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Which sign makes the statement true? $\newline$ $1.69 \times 10^{4} \,?\, 1.69 \times 10^{3}$ $\newline$ 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

1.69 \times 10^{4} \,?\, 1.69 \times 10^{3}

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Understand the problem: Understand the problem. $\newline$ We need to compare two numbers: $1.69 \times 10^4$ and $1.69 \times 10^3$ . We will do this by understanding the effect of the exponent on the base $10$ .
Compare the exponents: Compare the exponents. $\newline$ Since the base $(1.69)$ is the same for both numbers, we only need to compare the exponents of $10$ . The exponent $4$ in $10^4$ means that the base $10$ is multiplied by itself four times, while the exponent $3$ in $10^3$ means the base $10$ is multiplied by itself three times. Therefore, $10^4$ is ten times larger than $10^3$ .
Apply the comparison: Apply the comparison to the original numbers. $\newline$ Since $10^4$ is ten times larger than $10^3$ , it follows that $1.69 \times 10^4$ is ten times larger than $1.69 \times 10^3$ . Therefore, the correct sign to make the statement true is ＂ $>$ ＂.

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