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Which sign makes the statement true? $\newline$ $92,500$ $?$ $9.25 \times 10^5$ $\newline$ Choices: $\newline$ (A) $>$ $\newline$ (B) $<$ $\newline$ (C) $=$ $\newline$

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Compare numbers written in scientific notation

Full solution

Q. Which sign makes the statement true?

\newline

92,500

?

9.25 \times 10^5

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

\newline

Understand the problem: Understand the problem. $\newline$ We need to compare two numbers: $92,500$ and $9.25 \times 10^5$ . We will convert both numbers to the same format to make the comparison easier.
Convert to scientific notation: Convert $92,500$ to scientific notation. $\newline$ $92,500$ can be written as $9.25 \times 10^4$ in scientific notation because we move the decimal point $4$ places to the left.
Compare exponents: Compare the exponents of the scientific notations. $\newline$ We have $9.25 \times 10^4$ and $9.25 \times 10^5$ . The base numbers ( $9.25$ ) are the same, so we only need to compare the exponents. $\newline$ The exponent $5$ in $9.25 \times 10^5$ is greater than the exponent $4$ in $9.25 \times 10^4$ .
Determine inequality sign: Determine the correct inequality sign. $\newline$ Since $10^5$ is greater than $10^4$ , it follows that $9.25 \times 10^5$ is greater than $9.25 \times 10^4$ . $\newline$ Therefore, the correct sign is ＂ $>$ ＂. $\newline$ $92,500 < 9.25 \times 10^5$

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