What is the value of this expression? (1.25 * 10^-4) + (7.5 * 10^-5)/0.08 Choices: (A)2.5 * 10^3 (B)2.5 * 10^4 (C)2.5 * 10^-4 (D)2.5 * 10^-3

Divide and Simplify: Now, let's divide 7.5 * 10^-5 by 8 * 10^-2. (7.5 * 10^-5) / (8 * 10^-2) = (7.5/8) * (10^-5 / 10^-2) = 0.9375 * 10^-3.Addition of Terms: Next, we add the two terms together. (1.25 * 10^-4) + 0.9375 * 10^-3. Since the exponents are different, we need to make them the same before adding.Convert to Same Exponent: Let's convert 1.25 * 10^-4 to 10^-3 by multiplying it by 10. 1.25 * 10^-4 * 10 = 12.5 * 10^-3. Now we can add the two terms.Addition Result: Adding the two terms: 12.5 * 10^-3 + 0.9375 * 10^-3 = 13.4375 * 10^-3.Express in Scientific Notation: To match the answer choices, we need to express 13.4375 * 10^-3 in scientific notation. 13.4375 * 10^-3 is the same as 1.34375 * 10^-2.Round to One Decimal: Finally, we round 1.34375 * 10^-2 to one decimal place to match the answer choices. 1.34375 * 10^-2 rounds to 1.3 * 10^-2, which is not an option in the choices.

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What is the value of this expression? $\newline$ $(1.25 \times 10^{-4}) + \frac{(7.5 \times 10^{-5})}{0.08}$ $\newline$ Choices: $\newline$ (A) $2.5 \times 10^3$ $\newline$ (B) $2.5 \times 10^4$ $\newline$ (C) $2.5 \times 10^{-4}$ $\newline$ (D) $2.5 \times 10^{-3}$

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Math Problems

Algebra 1

Power rule with rational exponents

Full solution

Q. What is the value of this expression?

\newline

(1.25 \times 10^{-4}) + \frac{(7.5 \times 10^{-5})}{0.08}

\newline

Choices:

\newline

(A)

2.5 \times 10^3

\newline

(B)

2.5 \times 10^4

\newline

(C)

2.5 \times 10^{-4}

\newline

(D)

2.5 \times 10^{-3}

Divide and Simplify: Now, let's divide $7.5 \times 10^{-5}$ by $8 \times 10^{-2}$ . $\newline$ $\frac{7.5 \times 10^{-5}}{8 \times 10^{-2}} = \frac{7.5}{8} \times \frac{10^{-5}}{10^{-2}} = 0.9375 \times 10^{-3}.$
Addition of Terms: Next, we add the two terms together. $\newline$ $(1.25 \times 10^{-4}) + (0.9375 \times 10^{-3})$ . $\newline$ Since the exponents are different, we need to make them the same before adding.
Convert to Same Exponent: Let's convert $1.25 \times 10^{-4}$ to $10^{-3}$ by multiplying it by $10$ . $\newline$ $1.25 \times 10^{-4} \times 10 = 12.5 \times 10^{-3}$ . $\newline$ Now we can add the two terms.
Addition Result: Adding the two terms: $12.5 \times 10^{-3} + 0.9375 \times 10^{-3} = 13.4375 \times 10^{-3}$ .
Express in Scientific Notation: To match the answer choices, we need to express $13.4375 \times 10^{-3}$ in scientific notation. $\newline$ $13.4375 \times 10^{-3}$ is the same as $1.34375 \times 10^{-2}$ .
Round to One Decimal: Finally, we round $1.34375 \times 10^{-2}$ to one decimal place to match the answer choices. $\newline$ $1.34375 \times 10^{-2}$ rounds to $1.3 \times 10^{-2}$ , which is not an option in the choices.