Fractions, Decimals,
and Percents
Master the art of converting between fractions, decimals, and percents: three representations of the same value that unlock every quantitative problem.
SSAT Upper Level: Quantitative
Three Ways to Say the Same Thing
A single quantity can be written as a fraction, a decimal, or a percent. They are interchangeable: learning to move between them quickly is one of the most important skills on the SSAT.
Fraction
A ratio of two integers: \(\frac{a}{b}\) where \(b \neq 0\)
Decimal
A number in base-ten place value: \(0.75\)
Percent
"Per hundred": \(75\%\) means \(75\) out of \(100\)
One Value, Three Forms
Why Conversions Matter
On the SSAT, problems rarely hand you the form you need. A question may give a percent but require you to multiply, which is easier with a decimal or fraction. Quick, accurate conversion saves time and prevents errors.
Comparing
Convert to the same form to decide which value is larger.
Computing
Fractions simplify multiplication; decimals simplify addition.
Interpreting
Percent is the natural language of discounts, taxes, and data.
The Conversion Triangle
Fraction ↔ Decimal
1
Fraction → Decimal: Divide the numerator by the denominator. \(\frac{3}{8} = 3 \div 8 = 0.375\)
2
Decimal → Fraction: Read the decimal's place value, write it over that power of ten, then simplify. \(0.6 = \frac{6}{10} = \frac{3}{5}\)
Decimal ↔ Percent
1
Decimal → Percent: Multiply by \(100\) (move decimal point two places right). \(0.45 \times 100 = 45\%\)
2
Percent → Decimal: Divide by \(100\) (move decimal point two places left). \(12.5\% \div 100 = 0.125\)
Fraction ↔ Percent
1
Fraction → Percent: Divide, then multiply by \(100\). \(\frac{2}{5} = 0.4 \times 100 = 40\%\)
2
Percent → Fraction: Write the percent over \(100\) and simplify. \(60\% = \frac{60}{100} = \frac{3}{5}\)
3
Shortcut: If the denominator divides evenly into \(100\), scale directly. \(\frac{7}{20} = \frac{35}{100} = 35\%\)
Terminating vs. Repeating Decimals
Terminating
The decimal ends: \(\frac{1}{4} = 0.25\). Happens when the denominator (in lowest terms) has only factors of \(2\) and/or \(5\).
Repeating
The decimal cycles forever: \(\frac{1}{6} = 0.1\overline{6}\). Happens when the denominator has factors other than \(2\) or \(5\).
Step-by-Step Conversion Checklist
1
Identify the starting form: Is it a fraction, decimal, or percent?
2
Choose the target form: What does the problem ask for, or what form makes the math easier?
3
Apply the right operation: Use divide, multiply by \(100\), or write over \(100\) as needed.
4
Simplify: Reduce fractions to lowest terms. Round decimals only if the problem says to.
5
Check: Verify by converting back. Does \(\frac{3}{5} \to 0.6 \to 60\%\) round-trip?
Example 1: Convert \(\frac{7}{8}\)
Task: Express \(\frac{7}{8}\) as a decimal and as a percent.
Example 2: Convert \(0.4\%\)
Task: Express \(0.4\%\) as a decimal and as a fraction.
1
Percent → Decimal: \(0.4\% \div 100 = 0.004\)
2
Decimal → Fraction: \(0.004 = \frac{4}{1000}\)
3
Simplify: \(\frac{4}{1000} = \frac{1}{250}\)
Example 3: Convert \(2\frac{1}{3}\)
Task: Express the mixed number \(2\frac{1}{3}\) as a decimal and as a percent.
1
Mixed → Improper: \(2\frac{1}{3} = \frac{7}{3}\)
2
Divide: \(7 \div 3 = 2.333\ldots = 2.\overline{3}\)
3
Multiply by 100: \(2.\overline{3} \times 100 = 233.\overline{3}\%\)
Benchmark Values to Memorise
| Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{1}{2}\) | \(0.5\) | \(50\%\) |
| \(\frac{1}{3}\) | \(0.\overline{3}\) | \(33.\overline{3}\%\) |
| \(\frac{1}{4}\) | \(0.25\) | \(25\%\) |
| \(\frac{1}{5}\) | \(0.2\) | \(20\%\) |
| \(\frac{1}{8}\) | \(0.125\) | \(12.5\%\) |
| \(\frac{2}{3}\) | \(0.\overline{6}\) | \(66.\overline{6}\%\) |
| \(\frac{3}{4}\) | \(0.75\) | \(75\%\) |
Common Mistakes to Avoid
✕ Moving the Decimal Wrong Way
Going from percent to decimal means dividing by \(100\) (left two places), not multiplying. \(5\% = 0.05\), not \(500\).
✕ Forgetting to Simplify
Writing \(\frac{25}{100}\) when the answer should be \(\frac{1}{4}\). Always reduce to lowest terms.
✕ Confusing \(0.5\%\) and \(50\%\)
A percent with a decimal in it (like \(0.5\%\)) is tiny: \(0.005\). It is not the same as \(50\%\).
Question 1 of 5
What is \(\frac{5}{8}\) expressed as a percent?
\(\frac{5}{8} = 5 \div 8 = 0.625\), then \(0.625 \times 100 = 62.5\%\).
Question 2 of 5
Which fraction is equivalent to \(0.125\)?
\(0.125 = \frac{125}{1000} = \frac{1}{8}\). You can also recall that \(\frac{1}{8} = 0.125\) from the benchmark table.
Question 3 of 5
Express \(0.3\%\) as a decimal.
To convert a percent to a decimal, divide by \(100\): \(0.3 \div 100 = 0.003\). Don't be tricked: \(0.3\%\) is much smaller than \(3\%\) or \(30\%\).
Question 4 of 5
Which of the following is the largest value?
Convert all to decimals: \(\frac{7}{9} \approx 0.778\), \(0.72\), \(70\% = 0.70\), \(\frac{3}{4} = 0.75\). The largest is \(\frac{7}{9} \approx 0.778\).
Question 5 of 5
A store marks a shirt as \(\frac{2}{5}\) off the original price. What percent discount is this?
\(\frac{2}{5} = 2 \div 5 = 0.4\), and \(0.4 \times 100 = 40\%\). The discount is \(40\%\).