Question

REASONING Evaluate the expression. Write your answer in scientific notation.

$5,200,000\times (8.3\times {10}^2)–(3.1\times {10}^8)$

Answer 1

Evaluating the expression

$5,200,000\times (8.3\times {10}^2)–(3.1\times {10}^8)$

$=5.2\times {10}^6\times (8.3\times {10}^2)–(3.1\times {10}^8)$

$=5.2\times 8.3\times {10}^6\times {10}^2–(3.1\times {10}^8)$ (Rearranging terms to solve product)

$=43.16\times {10}^8–3.1\times {10}^8$

$={10}^8\times (43.16–3.1)$ (Taking ${10}^8$as common)

$={10}^8\times (40.06)$ (Solving bracket)

$=4.006\times {10}^9$ (Writing answer in scientific notation)

Hence, the expression in scientific notation is $4.006\times {10}^9$.