Question

please do the following calculations and round your answer to the correct number of significant figures. include a unit in your answer
1500 n ÷ 3 m²
5.25 mm² x 0.65 mm²

Explanation:

First Calculation: \( 1500\,\text{N} \div 3\,\text{m}^2 \)

Step 1: Perform the division

Divide the force (1500 N) by the area (3 m²).
\( \frac{1500\,\text{N}}{3\,\text{m}^2} = 500\,\text{N/m}^2 \) (or 500 Pa, since \( \text{N/m}^2 = \text{Pa} \)).
(The number of significant figures: 1500 has 1 or 4? Assuming 1500 is exact here, 3 is exact, so result is 500 with 1 significant figure? Wait, maybe 1500 is 1.5×10³, 3 is exact. So 1.5×10³ / 3 = 5×10², so 500 N/m² (1 significant figure? Or maybe 1500 is 4 sig figs, 3 is 1, so least is 1. But maybe the problem expects 500 as is.)

Second Calculation: \( 5.25\,\text{mm}^2 \times 0.65\,\text{mm}^2 \)

Step 1: Multiply the values

Multiply the two areas.
\( 5.25 \times 0.65 = 3.4125 \)

Step 2: Consider units and significant figures

Units: \( \text{mm}^2 \times \text{mm}^2 = \text{mm}^4 \)
Significant figures: 5.25 has 3, 0.65 has 2. Least is 2, so round to 3.4 (or 3.41? Wait, 5.25×0.65: 5.25×0.65 = 3.4125. Rounding to 2 significant figures: 3.4 (wait, 3.4125 rounded to two sig figs is 3.4? Wait, 3.4125: first two sig figs are 3 and 4, next digit is 1, which is less than 5, so 3.4? Wait, no: 3.4125, the first two significant figures are 3 (1st) and 4 (2nd), the next digit is 1, so we keep 3.4? Wait, no, 5.25 is three sig figs, 0.65 is two. When multiplying, the result should have the same number of sig figs as the least precise measurement, which is two. So 3.4125 rounded to two sig figs is 3.4? Wait, 3.4125: the first two sig figs are 3 and 4, the third is 1, so we round down, keeping 3.4. Wait, but 3.4125 is closer to 3.4 than 3.5? Wait, no, 3.4125 is 3.4 when rounded to two decimal places? No, significant figures: 3.4125, first sig fig 3, second 4, third 1. So two sig figs: 3.4.

Answer:

s:

1. \( 1500\,\text{N} \div 3\,\text{m}^2 = \boldsymbol{500\,\text{N/m}^2} \) (or \( 500\,\text{Pa} \))
2. \( 5.25\,\text{mm}^2 \times 0.65\,\text{mm}^2 = \boldsymbol{3.4\,\text{mm}^4} \) (or \( 3.41\,\text{mm}^4 \) if three sig figs, but 0.65 has two, so two sig figs: 3.4)