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Which sign makes the statement true? $\newline$ $2.02 \times 10^4$ $\text{?}$ $2,020$ $\newline$ 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

2.02 \times 10^4

\text{?}

2,020

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Express in Scientific Notation: We have $2.02 \times 10^4$ and $2,020$ . $\newline$ First, let's express $2,020$ in scientific notation to compare it easily with $2.02 \times 10^4$ . $\newline$ $2,020$ can be written as $2.02 \times 10^3$ because $2.02$ times $10$ to the power of $3$ equals $2,020$ .
Compare Exponents: Now we compare $2.02 \times 10^4$ with $2.02 \times 10^3$ . Since the base numbers ( $2.02$ ) are the same, we only need to compare the exponents of $10$ . The exponent in $2.02 \times 10^4$ is $4$ , and the exponent in $2.02 \times 10^3$ is $3$ . $4$ is greater than $3$ . Therefore, $2.02 \times 10^4$ is greater than $2.02 \times 10^3$ .

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