Question

Multiply$\mathbf{3}\mathbf{.}\mathbf{079}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}\mathbf{m}$by$\mathbf{0}\mathbf{.}\mathbf{068}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{1}}\mathbf{m}$, taking into account significant figures.

Short answer

The correct answer for multiplication is 2.1 m.

Step-by-step solution

Step 1. Stating the given data

The data given are as follows:

$A_1=3.079\times {10}^2\mathrm{m}$, and $A_2=0.068\times {10}^{-1}\mathrm{m}$.

Solving the multiplication using the rules of significant figures

The value of the multiplication of $3.079\times {10}^2\mathrm{m}$by $0.068\times {10}^{-1}\mathrm{m}$is 2.0937 m.

According to the rules of significant figures in multiplication, the final answer is written in numbers having the least significant digits.

Here, $0.068\times {10}^{-1}\mathrm{m}$has two significant figures, and $3.079\times {10}^2\mathrm{m}$has four significant digits.

Thus, the final value of multiplication is2.1 m.