Perform the following operations and report each result with the correct number of significant figur

What controls rounding here

Each part uses a different sig-fig rule:

• Addition and subtraction: round by decimal places (the least precise place value).
• Multiplication and division: round by significant figures (the fewest sig figs in the factors).

(a) Add after putting everything in the same unit

First convert centimeters to meters (conversion factor is exact): $$15.1000\,\text{cm}=15.1000\times 0.01\,\text{m}=0.151000\,\text{m}$$ Now add: $$81.155+0.151000+943.1=1024.406\,\text{m}$$ For addition, round to the least number of decimal places among the terms. $943.1\,\text{m}$ goes to the tenths place (1 decimal), so: $$1024.406\,\text{m}\rightarrow 1024.4\,\text{m}$$

(b) Multiply, then match the smallest sig-fig count

Compute the product: $$62.10\,\text{cm}\times 0.004\,\text{cm}=0.2484\,\text{cm}^2$$ Sig figs: $62.10$ has 4 sig figs, $0.004$ has 1 sig fig, so the result must have 1 sig fig: $$0.2484\rightarrow 0.2\,\text{cm}^2$$

(c) Divide, then keep the fewest sig figs

$$\frac{818.00\,\text{g}}{900.20\,\text{mL}}=0.908686\ldots\,\text{g/mL}$$ Both numbers have 5 sig figs, so keep 5 sig figs in the quotient: $$0.908686\ldots\rightarrow 0.90869\,\text{g/mL}$$