Questions: Use the References to access important values if needed for this question. It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. 9.24 × 10^5 + 4.15 × 10^4 = (7.62 × 10^-4 + 1.00 × 10^-8) / (1.86 × 10^-4) = 4.58 × 10^6 / ((9.24 × 10^5)(4.15 × 10^4)) = Submit Answer Retry Entire Group 4 more group attempts remaining

Use the References to access important values if needed for this question. It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations.

9.24 × 10^5 + 4.15 × 10^4 =

(7.62 × 10^-4 + 1.00 × 10^-8) / (1.86 × 10^-4) =

4.58 × 10^6 / ((9.24 × 10^5)(4.15 × 10^4)) =

Submit Answer Retry Entire Group 4 more group attempts remaining

Transcript text: Use the References to access important values if needed for this question. It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. \[ \begin{array}{l} 9.24 \times 10^{5}+4.15 \times 10^{4}= \\ \frac{7.62 \times 10^{-4}+1.00 \times 10^{-8}}{1.86 \times 10^{-4}}= \\ \frac{4.58 \times 10^{6}}{\left(9.24 \times 10^{5}\right)\left(4.15 \times 10^{4}\right)}= \end{array} \] $\square$ $\square$ Submit Answer Retry Entire Group 4 more group attempts remaining

Solution

Solution Steps

Step 1: Addition of Numbers in Scientific Notation

Convert $4.15 \times 10^4$ to the same power of ten as $9.24 \times 10^5$.
$4.15 \times 10^4 = 0.415 \times 10^5$.
Add the coefficients: $9.24 + 0.415 = 9.655$.
Result: $9.655 \times 10^5$.

Step 2: Division of Numbers in Scientific Notation

Add the numbers in the numerator: $7.62 \times 10^{-4} + 1.00 \times 10^{-8}$.
Convert $1.00 \times 10^{-8}$ to the same power of ten as $7.62 \times 10^{-4}$.
$1.00 \times 10^{-8} = 0.0001 \times 10^{-4}$.
Add the coefficients: $7.62 + 0.0001 = 7.6201$.
Divide by the denominator: $\frac{7.6201 \times 10^{-4}}{1.86 \times 10^{-4}}$.
Simplify: $\frac{7.6201}{1.86} \times 10^{0}$.
Result: $4.0968$.

Step 3: Division of a Number by a Product in Scientific Notation

Calculate the product in the denominator: $(9.24 \times 10^5) \times (4.15 \times 10^4)$.
Multiply the coefficients: $9.24 \times 4.15 = 38.346$.
Add the exponents: $10^5 \times 10^4 = 10^9$.
Result of the product: $38.346 \times 10^9$.
Divide the numerator by the product: $\frac{4.58 \times 10^6}{38.346 \times 10^9}$.
Simplify: $\frac{4.58}{38.346} \times 10^{-3}$.
Result: $0.1194 \times 10^{-3}$.