The GCD is the largest number that divides exactly into both the numerator and the denominator of the fraction. Finding the GCD is necessary to ensure the fraction is fully simplified (in its lowest terms). Decimal Place Values 0.1 = Tenths $$\frac{1}{10}$$ 0.01 = Hundredths $$\frac{1}{100}$$ 0.001 = Thousandths $$\frac{1}{1000}$$ Related Math Tools Fraction Calculator Decimal Calculator Mixed Number Converter Percentage Calculator GCD/GCF Calculator Basic Arithmetic
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