Fractions and Decimals
Grade 4 · Math · Study Guide
Understand the connection between fractions and decimals and how to convert between them.
Fractions and decimals are two different ways to show the same value. They both describe parts of a whole — they just use different notation. Once you see the connection, you'll flip between them without even thinking about it.
The easiest conversions involve tenths and hundredths. 3/10 = 0.3 because the tenths place in a decimal IS the denominator 10. Similarly, 47/100 = 0.47. Just place the numerator after the decimal point in the right position.
For fractions with other denominators, convert the denominator to 10 or 100 first. For example, 3/5: multiply top and bottom by 2 to get 6/10 = 0.6. For 3/4: multiply by 25 to get 75/100 = 0.75.
Decimal place value works just like whole-number place value. The tenths place is one place to the right of the decimal point, and hundredths is two places. So 0.35 = 3 tenths + 5 hundredths = 35/100. You can also say 35 hundredths. Both mean exactly the same thing.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 3/5 | 0.6 |
| 1/10 | 0.1 |
Key terms
- Decimal
- A number that uses a decimal point to show values less than one, like 0.7 or 0.35.
- Tenths
- The first place to the right of the decimal point; represents 1/10.
- Hundredths
- The second place to the right of the decimal point; represents 1/100.
- Equivalent
- Having the same value. For example, 1/2 and 0.5 are equivalent.
Flashcards
- 1/10 as a decimal
- 0.1
- 1/4 as a decimal
- 0.25
- 3/4 as a decimal
- 0.75
- 1/2 as a decimal
- 0.5
- 0.6 as a fraction
- 6/10 = 3/5
- 0.25 as a fraction
- 25/100 = 1/4
Practice questions
What decimal is equal to 3/10?
- 0.03
- 0.3
- 3.0
- 0.003
Show answer
Answer: 0.3
3/10 means 3 tenths. In decimal form, the tenths place is one place after the decimal: 0.3.
0.75 is the same as 3/4.
Show answer
Answer: True
3/4 × 25/25 = 75/100 = 0.75. They are equivalent values.
47/100 written as a decimal is ___.
Show answer
Answer: 0.47
47/100 means 47 hundredths. In decimal form: 0.47 (4 in tenths place, 7 in hundredths place).
What fraction is equal to 0.6?
- 6/100
- 3/5
- 1/6
- 6/60
Show answer
Answer: 3/5
0.6 = 6/10. Simplify 6/10 by dividing both by 2: 3/5.
The decimal 0.5 is the same as the fraction ___.
Show answer
Answer: 1/2
0.5 = 5/10. Simplify 5/10 by dividing both by 5: 1/2.
Fun facts
- Money uses decimals every day: $0.25 is the same as 25/100 of a dollar — that is exactly one quarter!
- Baseball batting averages are decimals: a .300 average means a player gets a hit 3 out of every 10 times at bat.
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