How to convert between fractions, decimals and percents
TEAS 7 outline: Convert between non-negative fractions, decimals and percentages
Also covers HESI A2 Math (Fractions ↔ decimals, Percentages)
- Fraction to decimal: divide the top by the bottom (3/5 = 0.6).
- Decimal to percent: move the point two places right and add %.
- Percent to decimal: drop the % and move the point two places left.
- Percent to fraction: put the number over 100, then simplify (40% = 2/5).
- A tiny percent is a tiny decimal: 0.6% = 0.006.
Key facts
- Fraction to decimal: divide the numerator (top) by the denominator (bottom), so 3/5 = 3 ÷ 5 = 0.6.
- Decimal to percent: multiply by 100, which moves the decimal point two places to the right (0.6 = 60%).
- Percent to decimal: divide by 100, which moves the decimal point two places to the left (12.5% = 0.125).
Show all 7 key factsShow fewer
- Percent to fraction: write the number over 100, then simplify (40% = 40/100 = 2/5).
- Decimal to fraction: the last digit's place value is the denominator (0.65 is 65 hundredths = 65/100 = 13/20), then simplify.
- A number bigger than 1 is more than 100% (1 3/4 = 1.75 = 175%), and a percent below 1% is a decimal below 0.01 (0.6% = 0.006).
- Some fractions repeat forever as decimals (2/3 = 0.666...), so round only at the very end and only as the question tells you.
Quick check1 question · 2 more at the end
A kitchen scale shows that a portion of cheese weighs 0.45 pound. Which fraction, in simplest form, is equal to 0.45?
Correct answer: C.
The last digit of 0.45 is in the hundredths place, so 0.45 = 45/100. Simplify by dividing the top and bottom by the same number, 5: 45 ÷ 5 = 9 and 100 ÷ 5 = 20, giving 9/20. Check: 9 ÷ 20 = 0.45.
A This divides the top by 5 but the bottom by 4; 9/25 = 0.36, not 0.45.
B This uses thousandths (45/1,000) instead of hundredths; 9/200 = 0.045.
C Correct: 0.45 = 45/100, and dividing top and bottom by 5 gives 9/20.
D This uses tenths (45/10) instead of hundredths; 9/2 = 4.5, which is ten times too big.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: To turn a fraction into a decimal, divide the top number by the bottom number. To turn a decimal into a percent, move the decimal point two places right and add %. To go back, move it two places left. To turn a percent into a fraction, write it over 100 and simplify.
1 Why are there three ways to write the same amount?Fractions, decimals and percents are three ways of writing one number. 1 min
Fractions, decimals and percents are three ways of writing one number. If a patient ate 3/5 of a meal, that is also 0.6 of the meal, or 60% of it. Five short moves get you from any form to any other.
| From → To | What you do | Example |
|---|---|---|
| Fraction → decimal | Divide top by bottom | 3/8 = 3 ÷ 8 = 0.375 |
| Decimal → percent | Move the point 2 places right, add % | 0.375 = 37.5% |
| Percent → decimal | Drop %, move the point 2 places left | 37.5% = 0.375 |
| Percent → fraction | Put the number over 100, simplify | 40% = 40/100 = 2/5 |
| Decimal → fraction | Use the place value as the bottom, simplify | 0.65 = 65/100 = 13/20 |
2 How do I turn a fraction into a decimal or a percent?The fraction bar means divide, so always divide the top number by the bottom number. 1 min
The fraction bar means divide, so always divide the top number by the bottom number. The top is the numerator and the bottom is the denominator. This is the one rule to remember.
Example 1. A meal log says a patient ate 3/5 of breakfast. Write it as a decimal and a percent.
- Divide top by bottom: 3 ÷ 5 = 0.6.
- Move the point two places right, adding a zero to fill the gap: 0.60 becomes 60.
- Add the sign: 60%.
Classic wrong turn: copying the digits and writing 0.35 or 35%. Quick check: 3/5 is more than half, so the answer must be more than 50%.
Some fractions never end. 2/3 = 0.666..., a repeating decimal, so keep the full number and round once at the end, the way the question asks.
3 How do I turn a percent into a decimal or a fraction?A percent is a number out of 100, so rewriting it always means dividing by 100. 1 min
A percent is a number out of 100, so rewriting it always means dividing by 100. Percent means "per hundred." For a decimal, drop the % and move the point two places left. For a fraction, put the number over 100 and simplify (divide top and bottom by the same number).
Example 2. A juice label says the drink is 12.5% real fruit juice. Write 12.5% as a decimal and a fraction.
- Drop the % and move the point two places left: 0.125.
- Read it by place value: 125 thousandths = 125/1,000.
- Divide top and bottom by 125: 1/8.
Classic wrong turn: moving the point right and getting 1.25, which is more than the whole drink. A percent under 100% always becomes a decimal under 1.
Tiny percents follow the same rule: 0.6% = 0.006 = 6/1,000 = 3/500.
4 How do I turn a decimal into a fraction?Read the decimal out loud by place value and the fraction appears. 1 min
Read the decimal out loud by place value and the fraction appears. 0.65 is "sixty-five hundredths," so it is 65/100. The place value of the last digit (tenths, hundredths, thousandths) is the denominator.
Example 3. A recipe scaled on a calculator now calls for 1.75 cups of flour. Your measuring cups use fractions. What do you measure?
- Keep the whole number: 1.
- The last digit, 5, is in the hundredths place, so 0.75 = 75/100.
- Divide top and bottom by 25: 3/4.
- Answer: 1 3/4 cups. Since 1.75 is more than 1, it is also more than 100% (175%).
Classic wrong turn: writing 1 7/5 or 1 75/10. Two digits after the point means hundredths, so the bottom is 100.
5 When should I use the calculator?Use the calculator for awkward division and your head for moving decimal points. 1 min
Use the calculator for awkward division and your head for moving decimal points. The TEAS 7 has a basic on-screen calculator in every section. It is perfect for 7 ÷ 16, but shifting a point two places is faster done mentally.
Knowing these pairs by heart saves time:
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4, 3/4 | 0.25, 0.75 | 25%, 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333... | about 33.3% |
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: 3/5 is 0.6, not 0.35: the digits of a fraction are not the digits of its decimal; you must divide.
Watch out: Percent to decimal moves the point left, not right: 12.5% is 0.125, not 1.25 or 12.5.
Watch out: 0.6% is 0.006, not 0.6 or 0.06: a tiny percent becomes a tiny decimal.
Watch out: When you simplify, divide the top and bottom by the same number, not different numbers (65/100 is 13/20, not 13/25).
Watch out: Divide top by bottom, not bottom by top: 5/8 is 0.625, not 1.6.
How to remember it
A percent is just a number per hundred, so the point always moves two places. Going to a percent, the number looks bigger (point moves right). Coming from a percent, it looks smaller (point moves left).
Self-check:
- Convert 5/8 to a decimal and a percent without the table.
- Write 35% as a fraction in simplest form.
- Decide whether 0.9% is bigger or smaller than 1/10, and say how you know.
Show answers
- 0.625 and 62.5%.
- Divide top by bottom: 5 ÷ 8 = 0.625.
- Move the point two places right and add %: 62.5%.
- Check: 5/8 is more than half, and 62.5% is more than 50%.
- 7/20.
- Put the number over 100: 35/100.
- Divide top and bottom by 5: 7/20.
- 0.9% is smaller.
- 0.9% as a decimal: move the point two places left, 0.009.
- 1/10 as a decimal: 1 ÷ 10 = 0.1, or 0.100.
- Pad and compare: 0.009 < 0.100. (Also, 1/10 = 10%, and 0.9% is less than 1%.)