Which sign makes the statement true? 6,400 ? 6.4 × 10^5 Choices: (A)> (B)< (C)=

Understand the problem: Understand the problem. We need to compare two numbers: 6,400 and 6.4 × 10^5. We will convert both numbers to the same format to make the comparison easier.Convert to scientific notation: Convert 6,400 to scientific notation. 6,400 can be written as 6.4 × 10^3 in scientific notation.Compare exponents: Compare the exponents of the scientific notations. We have 6.4 × 10^3 and 6.4 × 10^5. The base number (6.4) is the same, so we only need to compare the exponents. The exponent 5 in 6.4 × 10^5 is greater than the exponent 3 in 6.4 × 10^3.Determine inequality sign: Determine the correct inequality sign. Since 10^5 is greater than 10^3, it follows that 6.4 × 10^5 is greater than 6.4 × 10^3. Therefore, the correct sign is ＂>＂.

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Which sign makes the statement true? $\newline$ $6,400 \, ? \, 6.4 \times 10^5$ $\newline$ Choices: $\newline$ (A) > $\newline$ (B) < $\newline$ (C) $=$

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Math Problems

Grade 8

Compare numbers written in scientific notation

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Q. Which sign makes the statement true?

\newline

6,400 \, ? \, 6.4 \times 10^5

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Understand the problem: Understand the problem. $\newline$ We need to compare two numbers: $6,400$ and $6.4 \times 10^5$ . We will convert both numbers to the same format to make the comparison easier.
Convert to scientific notation: Convert $6,400$ to scientific notation. $\newline$ $6,400$ can be written as $6.4 \times 10^3$ in scientific notation.
Compare exponents: Compare the exponents of the scientific notations. $\newline$ We have $6.4 \times 10^3$ and $6.4 \times 10^5$ . The base number ( $6.4$ ) is the same, so we only need to compare the exponents. $\newline$ The exponent $5$ in $6.4 \times 10^5$ is greater than the exponent $3$ in $6.4 \times 10^3$ .
Determine inequality sign: Determine the correct inequality sign. $\newline$ Since $10^5$ is greater than $10^3$ , it follows that $6.4 \times 10^5$ is greater than $6.4 \times 10^3$ . $\newline$ Therefore, the correct sign is ＂>＂.