Questions: It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. (5.30 × 10^-5)(9.46 × 10^5)=□ (3.47 × 10^4) / (9.60 × 10^4)=□ ((5.30 × 10^-5)(9.60 × 10^4)) / ((1.00 × 10^-8)(3.47 × 10^4))=□

It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. (5.30 × 10^-5)(9.46 × 10^5)=□ (3.47 × 10^4) / (9.60 × 10^4)=□ ((5.30 × 10^-5)(9.60 × 10^4)) / ((1.00 × 10^-8)(3.47 × 10^4))=□
Transcript text: It is often necessary to do calculations using scientific notation when working chemistry problems. For practice, perform each of the following calculations. \[ \begin{array}{l} \left(5.30 \times 10^{-5}\right)\left(9.46 \times 10^{5}\right)=\square \\ \frac{3.47 \times 10^{4}}{9.60 \times 10^{4}}=\square \\ \frac{\left(5.30 \times 10^{-5}\right)\left(9.60 \times 10^{4}\right)}{\left(1.00 \times 10^{-8}\right)\left(3.47 \times 10^{4}\right)}=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Multiply Numbers in Scientific Notation
  • Multiply the coefficients: \(5.30 \times 9.46\).
  • Multiply the powers of ten: \(10^{-5} \times 10^{5}\).
  • Use the property of exponents: \(10^{-5 + 5} = 10^{0}\).
Step 2: Divide Numbers in Scientific Notation
  • Divide the coefficients: \(\frac{3.47}{9.60}\).
  • Divide the powers of ten: \(\frac{10^{4}}{10^{4}}\).
  • Use the property of exponents: \(10^{4 - 4} = 10^{0}\).
Step 3: Complex Fraction in Scientific Notation
  • Multiply the coefficients in the numerator: \(5.30 \times 9.60\).
  • Multiply the powers of ten in the numerator: \(10^{-5} \times 10^{4}\).
  • Multiply the coefficients in the denominator: \(1.00 \times 3.47\).
  • Multiply the powers of ten in the denominator: \(10^{-8} \times 10^{4}\).
  • Use the property of exponents for both numerator and denominator.
  • Divide the resulting coefficients and powers of ten.

Final Answer

\[ \begin{array}{l} \left(5.30 \times 10^{-5}\right)\left(9.46 \times 10^{5}\right) = \boxed{5.01} \\ \frac{3.47 \times 10^{4}}{9.60 \times 10^{4}} = \boxed{0.362} \\ \frac{\left(5.30 \times 10^{-5}\right)\left(9.60 \times 10^{4}\right)}{\left(1.00 \times 10^{-8}\right)\left(3.47 \times 10^{4}\right)} = \boxed{1.60 \times 10^{0}} \end{array} \]

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