Question

perform the two calculations using significant figures and units.
(2.50×10⁻⁴ μm)(1.007×10⁻³ μm) = 1
(3.456×10⁵ nm) / (2.00000×10³ s) = 2
a. 2.5×10⁻⁷ b. 2.52×10⁻⁷ μm c. 2.52×10⁻⁷ μm² d. 1.728×10²
e. 1.728×10² nm/s f. 1.73×10² nm/s

Explanation:

Step1: Multiply numbers and exponents for first calculation

First, multiply the non - exponential parts: $2.50\times1.007 = 2.5175$. Then, add the exponents of 10: $10^{-4}\times10^{-3}=10^{-4 - 3}=10^{-7}$. So the result is $2.5175\times10^{-7}\ \mu m^2$. Rounding to three significant figures (since 2.50 has three significant figures), we get $2.52\times10^{-7}\ \mu m^2$.

Step2: Divide numbers and exponents for second calculation

Divide the non - exponential parts: $\frac{3.456}{2.00000}=1.728$. Subtract the exponents of 10: $10^{5}\div10^{3}=10^{5 - 3}=10^{2}$. So the result is $1.728\times10^{2}\ nm/s$. Rounding to three significant figures (since 3.456 has four significant figures and 2.00000 has six significant figures, we go by the least number of significant figures in the operation for division), we get $1.73\times10^{2}\ nm/s$.

Answer:

1. C. $2.52\times 10^{-7}\ \mu m^2$
2. F. $1.73\times 10^{2}\ nm/s$