1. **Problem Statement:** Round numbers to specified accuracy and express decimals to given decimal places and significant figures. 2. **Rounding to nearest 100, 1,000, 10,000:** - To round to the nearest 100, look at the tens digit. - To round to the nearest 1,000, look at the hundreds digit. - To round to the nearest 10,000, look at the thousands digit. 3. **Rounding to nearest whole number:** - If decimal part is 0.5 or more, round up. - Otherwise, round down. 4. **Rounding to decimal places:** - 1 d.p. means one digit after the decimal point. - 2 d.p. means two digits after the decimal point. 5. **Rounding to significant figures:** - Count digits from left, starting with first non-zero digit. - Round the number to the specified number of significant figures. --- **Step-by-step solutions:** **1. Round 86,343:** 1.a Nearest 100: Look at tens digit (4), less than 5, so round down. $$86,343 \to 86,300$$ 1.b Nearest 1,000: Look at hundreds digit (3), less than 5, round down. $$86,343 \to 86,000$$ 1.c Nearest 10,000: Look at thousands digit (6), 5 or more, round up. $$86,343 \to 90,000$$ **2. Round to nearest whole number:** 2.a 35,946 is already whole, so: $$35,946 \to 35,946$$ 2.b 45.1999: Decimal part 0.1999 < 0.5, round down. $$45.1999 \to 45$$ 2.c 7/8 = 0.875: Decimal part 0.875 ≥ 0.5, round up. $$0.875 \to 1$$ 2.d $\sqrt{5} \approx 2.236$: Decimal part 0.236 < 0.5, round down. $$2.236 \to 2$$ **3. Express decimals to 1 d.p. and 2 d.p.:** 3.a 1.936 - 1 d.p.: Look at second decimal (3), less than 5, round down. $$1.936 \to 1.9$$ - 2 d.p.: Look at third decimal (6), 5 or more, round up. $$1.936 \to 1.94$$ 3.b 4.752 - 1 d.p.: Second decimal (5), 5 or more, round up. $$4.752 \to 4.8$$ - 2 d.p.: Third decimal (2), less than 5, round down. $$4.752 \to 4.75$$ 3.c 12.998 - 1 d.p.: Second decimal (9), 5 or more, round up. $$12.998 \to 13.0$$ - 2 d.p.: Third decimal (8), 5 or more, round up. $$12.998 \to 13.00$$ **4. Write numbers to specified significant figures:** 4.a 28,645 (1 s.f.): First digit 2, next digit 8 ≥ 5, round up. $$28,645 \to 30,000$$ 4.b 41,909 (3 s.f.): First three digits 4,1,9; next digit 0 < 5, round down. $$41,909 \to 41,900$$ 4.c 4.5568 (3 s.f.): First three digits 4,5,5; next digit 6 ≥ 5, round up. $$4.5568 \to 4.56$$ --- **Final answers:** 1.a 86,300 1.b 86,000 1.c 90,000 2.a 35,946 2.b 45 2.c 1 2.d 2 3.a 1.9 (1 d.p.), 1.94 (2 d.p.) 3.b 4.8 (1 d.p.), 4.75 (2 d.p.) 3.c 13.0 (1 d.p.), 13.00 (2 d.p.) 4.a 30,000 (1 s.f.) 4.b 41,900 (3 s.f.) 4.c 4.56 (3 s.f.)