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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 number \(978.65 \times 10^{12}\) into E notation (scientific notation). Answer: \(9.7865 \times 10^{14}\)

Step by step solution

01

Identify the base and exponent in the E notation

The given number is already in the form of \(a \times 10^b\). We need to make sure that \(1 \leq a < 10\). In this case, \(a=978.65\) and \(b=12\).
02

Adjust the base to fit the E notation range

We need to adjust the base \(a=978.65\) to fit the range \(1 \leq a < 10\). We do this by moving the decimal point two places to the left, and compensating by increasing the exponent \(b\) by 2. This gives us \(a=9.7865\) and \(b=14\).
03

Write the final E notation form

Writing the number in the E notation form, we get the final answer as \(9.7865 \times 10^{14}\).

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