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!
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: **3.4** **2. 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: **5.67** **3. 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.