Question

the length of a rectangle measures 4.7×10² cm and the width measures 3.6×10³ cm. calculate the area of the rectangle. hint: use the formula sheet to determine the formula(s) needed to solve the problem. a 4.07×10³ cm² b 8.14×10³ cm² c 1.692×10⁶ cm² d 4.07×10⁶ cm² e 1.692×10⁷ cm²

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Substitute given values

Given $l = 4.7\times10^{2}$ cm and $w=3.6\times 10^{3}$ cm. Then $A=(4.7\times10^{2})\times(3.6\times 10^{3})$.

Step3: Use multiplication rule of exponents

According to the rule $a^{m}\times a^{n}=a^{m + n}$, we have $(4.7\times3.6)\times(10^{2}\times10^{3})$. Calculate $4.7\times3.6 = 16.92$, and $10^{2}\times10^{3}=10^{2 + 3}=10^{5}$. So $A = 16.92\times10^{5}$.

Step4: Convert to scientific - notation

Rewrite $16.92\times10^{5}$ in proper scientific - notation. Move the decimal point one place to the left to get $1.692$, and increase the exponent of 10 by 1. So $A=1.692\times10^{6}$ $cm^{2}$.

Answer:

C. $1.692\times 10^{6}$ $cm^{2}$