Question
How much bigger is \( 4.2 \times 10^{5} \) than \( 6.1 \times 10^{4} \) ?
Ask by Vaughn Weber. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(4.2 \times 10^{5}\) is \(3.59 \times 10^{5}\) bigger than \(6.1 \times 10^{4}\).
Solution
1. Write the difference between the two numbers:
\[
4.2 \times 10^{5} - 6.1 \times 10^{4}
\]
2. Express both numbers with the same power of \(10\). Notice that:
\[
6.1 \times 10^{4} = 0.61 \times 10^{5}
\]
3. Substitute back into the difference:
\[
4.2 \times 10^{5} - 0.61 \times 10^{5}
\]
4. Factor out \(10^{5}\):
\[
(4.2 - 0.61) \times 10^{5}
\]
5. Perform the subtraction:
\[
4.2 - 0.61 = 3.59
\]
6. Write the final result:
\[
3.59 \times 10^{5}
\]
Thus, \(4.2 \times 10^{5}\) is \(3.59 \times 10^{5}\) bigger than \(6.1 \times 10^{4}\).
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Simplify this solution Bonus Knowledge
To find out how much bigger \( 4.2 \times 10^{5} \) is than \( 6.1 \times 10^{4} \), we can first convert them to the same exponent. We know that \( 6.1 \times 10^{4} \) can be rewritten as \( 0.61 \times 10^{5} \) (since \( 10^{5} = 10^{4} \times 10^{1} \)). Now, we can subtract: \[ 4.2 \times 10^{5} - 0.61 \times 10^{5} = (4.2 - 0.61) \times 10^{5} = 3.59 \times 10^{5} \] Thus, \( 4.2 \times 10^{5} \) is \( 3.59 \times 10^{5} \) bigger than \( 6.1 \times 10^{4} \).
