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

Understand the problem: Understand the problem. We need to compare two numbers: 92,500 and 9.25 × 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. 92,500 can be written as 9.25 × 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. We have 9.25 × 10^4 and 9.25 × 10^5. The base numbers (9.25) are the same, so we only need to compare the exponents. The exponent 5 in 9.25 × 10^5 is greater than the exponent 4 in 9.25 × 10^4.Determine inequality sign: Determine the correct inequality sign. Since 10^5 is greater than 10^4, it follows that 9.25 × 10^5 is greater than 9.25 × 10^4. Therefore, the correct sign is ＂>＂. 92,500 < 9.25 × 10^5

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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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Math Problems

Grade 8

Compare numbers written in scientific notation

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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