Question

456.2 km has (a) 4 sig. fig.

x 24.6 km has (b) 3 sig. fig.
(c)11 200 km2 has (d) 3 sig. fig.
Problem to solve:

204 m has
sig. fig.
÷ 6 m has 1 sig. fig.
has
sig. fig.

Answer 1

The division has the same number of significant figures as the measurement with the fewest, which is 3 in
`\(11,200 \ \text{km}^2\)`. Therefore, the result is
`\(0.04075 \`,
`\text{km}\) (3 sig. fig.)`.

Let's calculate each part of the problem while considering significant figures:

`(a) \(456.2 \, \text{km} * 24.6 \, \text{km}\)`

The product has the same number of significant figures as the measurement with the fewest, which is 3 in
`\(24.6 \, \text{km\,}\)`. Therefore, the result is
`\(11223 \, \text{km}^2\) (3 sig. fig.)\\`.

`(b) \(204 \, \text{m} / 6 \, \text{m}\)`

The division has the same number of significant figures as the measurement with the fewest, which is 1 in
`\(6 \, \text{m}\)`. Therefore, the result is
`\(34 \, \text{m}\) (1 sig. fig.)`.

`(c) \(456.2 \, \text{km} / 11,200 \, \text{km}^2\)`

The division has the same number of significant figures as the measurement with the fewest, which is 3 in
`\(11,200 \ \text{km}^2\)`. Therefore, the result is
`\(0.04075 \`,
`\text{km}\) (3 sig. fig.)`.