Question
Work out \( \left(7.3 \times 10^{5}\right)+\left(4 \times 10^{5}\right) \) Give your answer in standard index form.
Ask by Robbins Nguyen. in the United Kingdom
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum is \(1.13 \times 10^{6}\).
Solution
To compute \( \left(7.3 \times 10^{5}\right) + \left(4 \times 10^{5}\right) \) and express the result in standard index (scientific) form, follow these steps:
1. **Add the Coefficients:**
\[
7.3 + 4 = 11.3
\]
2. **Combine with the Common Exponent:**
\[
11.3 \times 10^{5}
\]
3. **Adjust to Proper Scientific Notation:**
In standard scientific notation, the coefficient should be between 1 and 10. To adjust:
\[
11.3 \times 10^{5} = 1.13 \times 10^{6}
\]
(Here, \(11.3 \times 10^{5}\) is rewritten by moving the decimal one place to the left, which increases the exponent by 1.)
**Final Answer:**
\[
1.13 \times 10^{6}
\]
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Simplify this solution Beyond the Answer
To work out \( \left(7.3 \times 10^{5}\right)+\left(4 \times 10^{5}\right) \), notice that both terms have the same power of ten. You can simply add the coefficients: \[ 7.3 + 4 = 11.3 \] Now, combine this with the \(10^{5}\): \[ 11.3 \times 10^{5} \] To express it in standard index form, since \(11.3\) can be written as \(1.13 \times 10^{1}\), we can rewrite it: \[ 1.13 \times 10^{1} \times 10^{5} = 1.13 \times 10^{6} \] So, the answer in standard index form is: \[ 1.13 \times 10^{6} \]
