Converting Decimals
& Percents
Master the skill of moving between decimals and percents so you can describe quantities, compare values, and solve real-world problems with confidence.
Pre-Algebra
What Are Decimals and Percents?
Decimal
A number expressed using a decimal point to represent parts of a whole: \(0.75\) means 75 hundredths.
Percent
A number that describes parts per hundred: \(75\%\) means 75 out of 100.
Seeing the Connection
Why Converting Matters
Decimals and percents appear everywhere: store discounts, test scores, statistics, and science measurements. Being able to convert quickly lets you:
Compare
Is \(0.6\) or \(55\%\) larger? Converting puts both in the same form so you can compare easily.
Calculate
Finding \(20\%\) of a price requires converting to \(0.20\) first, then multiplying.
Communicate
Saying "\(85\%\) of students passed" is often clearer than "\(0.85\) of students passed."
Decimal → Percent
Percent → Decimal
Multiplying vs Dividing by \(100\)
| Decimal → Percent | Percent → Decimal | |
|---|---|---|
| Operation | \(\times 100\) | \(\div 100\) |
| Decimal point moves | Two places right → | ← Two places left |
| Symbol action | Add \(\%\) | Remove \(\%\) |
| Example | \(0.08 \to 8\%\) | \(125\% \to 1.25\) |
Step-by-Step Method
1
Identify the direction. Are you going from decimal to percent, or percent to decimal?
2
Move the decimal point two places. Right for decimal → percent. Left for percent → decimal.
3
Add or drop the \(\%\) symbol. Add it when writing a percent. Drop it when writing a decimal.
4
Check with a quick estimate. Does the answer make sense? A decimal less than \(1\) should give a percent less than \(100\%\).
Example 1: Convert \(0.35\) to a Percent
Example 2: Convert \(6\%\) to a Decimal
Example 3: Percents Greater Than \(100\%\)
\(250\% \to\) Decimal
\(250 \div 100 = \) \(2.50\)
A percent above \(100\%\) gives a decimal greater than \(1\).
A percent above \(100\%\) gives a decimal greater than \(1\).
\(1.5 \to\) Percent
\(1.5 \times 100 = \) \(150\%\)
A decimal greater than \(1\) gives a percent above \(100\%\).
A decimal greater than \(1\) gives a percent above \(100\%\).
Example 4: Tiny Decimals
Common Mistakes to Avoid
✕ Wrong Direction
Moving the decimal left when going to percent (instead of right). Example: writing \(0.4 = 0.004\%\) instead of \(40\%\).
✕ Forgetting Zeros
Writing \(6\% = 0.6\) instead of \(0.06\). When there aren't enough digits, you must add placeholder zeros.
✕ Dropping the \(\%\)
Converting \(0.75\) to "75" without the \(\%\) symbol. Without the symbol, \(75\) and \(75\%\) mean very different things.
Quick Reference Table
| Decimal | Percent | Meaning |
|---|---|---|
| \(0.01\) | \(1\%\) | 1 out of 100 |
| \(0.1\) | \(10\%\) | 10 out of 100 |
| \(0.25\) | \(25\%\) | One quarter |
| \(0.5\) | \(50\%\) | One half |
| \(0.75\) | \(75\%\) | Three quarters |
| \(1.0\) | \(100\%\) | The whole |
| \(2.0\) | \(200\%\) | Two wholes |
Using It in the Real World
A store offers a \(30\%\) discount on a \(\$50\) jacket. To calculate the savings, convert the percent to a decimal first:
1
Convert: \(30\% \div 100 = \) \(0.30\)
2
Multiply: \(\$50 \times 0.30 = \) \(\$15\) savings
3
Subtract: \(\$50 - \$15 = \) \(\$35\) final price
Question 1 of 5
What is \(0.62\) written as a percent?
To convert a decimal to a percent, multiply by \(100\): \(0.62 \times 100 = 62\). So \(0.62 = 62\%\).
Question 2 of 5
What is \(5\%\) written as a decimal?
Divide by \(100\): \(5 \div 100 = 0.05\). Move the decimal two places left: \(5. \to 0.5 \to 0.05\). A common error is stopping at \(0.5\), which would be \(50\%\).
Question 3 of 5
A student scored \(0.88\) on a test. What percent did they earn?
Multiply by \(100\): \(0.88 \times 100 = 88\). The student earned \(88\%\). Notice the decimal moved two places to the right.
Question 4 of 5
Which decimal is equal to \(150\%\)?
Divide by \(100\): \(150 \div 100 = 1.5\). Since \(150\%\) is greater than \(100\%\), the decimal must be greater than \(1\).
Question 5 of 5
A recipe calls for \(0.375\) of a cup of sugar. What is this as a percent?
Multiply by \(100\): \(0.375 \times 100 = 37.5\). So \(0.375 = \) \(37.5\%\). Percents can include decimals too.