Decimals: Place Value and Operations: Grade 5 Study Guide
Grade 5 extends the base-ten system to thousandths and uses it to calculate with decimals.
Each place in our number system is ten times the place to its right and one tenth of the place to its left. In 4.536, the 5 is in the tenths place (0.5), the 3 is in the hundredths place (0.03) and the 6 is in the thousandths place (0.006). Fifth graders read, write, compare and round decimals to thousandths.
They then add, subtract, multiply and divide decimals to hundredths, using place value, models and the relationship between operations. Money, measurement and sports statistics give plenty of real examples.
Place value and comparing
To compare decimals, line up the decimal points and compare from the left. 0.47 versus 0.5: write 0.5 as 0.50, and 50 hundredths is greater than 47 hundredths. In expanded form, 2.345 = 2 + 3/10 + 4/100 + 5/1000. Multiplying by 10 shifts every digit one place left; dividing by 10 shifts it one place right.
| Number | Tenths | Hundredths | Thousandths | Words |
|---|---|---|---|---|
| 0.375 | 3 | 7 | 5 | three hundred seventy-five thousandths |
| 6.08 | 0 | 8 | 0 | six and eight hundredths |
| 12.4 | 4 | 0 | 0 | twelve and four tenths |
Rounding
To round to the nearest tenth, look at the hundredths digit. If it is 5 or more, round up. 3.47 rounds to 3.5, and 3.42 rounds to 3.4. Rounding is useful for estimating: $4.89 + $6.12 is about $5 + $6 = $11.
Tenths, hundredths or whole.
Is it 5 or more?
Change only that digit.
3.47 → 3.5.
Adding, subtracting, multiplying and dividing
Line up the decimal points to add or subtract: 12.40 + 3.75 = 16.15. To multiply 3.2 × 1.5, ignore the points and multiply 32 × 15 = 480, then count the decimal places in the factors (one + one = two), giving 4.80 = 4.8. To divide 7.2 ÷ 0.6, multiply both numbers by 10 to get 72 ÷ 6 = 12. Always check with an estimate: 3 × 1.5 = 4.5, so 4.8 is reasonable.
Worked examples and common mistakes
Example: Four notebooks cost $2.35 each. 4 × 2.35 = $9.40. Common mistakes: lining up the last digits instead of the decimal points, thinking 0.3 is smaller than 0.25 because 3 < 25 and putting the decimal point in the wrong place after multiplying. An estimate catches most of these slips.
Check your understanding: model answers
1. 5.68. 2. 4.65. 3. 6 × 4 = 24, with two decimal places, so 0.24.
✨ Key Takeaways
- Each place is ten times the place to its right.
- Compare decimals from the left, place by place.
- Line up the decimal points to add or subtract.
- Estimate to check multiplication and division.
💬 Questions for Discussion & Reflection
- Round 5.678 to the nearest hundredth.
- Find 8.4 − 3.75.
- Find 0.6 × 0.4.