Question
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
Upstudy AI Solution
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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Extra Insights
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 \( 2.4 \times 10^{2} \).