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Which sign makes the statement true? $\newline$ $2.43 \times 10^3$ $?$ $24,300$ $\newline$ 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

2.43 \times 10^3

?

24,300

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

\newline

Convert to Scientific Notation: We have $2.43 \times 10^3$ and $24,300$ . Let's first express $24,300$ in scientific notation to compare it easily with $2.43 \times 10^3$ . $24,300$ can be written as $2.43 \times 10^4$ because $24,300$ is the same as $2.43$ multiplied by $10,000$ (which is $10^4$ ).
Compare in Scientific Notation: Now we compare the two expressions in scientific notation. $\newline$ We have $2.43 \times 10^3 ? 2.43 \times 10^4$ . $\newline$ Since the base ( $2.43$ ) is the same, we only need to compare the exponents to determine the inequality. $\newline$ The exponent $3$ in $10^3$ is less than the exponent $4$ in $10^4$ . $\newline$ Therefore, $2.43 \times 10^3 < 2.43 \times 10^4$ .
Final Comparison: Since $2.43 \times 10^4$ is another way of writing $24,300$ , we can replace it back into our original comparison. $\newline$ So, $2.43 \times 10^3 < 24,300$ .

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