Select all of the true statements. $\newline$ Multi-select Choices: $\newline$ (A) $8 \times 10^{-3}$ is $200$ times as much as $4 \times 10^{-5}$ . $\newline$ (B) $2 \times 10^{6}$ is $50$ times as much as $4 \times 10^{4}$ . $\newline$ (C) $3 \times 10^{-2}$ is $0.1$ times as much as $3 \times 10^{-3}$ . $\newline$ (D) $6 \times 10^{4}$ is $200$ $0$ times as much as $200$ $1$ .

Full solution

Q. Select all of the true statements.

\newline

Multi-select Choices:

\newline

(A)

8 \times 10^{-3}

200

times as much as

4 \times 10^{-5}

\newline

(B)

2 \times 10^{6}

50

times as much as

4 \times 10^{4}

\newline

(C)

3 \times 10^{-2}

0.1

times as much as

3 \times 10^{-3}

\newline

(D)

6 \times 10^{4}

200

0

times as much as

200

1

Evaluate Statement (A): First, let's evaluate statement (A): $8 \times 10^{-3}$ is $200$ times as much as $4 \times 10^{-5}$ . To check if this is true, we need to divide $8 \times 10^{-3}$ by $4 \times 10^{-5}$ and see if the result is $200$ . $\newline$ Calculation: ($8$ \times $10$^{$-3$}) / ($4$ \times $10$^{$-5$}) = $8$/$4$ \times $10$^{($-3$ + $5$)} = $2$ \times $10$^$2$ = $200$.
Evaluate Statement (B): Now, let's look at statement (B): $2 \times 10^6$ is $50$ times as much as $4 \times 10^4$. We divide $2 \times 10^6$ by $4 \times 10^4$ to check if the result is $50$.$\newline$Calculation: ( $2$ \times $10$ ^ $6$ ) / ( $4$ \times $10$ ^ $4$ ) = $2$ / $4$ \times $10$ ^{ $6$ - $4$ } = $0$ . $5$ \times $10$ ^ $2$ = $50$ .