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Which sign makes the statement true? $\newline$ $5.763 \times 10^2 \,?\, 5.73 \times 10^3$ $\newline$ 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

5.763 \times 10^2 \,?\, 5.73 \times 10^3

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Identify Exponents: We have: $\newline$ $5.763 \times 10^2$ and $5.73 \times 10^3$ $\newline$ Are the exponents the same or different? $\newline$ Exponents are $2$ and $3$ . $\newline$ Both exponents are different.
Compare Exponents: Exponents are different. $\newline$ $5.763 \times 10^2$ ____ $5.73 \times 10^3$ $\newline$ Which sign makes the statement true? $\newline$ Compare the exponents because they are different. $\newline$ $2 < 3$ $\newline$ This means that $5.763 \times 10^2$ is less than $5.73 \times 10^3$ because the exponent on the $10$ is larger in the second expression, indicating it is a larger number.
Convert to Standard Form: Convert both numbers to their standard form to confirm. $\newline$ $5.763 \times 10^2 = 576.3$ $\newline$ $5.73 \times 10^3 = 5730$ $\newline$ Now compare the numbers in standard form. $\newline$ $576.3 < 5730$

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