Question

a rectangle has length 8×10⁴ mm and width 4×10⁴ mm. the rectangle’s length is how many times its width? the rectangles length is times its width. (type a whole number.)

Explanation:

Step1: Set up the division

We need to find out how many times the length is of the width. So we divide the length by the width. The length is $8\times 10^{4}$ mm and the width is $4\times 10^{4}$ mm. The division is $\frac{8\times 10^{4}}{4\times 10^{4}}$.

Step2: Divide the coefficients and the powers of 10 separately

First, divide the coefficients: $\frac{8}{4}=2$. Then, divide the powers of 10: $\frac{10^{4}}{10^{4}} = 10^{4 - 4}=10^{0}=1$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step3: Multiply the results

Multiply the result of the coefficient - division and the result of the power - of - 10 division: $2\times1 = 2$.

Answer:

2