Question
Using a calcularor, wark out \( \left(4.57 \times 10^{10}\right)-\left(3.78 \times 10^{11}\right) \) Give your answer in standard torm
Ask by Carlson Pearson. in the United Kingdom
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-3.323 \times 10^{11}\)
Solution
To calculate the expression:
\[
\left(4.57 \times 10^{10}\right) - \left(3.78 \times 10^{11}\right)
\]
Let's break it down step by step.
1. **Convert to the Same Exponent:**
To subtract the two numbers, it's easier if both are expressed with the same exponent. Let's use \(10^{11}\):
\[
4.57 \times 10^{10} = 0.457 \times 10^{11}
\]
2. **Perform the Subtraction:**
\[
0.457 \times 10^{11} - 3.78 \times 10^{11} = -3.323 \times 10^{11}
\]
3. **Express in Standard (Scientific) Form:**
The result is already in standard scientific notation:
\[
-3.323 \times 10^{11}
\]
**Final Answer:**
\(-3.323 \times 10^{11}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the expression \( \left(4.57 \times 10^{10}\right)-\left(3.78 \times 10^{11}\right) \), we can first express both numbers with the same power of 10. Convert \( 4.57 \times 10^{10} \) to the power of \( 10^{11} \): \[ 4.57 \times 10^{10} = 0.457 \times 10^{11} \] Now rewrite the expression: \[ (0.457 \times 10^{11}) - (3.78 \times 10^{11}) = (-3.78 + 0.457) \times 10^{11} \] Calculating the subtraction: \[ -3.78 + 0.457 = -3.323 \] Thus, we have: \[ -3.323 \times 10^{11} \] Now to express this in standard form: \[ -3.323 \times 10^{11} \] So the final answer is: \[ \boxed{-3.323 \times 10^{11}} \]
