Convert fractions and mixed numbers to decimals - denominators of 10 and 100
Fractions and decimals are two ways of showing the same value. 🤝 Learning to convert between them is easy when the fraction's denominator is a power of 10, like 10 or 100!
Do this: Read the concept below, then try the quiz or activity.
Concept
Fractions with denominators of 10 or 100 have a direct connection to our decimal place value system (tenths and hundredths).
1. Fractions with a Denominator of 10
A fraction like 7/10 means "seven tenths". In our decimal system, the first place after the decimal point is the tenths place. * So, 7/10 is written as 0.7.
* Mixed Number Example: 3 4/10
* The whole number (3) goes before the decimal point.
* The fraction (4/10) becomes the tenths place.
* Result: 3.42. Fractions with a Denominator of 100
A fraction like 23/100 means "twenty-three hundredths". The second place after the decimal point is the hundredths place. * So, 23/100 is written as 0.23.
* What about 7/100?
* This is "seven hundredths". We need to make sure the 7 is in the hundredths place (the second spot). We use a zero as a placeholder.
* Result: 0.07* Mixed Number Example: 5 67/100
* The whole number (5) goes before the decimal point.
* The fraction (67/100) becomes the hundredths place.
* Result: 5.673. Converting Other Fractions (like ½, ¼, ⅕) to Decimals
What if the denominator isn't 10 or 100? You can make it so! Find an equivalent fraction.
* Example: Convert 1/2 to a decimal.
1. Can we make the denominator 10? Yes! 2 x 5 = 10.
2. Create an equivalent fraction: (1 x 5) / (2 x 5) = 5/10.
3. Now convert 5/10 to a decimal: 0.5.* Example: Convert 3/4 to a decimal.
1. Can we make the denominator 10? No. Can we make it 100? Yes! 4 x 25 = 100.
2. Create an equivalent fraction: (3 x 25) / (4 x 25) = 75/100.
3. Now convert 75/100 to a decimal: 0.75.Key Idea: The number of zeros in the denominator tells you how many decimal places you need. 10 has one zero -> one decimal place. 100 has two zeros -> two decimal places.
Try it
Practice converting fractions to decimals!
Convert these fractions (denominator 10 or 100): 1. 3/10 = ? 2. 45/100 = ? 3. 9/100 = ? 4. 8/10 = ?
Convert these mixed numbers: 5. 4 5/10 = ? 6. 12 34/100 = ? 7. 7 2/100 = ?
Convert by making an equivalent fraction first: 8. 2/5 = ?/10 = ? (decimal) 9. 1/4 = ?/100 = ? (decimal) 10. 9/20 = ?/100 = ? (decimal) 11. 3/50 = ?/100 = ? (decimal)
Word Problems: 12. You scored 80/100 on a test. What is your score as a decimal? 13. You have 6 5/10 dollars. Write this as a decimal amount. 14. A recipe calls for 1/2 cup of milk. Write this as a decimal.
Challenge Problems: 15. Convert 3/25 to a decimal. 16. Write 5.12 as a mixed number.