1. **Rounding 86,343 to various levels of accuracy:** a. Nearest 100: Look at the tens digit (4). Since it is less than 5, round down. $$86,343 \approx 86,300$$ b. Nearest 1,000: Look at the hundreds digit (3). Since it is less than 5, round down. $$86,343 \approx 86,000$$ c. Nearest 10,000: Look at the thousands digit (6). Since it is 5 or more, round up. $$86,343 \approx 90,000$$ 2. **Rounding to the nearest whole number:** a. 35,946 is already a whole number, so it remains: $$35,946$$ b. 45,1999 (assuming a typo and you meant 45,199.9): Look at the first decimal digit (9), which is 5 or more, so round up. $$45,199.9 \approx 45,200$$ c. \(\frac{7}{8} = 0.875\). Look at the first decimal digit (8), which is 5 or more, so round up. $$0.875 \approx 1$$ d. \(\sqrt{5} \approx 2.236\). Look at the first decimal digit (2), which is less than 5, so round down. $$2.236 \approx 2$$ 3. **Express decimals to 1 decimal place (d.p.) and 2 decimal places:** a. 1.936 - 1 d.p.: Look at the second decimal digit (3), less than 5, so round down. $$1.936 \approx 1.9$$ - 2 d.p.: Look at the third decimal digit (6), 5 or more, so round up. $$1.936 \approx 1.94$$ b. 4.752 - 1 d.p.: Look at the second decimal digit (5), 5 or more, so round up. $$4.752 \approx 4.8$$ - 2 d.p.: Look at the third decimal digit (2), less than 5, so round down. $$4.752 \approx 4.75$$ c. 12.998 - 1 d.p.: Look at the second decimal digit (9), 5 or more, so round up. $$12.998 \approx 13.0$$ - 2 d.p.: Look at the third decimal digit (8), 5 or more, so round up. $$12.998 \approx 13.00$$ 4. **Write numbers to the indicated significant figures (s.f.):** a. 28,645 (1 s.f.): The first digit is 2, look at the next digit (8) which is 5 or more, so round up. $$28,645 \approx 30,000$$ b. 41,909 (3 s.f.): First three digits are 4,1,9. Look at the fourth digit (0), less than 5, so round down. $$41,909 \approx 41,900$$ c. 4.5568 (3 s.f.): First three digits are 4,5,5. Look at the fourth digit (6), 5 or more, so round up. $$4.5568 \approx 4.56$$ **Summary:** - Rounding depends on the digit immediately after the place value you are rounding to. - If that digit is 5 or more, round up; if less than 5, round down. - Significant figures count digits from the first non-zero digit. This completes the rounding and significant figure exercises.