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Chapter 5: Problem 148

How do you know if a number is written in scientific notation?

Short Answer

Expert verified
A number is in scientific notation if it has one non-zero digit before the decimal, followed by \( \times 10 \) and an integer exponent.

Step by step solution

01

- Identifying the Number of Digits before Decimal

To identify whether a number is in scientific notation, first look at the part of the number before the decimal. In scientific notation, there should only be one non-zero digit before the decimal. This number should be between 1 to 9, inclusive.
02

- Recognize the magnitude part

The next part of the number in scientific notation is a power of 10. This is signified by the \( \times 10 \) symbol, following the decimal number. The power of 10 reflects the number of places the decimal would need to move to give the original number.
03

- Recognizing Integer as Exponent

The power of 10 must be an integer. It could either be positive or negative depending on whether the original number was large or small respectively. A positive exponent expresses large numbers, whereas a negative exponent expresses small numbers.

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