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Chapter 2: Problem 7

\(978.65 \times 10^{12}\) would be written in \(\mathrm{E}\) notation as ___________.

Short Answer

Expert verified
Question: Convert the given value into E-notation: \(978.65 \times 10^{12}\). Answer: \(9.7865 \times 10^{14}\)

Step by step solution

01

Identify the value to be converted

The value we need to convert into E-notation is \(978.65 \times 10^{12}\).
02

Rewrite the value in a form with only one non-zero digit to the left of the decimal point

We need to rewrite the value as \(9.7865 \times 10^{x}\), where \(x\) is an integer. To do this, we can divide 978.65 by 100. So, $$ 9.7865 = \frac{978.65}{10^2} $$
03

Adjust the original exponent

Since we have divided 978.65 by 100, we need to adjust the original exponent \(10^{12}\) to account for this change. Since we divided by \(10^2\), we need to add 2 to the exponent 12. So, $$ 10^{12+2} = 10^{14} $$
04

Write the number in E-notation

Now that we have a value with only one non-zero digit to the left of the decimal point and we have adjusted the exponent, we can write the number in E-notation. Combining the value from Step 2 and the adjusted exponent from Step 3, we have: $$ 978.65 \times 10^{12} = 9.7865 \times 10^{14} $$ The number \(978.65 \times 10^{12}\) in E-notation is \(9.7865 \times 10^{14}\).

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