1. The first problem is to multiply 18 by 0.01 and verify the result. 2. The formula for multiplication is $a \times b = c$ where $a$ and $b$ are numbers and $c$ is the product. 3. Multiply 18 by 0.01: $$18 \times 0.01 = 0.18$$ 4. This matches the given answer, so it is correct. 5. The second problem is to write numbers correct to a given number of significant figures (s.f.). 6. To round to significant figures, identify the digit at the place of the last significant figure and round accordingly. 7. For 8712 to 3 s.f.: - The first three digits are 8, 7, and 1. - The next digit is 2, which is less than 5, so we do not round up. $$8712 \approx 8710$$ 8. For 48487 to 2 s.f.: - The first two digits are 4 and 8. - The next digit is 4, less than 5, so no rounding up. $$48487 \approx 48000$$ 9. For 58 to 1 s.f.: - The first digit is 5. - The next digit is 8, which is 5 or more, so round up. $$58 \approx 60$$ 10. The third problem is to convert fractions to decimals and decide if they are terminating or non-terminating. 11. For $\frac{3}{5}$: $$\frac{3}{5} = 0.6$$ - This decimal terminates because the denominator's prime factors are only 2 and/or 5. 12. For $\frac{5}{6}$: $$\frac{5}{6} = 0.8333\ldots$$ - This decimal is non-terminating repeating because 6 has prime factors 2 and 3, and 3 causes repeating decimals. 13. The fourth problem is to work out $1 \frac{1}{3} - \frac{2}{3}$. 14. Convert mixed number to improper fraction: $$1 \frac{1}{3} = \frac{4}{3}$$ 15. Subtract fractions: $$\frac{4}{3} - \frac{2}{3} = \frac{4-2}{3} = \frac{2}{3}$$ Final answers: - 18 x 0.01 = 0.18 - 8712 to 3 s.f. = 8710 - 48487 to 2 s.f. = 48000 - 58 to 1 s.f. = 60 - $\frac{3}{5} = 0.6$ (terminating) - $\frac{5}{6} = 0.8333\ldots$ (non-terminating repeating) - $1 \frac{1}{3} - \frac{2}{3} = \frac{2}{3}$