✓ Quick Check 2 — Key fraction facts and the denominator-to-power-of-10 method
Question 1 of 10
Terminating and Recurring Decimals
When you divide to convert a fraction, the decimal either terminates (stops) or recurs (repeats forever).
Type
Meaning
Example
Notation
Terminating
The decimal ends
\(\frac{3}{8} = 0.375\)
Write normally
Recurring
One or more digits repeat forever
\(\frac{1}{3} = 0.333...\)
\(0.\dot{3}\) (dot above)
Terminating decimal: A decimal that ends. Examples: \(\frac{1}{4} = 0.25\) and \(\frac{3}{8} = 0.375\). Other fractions give recurring decimals that repeat forever — like \(\frac{1}{3} = 0.333...\) — and we round these as instructed.
Example 4 — Convert \(\frac{5}{6}\) and state the type
Step 1
\(5 \div 6 = 0.8333...\)
Step 2
The digit 3 repeats forever — this is a recurring decimal
Step 3
Written formally: \(0.8\dot{3}\)
Step 4
Rounded to 2 d.p.: \(\mathbf{0.83}\)
Example 5 — Convert \(\frac{9}{16}\) to a decimal
Step 1
\(9 \div 16 = 0.5625\)
Step 2
The decimal ends after 4 digits — this is a terminating decimal
Step 3
Answer: \(\frac{9}{16} = \mathbf{0.5625}\)
✓ Quick Check 3 — Terminating and Recurring Decimals
Question 1 of 5
Mixed Numbers to Decimals
A mixed number has a whole-number part and a fraction part. Convert the fraction part separately, then add to the whole number.
Mixed number → decimal: keep the whole number, convert the fraction part only
Example 6 — Convert \(3\frac{5}{8}\) to a decimal
Step 1
Whole number part: 3
Step 2
Fraction part: \(\frac{5}{8} = 5 \div 8 = 0.625\)
Step 3
Combine: \(3 + 0.625 = \mathbf{3.625}\)
Example 7 — Convert \(2\frac{1}{3}\) to a decimal (round to 2 d.p.)
Step 1
Whole number: 2
Step 2
\(\frac{1}{3} = 0.333...\)
Step 3
\(2 + 0.333... = 2.333...\)
Step 4
Rounded to 2 d.p.: \(\mathbf{2.33}\)
Example 8 — Compare \(1\frac{3}{4}\) and \(1\frac{4}{5}\) — which is larger?
Step 1
\(1\frac{3}{4} = 1 + 0.75 = 1.75\)
Step 2
\(1\frac{4}{5} = 1 + 0.8 = 1.8\)
Step 3
\(1.8 > 1.75\), so \(1\frac{4}{5}\) is larger
Common mistake: Do not convert the whole number — only convert the fraction part. \(3\frac{1}{4} = 3.25\), NOT \(0.325\).
Convert each fraction to a decimal, type your answer, then click Check All.
#
Question
Answer
Result
1
1/2
2
1/4
3
3/4
4
1/5
5
3/8
6
7/10
7
2/5
8
5/8
9
1/3
10
7/20
⚠ Things to Watch Out For
Dividing denominator by numerator: ¾ = 3 ÷ 4 = 0.75. Always divide the TOP (numerator) by the BOTTOM (denominator). Getting this backwards gives a completely different decimal.
Recurring decimals — not rounding: 1/3 = 0.333... This is recurring. If asked to 2 d.p., write 0.33. State that it is recurring or round as instructed.
Forgetting the zero before the decimal: 3 ÷ 4 = 0.75, not .75. Always write 0.75 with the leading zero.
Mixed numbers: 1¾ = 1 + 0.75 = 1.75. Convert the fraction part only, then add the whole number. Don't convert 7/4 = 1.75 and forget the extra whole number.
Not checking with multiplication: If ¾ = 0.75, check: 0.75 × 4 = 3. ✓ This inverse check confirms your answer.