Example 4 — Convert 0.35 to a fraction in simplest form
Step 1
2 decimal places → \(\frac{35}{100}\)
Step 2
Largest common factor of 35 and 100: factors of 35 are 1, 5, 7, 35. Common factors = 5
Step 3
\(\frac{35 \div 5}{100 \div 5} = \frac{7}{20}\)
Step 4
Answer: \(\mathbf{\frac{7}{20}}\)
Example 5 — Convert 0.48 to a fraction in simplest form
Step 1
\(\frac{48}{100}\)
Step 2
Largest common factor of 48 and 100: both divisible by 4. \(\frac{48 \div 4}{100 \div 4} = \frac{12}{25}\)
Step 3
Check: largest common factor of 12 and 25 is 1 — fully simplified
Step 4
Answer: \(\mathbf{\frac{12}{25}}\)
Example 6 — Convert 0.75 to a fraction
Step 1
\(\frac{75}{100}\)
Step 2
Largest common factor = 25: \(\frac{75 \div 25}{100 \div 25} = \frac{3}{4}\)
Step 3
Answer: \(\mathbf{\frac{3}{4}}\) — this matches the known fact!
How to find the largest common factor quickly: List the factors of both numbers, pick the largest one they share. Alternatively, keep dividing both by common factors until you can't.
Common mistake: Writing 0.35 as \(\frac{35}{10}\) instead of \(\frac{35}{100}\). Count the decimal places carefully — 0.35 has 2, so the denominator is 100.
✓ Quick Check 2 — Hundredths
Question 1 of 10
Decimals with 3 Decimal Places → Thousandths
Three decimal places → write over 1000, then simplify.
Largest common factor of 125 and 1000: both divisible by 125. \(\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\)
Step 3
Answer: \(\mathbf{\frac{1}{8}}\)
Example 8 — Convert 0.625 to a fraction
Step 1
\(\frac{625}{1000}\)
Step 2
Divide by 25: \(\frac{25}{40}\). Divide by 5: \(\frac{5}{8}\)
Step 3
Answer: \(\mathbf{\frac{5}{8}}\)
✓ Quick Check 2b — Thousandths
Question 1 of 10
Recurring Decimals — A Special Case
Some decimals repeat forever. These cannot be converted using the standard place value method — they need an algebraic approach or fraction recognition.
Important: The standard method (write digits over 10/100/1000) only works for terminating decimals. Recurring decimals like 0.333... cannot be written as 3/10 — the correct fraction is 1/3, found by algebraic method or recognition.
Example 8 — The algebraic method: convert 0.454545... (0.\(\overline{45}\)) to a fraction
Step 1
Let \(x = 0.454545...\)
Step 2
The repeating block is 2 digits long ("45"), so multiply both sides by 100 to shift the decimal point past one full repeat: \(100x = 45.454545...\)
Step 3
Subtract the original equation from this one — the recurring parts cancel exactly: \(100x - x = 45.454545... - 0.454545...\) → \(99x = 45\)
💡 How much to multiply by: multiply by 10 if 1 digit repeats, by 100 if 2 digits repeat, by 1000 if 3 digits repeat — enough to shift the decimal point exactly one full repeating block to the right. This works for any recurring decimal, not just the ones worth memorising in the table above.
Decimals Greater Than 1 → Mixed Numbers
If the decimal is greater than 1, the whole number part becomes the integer part of a mixed number.
Example 9 — Convert 3.4 to a mixed number fraction
Example 10 — Convert 2.75 to a mixed number fraction
Step 1
Whole number: 2
Step 2
0.75 = \(\frac{75}{100} = \frac{3}{4}\)
Step 3
Answer: \(\mathbf{2\frac{3}{4}}\)
Tip: You can also convert to an improper fraction: \(2\frac{3}{4} = \frac{11}{4}\). But a mixed number is usually the required form unless asked otherwise.
Work out each answer, then type it in and click Check to see if you're right. Write fractions as a/b (e.g. 1/2).
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Question
Your answer
Result
1
Convert 0.5 to a fraction in its simplest form.
2
Convert 0.25 to a fraction in its simplest form.
3
Convert 0.75 to a fraction in its simplest form.
4
Convert 0.1 to a fraction in its simplest form.
5
Convert 0.4 to a fraction in its simplest form.
6
Convert 0.125 to a fraction in its simplest form.
7
Convert 0.2 to a fraction in its simplest form.
⚠ Things to Watch Out For
Wrong denominator for the decimal places: 0.3 = 3/10 (one decimal place = tenths = /10). 0.03 = 3/100. 0.003 = 3/1000. The number of decimal places tells you the denominator.
Not simplifying: 0.75 = 75/100 = 3/4. Always simplify the fraction by dividing by the largest common factor.
Recurring decimals: 0.333... = 1/3. These cannot be expressed as exact fractions using the standard method — you need the algebraic method or must recognise them.
Mixed decimals: 1.25 = 1 + 0.25 = 1 + 1/4 = 1¼. Don't write 125/100 and then forget to express as a mixed number if the decimal is greater than 1.
Confusing 0.5 and 0.05: 0.5 = 5/10 = ½. 0.05 = 5/100 = 1/20. These are very different fractions — count decimal places carefully.