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Which sign makes the statement true? $\newline$ $6.5 \times 10^4$ $\text{?}$ $5.6 \times 10^4$ $\newline$ Choices: $\newline$ (A) $>$ $\newline$ (B) $<$ $\newline$ (C) $=$

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Compare numbers written in scientific notation

Full solution

Q. Which sign makes the statement true?

\newline

6.5 \times 10^4

\text{?}

5.6 \times 10^4

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Compare Coefficients: Compare the coefficients of the two expressions. $\newline$ We have $6.5$ and $5.6$ as coefficients. Since $6.5$ is greater than $5.6$ , we can say that $6.5 \times 10^4$ is greater than $5.6 \times 10^4$ if the powers of $10$ are the same.
Compare Powers: Compare the powers of $10$ . Both expressions have the same power of $10$ , which is $10^4$ . This means that the comparison of the coefficients directly determines the comparison of the entire expressions.
Choose Correct Sign: Choose the correct sign based on the comparison. $\newline$ Since $6.5$ is greater than $5.6$ , and the powers of $10$ are the same, the correct sign to make the statement true is ' $>$ '.

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