Decimals: Tenths and Hundredths: Grade 4 Study Guide
Decimals are another way to write fractions whose denominators are 10 or 100.
A decimal point separates whole numbers from parts of a whole. The first place after it is tenths and the second is hundredths. So 0.7 is 7/10 and 0.07 is 7/100. Grade 4 limits decimals to these two places, which links directly to money: 25 cents is $0.25, or 25/100 of a dollar.
Children use hundredths grids (a square cut into 100 small squares) and number lines to see that 0.3 and 0.30 are the same amount, and to compare numbers like 0.4 and 0.38.
Place value of decimals
Each place is ten times smaller than the place to its left. In 3.45, the 3 is ones, the 4 is tenths (4/10) and the 5 is hundredths (5/100).
| Fraction | Decimal | Words |
|---|---|---|
| 3/10 | 0.3 | three tenths |
| 47/100 | 0.47 | forty-seven hundredths |
| 2 5/10 | 2.5 | two and five tenths |
| 6/100 | 0.06 | six hundredths |
Fractions with denominator 10 and 100
To add 3/10 + 4/100, rewrite 3/10 as 30/100, so the sum is 34/100 = 0.34. A tenth is worth ten hundredths, which is why 0.3 = 0.30.
10 and 100.
3/10 = 30/100.
30/100 + 4/100 = 34/100.
0.34.
Comparing decimals
Line up the decimal points and compare from the left. 0.6 versus 0.58: write 0.6 as 0.60, and 60 hundredths is greater than 58 hundredths. A longer decimal is not always larger. Check by marking both on a number line between 0 and 1.
Worked examples and common mistakes
Example: Write 7/100 as a decimal: 0.07, with a zero holding the tenths place. Example: $0.30 is 3 dimes, or 30 hundredths of a dollar. Common mistakes: writing 7/100 as 0.7, thinking 0.35 is bigger than 0.5 because 35 > 5, and forgetting the zero placeholder. Always read the decimal aloud: 'seven hundredths'.
Check your understanding: model answers
1. 0.09. 2. 0.4 = 0.40, which is greater than 0.39. 3. 50/100 + 6/100 = 56/100 = 0.56.
✨ Key Takeaways
- Tenths and hundredths are the first two decimal places.
- 0.3 equals 0.30.
- Compare decimals place by place from the left.
- Money is a decimal system.
💬 Questions for Discussion & Reflection
- Write 9/100 as a decimal.
- Which is greater: 0.4 or 0.39?
- Add 5/10 and 6/100.