1. **Problem Statement:** Round the given decimals to the nearest thousandth, hundredth, and tenth. 2. **Rounding Rules:** - To round to the nearest thousandth, look at the fourth decimal place. - To round to the nearest hundredth, look at the third decimal place. - To round to the nearest tenth, look at the second decimal place. 3. **Rounding each number:** **a) 0.1234** - Thousandth: Look at 4th decimal (4), since 4 < 5, keep 3rd decimal as is. $$0.1234 \to 0.123$$ - Hundredth: Look at 3rd decimal (3), since 3 < 5, keep 2nd decimal as is. $$0.1234 \to 0.12$$ - Tenth: Look at 2nd decimal (2), since 2 < 5, keep 1st decimal as is. $$0.1234 \to 0.1$$ **b) 0.0322** - Thousandth: 4th decimal is 2 < 5, keep 3rd decimal. $$0.0322 \to 0.032$$ - Hundredth: 3rd decimal is 2 < 5, keep 2nd decimal. $$0.0322 \to 0.03$$ - Tenth: 2nd decimal is 3 < 5, keep 1st decimal. $$0.0322 \to 0.0$$ **c) 4.5678** - Thousandth: 4th decimal is 8 ≥ 5, add 1 to 3rd decimal. $$0.567\to 0.568$$ so $$4.5678 \to 4.568$$ - Hundredth: 3rd decimal is 7 ≥ 5, add 1 to 2nd decimal. $$4.56 \to 4.57$$ - Tenth: 2nd decimal is 6 ≥ 5, add 1 to 1st decimal. $$4.5 \to 4.6$$ **d) 5.1764** - Thousandth: 4th decimal is 4 < 5, keep 3rd decimal. $$5.1764 \to 5.176$$ - Hundredth: 3rd decimal is 6 ≥ 5, add 1 to 2nd decimal. $$5.17 \to 5.18$$ - Tenth: 2nd decimal is 7 ≥ 5, add 1 to 1st decimal. $$5.1 \to 5.2$$ 4. **Round measurements to 1 decimal place:** - Round by looking at the 2nd decimal digit. a) 20.234 kg → 20.2 kg b) 300.06 m → 300.1 m c) 7.026 mm → 7.0 mm d) 0.693 km → 0.7 km e) 0.084 cm → 0.1 cm f) 953.58 g → 953.6 g g) 359.87 L → 359.9 L h) 57.99 g → 58.0 g 5. **Round numbers to 0 or 1 whichever is closer:** - If number ≥ 0.5, round to 1; else 0. a) 0.8 → 1 b) 0.2 → 0 c) 0.5 → 1 d) 0.97 → 1 e) 0.43 → 0 f) 0.55 → 1 6. **Estimate using calculator and round to nearest hundredth:** a) 1 ÷ 2 = 0.5 b) 2 ÷ 3 ≈ 0.6667 → 0.67 c) 22 ÷ 7 ≈ 3.1429 → 3.14 d) 45 ÷ 13 ≈ 3.4615 → 3.46 7. **Estimate by rounding to nearest whole number:** a) 3.0 + 4.16 = 3 + 4 = 7 b) 25.3 + 10.657 = 25 + 11 = 36 c) 2.7 - 5.4 = 3 - 5 = -2 d) 28.26 + 7.25 = 28 + 7 = 35 e) 0.64 + 0.213 = 1 + 0 = 1 f) 4.39 ÷ 2.567 = 4 ÷ 3 = 1.33 g) 12.82 - 2.57 = 13 - 3 = 10 h) 73.54 - 20.67 = 74 - 21 = 53 i) 39.86 + 4.974 = 40 + 5 = 45 8. **Estimate by rounding both numbers to nearest whole number:** a) 92.7 + 4.16 = 93 + 4 = 97 b) 0.7 × 8.3 = 1 × 8 = 8 c) 9.2 × 10.3 = 9 × 10 = 90 d) 9.72 - 0.9 = 10 - 1 = 9 e) 88.2 + 9.8 = 88 + 10 = 98 f) 54.3 - 5.0 = 54 - 5 = 49 9. **Smallest hundredth rounding to 5.3:** - Numbers from 5.25 up to 5.34 round to 5.3. 10. **How many decimal hundredths round to 9.47?** - Numbers from 9.465 up to 9.474 round to 9.47. - This range covers 10 hundredths (from 9.465 to 9.474 inclusive). **Final answers:** **Rounding decimals:** a) 0.123 0.12 0.1 b) 0.032 0.03 0.0 c) 4.568 4.57 4.6 d) 5.176 5.18 5.2 **Measurements rounded to 1 decimal:** a) 20.2 b) 300.1 c) 7.0 d) 0.7 e) 0.1 f) 953.6 g) 359.9 h) 58.0 **Round to 0 or 1:** a) 1 b) 0 c) 1 d) 1 e) 0 f) 1 **Calculator estimates rounded to hundredth:** a) 0.5 b) 0.67 c) 3.14 d) 3.46 **Estimates rounding to whole numbers:** b) 36 c) -2 d) 35 e) 1 f) 1.33 g) 10 h) 53 i) 45 **Rounding both numbers to whole numbers:** a) 97 b) 8 c) 90 d) 9 e) 98 f) 49 **Decimal hundredths rounding to 9.47:** 10