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What is the quotient of \( 1.44 \times 10^{8} \) and \( 6.0 \times 10^{5} \) expressed in scientific notation? Answer Attempt 1 out of 2 Answer: \( \square \times 10 \square \) Submit Answer

Ask by Perkins Barnett. in the United States
Mar 11,2025

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Tutor-Verified Answer

Answer

The quotient is \(2.4 \times 10^{2}\).

Solution

\[ \textbf{Step 1: Divide the Coefficients} \] Divide the numbers: \[ \frac{1.44}{6.0} = 0.24 \] \[ \textbf{Step 2: Divide the Powers of Ten} \] Subtract the exponents: \[ \frac{10^8}{10^5} = 10^{8 - 5} = 10^3 \] \[ \textbf{Step 3: Combine the Results} \] Multiply the coefficient by the power of ten: \[ 0.24 \times 10^3 \] \[ \textbf{Step 4: Convert to Standard Scientific Notation} \] Since the coefficient \(0.24\) is less than 1, we adjust it by multiplying by \(10\) and reducing the exponent by 1: \[ 0.24 \times 10^3 = 2.4 \times 10^2 \] \[ \boxed{2.4 \times 10^2} \]

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To find the quotient of \( 1.44 \times 10^{8} \) and \( 6.0 \times 10^{5} \), start by dividing the coefficients, which gives \( \frac{1.44}{6.0} = 0.24 \). Next, subtract the exponents: \( 8 - 5 = 3 \). So, we combine them to express in scientific notation: \( 0.24 \times 10^{3} \). Since scientific notation requires the coefficient to be between 1 and 10, we rewrite \( 0.24 \) as \( 2.4 \times 10^{-1} \). Thus, the final expression becomes \( 2.4 \times 10^{-1} \times 10^{3} = 2.4 \times 10^{2} \). The answer is \( 2.4 \times 10^{2} \).

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