Explore 15+ fully worked examples showing every step of the conversion process, from simple tenths to complex repeating decimals.
0.5 / 1
5 / 10
5÷5 / 10÷5
1/2
0.25 / 1
25 / 100
25÷25 / 100÷25
1/4
0.75 / 1
75 / 100
75÷25 / 100÷25
3/4
0.1 / 1
1 / 10
Already simple
1/10
0.4 / 1
4 / 10
4÷2 / 10÷2
2/5
0.125 / 1
125 / 1000
125÷125 / 1000÷125
1/8
0.875 / 1
875 / 1000
875÷125 / 1000÷125
7/8
0.025 / 1
25 / 1000
25÷25 / 1000÷25
1/40
1.5 / 1
15 / 10
15÷5 / 10÷5 = 3/2
1 1/2
4.1 / 1
41 / 10
41 and 10 are coprime
4 1/10
3.125 / 1
3125 / 1000
3125÷125 / 1000÷125 = 25/8
3 1/8
x = 0.333...
10x = 3.333...
10x - x = 3.333... - 0.333...
9x = 3
1/3
x = 6.666...
10x = 66.666...
10x - x = 66.666... - 6.666...
9x = 60
x = 60/9 = 20/3
6 2/3
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Converting decimals to fractions manually boils down to understanding place value. The first decimal place represents tenths, the second represents hundredths, the third thousandths, and so on. By putting the decimal over the corresponding power of ten, you create an unsimplified fraction.
Common questions about decimal to fraction examples
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The most useful ones are halves (0.5 = 1/2), quarters (0.25 = 1/4, 0.75 = 3/4), and thirds (0.333... = 1/3, 0.666... = 2/3).
Start with simple terminating decimals (like 0.2 or 0.4) and practice writing them over 10 or 100, then simplifying. Check your answers with a calculator.
Memorize the common conversions first. Then, understand the place value method for terminating decimals. Finally, learn the algebraic method for repeating decimals.
Different situations require different formats. Fractions are great for exact math and splitting items, while decimals are easier for comparing sizes and using calculators.
Yes, knowing that 10^1=10, 10^2=100, 10^3=1000 is crucial for quickly converting terminating decimals by placing them over the correct denominator.
0.375 as a fraction is 3/8. To convert: write 0.375 as 375/1000, then find the GCD of 375 and 1000 (which is 125). Divide both by 125 to get 3/8. This is a common measurement fraction used in cooking and engineering.
1.75 as a fraction is 7/4, or as a mixed number, 1 3/4 (one and three-quarters). Write 1.75 as 175/100, find the GCD (25), and divide both to get 7/4. This value frequently appears on tape measures and in recipes.
0.2 as a fraction is 1/5. Since 0.2 has one decimal place, write it as 2/10. The GCD of 2 and 10 is 2, so divide both to get 1/5. This is equivalent to 20% and is one of the most commonly used decimal-fraction pairs.
0.5 as a fraction is 1/2 (one half). Write 0.5 as 5/10 and simplify by dividing both by the GCD of 5. This is the most fundamental decimal-to-fraction conversion — half is used in everyday contexts from cooking to measurements to percentages (50%).
0.75 as a fraction is 3/4 (three-quarters). Write 0.75 as 75/100, find the GCD (25), and divide both to get 3/4. Three-quarters (75%) is one of the most frequently encountered fractions in daily life, from recipes to time (45 minutes is 3/4 of an hour).
0.625 as a fraction is 5/8. To convert: write 0.625 as 625/1000. The GCD of 625 and 1000 is 125. Divide both by 125 to get 5/8. This fraction commonly appears in measurement contexts, particularly in inches.