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Chapter 0: Problem 126

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

Short Answer

Expert verified
A number is written in scientific notation if it is the product of a number between 1 and 10 (inclusive) and a power of 10, and the part of the number that is between 1 and 10 (inclusive) contains not more than one digit before the decimal point and any numbers of digits after it.

Step by step solution

01

Identification

Firstly, identify whether the number consists of a part that is between 1 and 10 (inclusive) and another part that is a power of 10. For example, in \( 1.23 * 10^4 \), 1.23 is the digit between 1 and 10 and \( 10^4 \) is the power of 10.
02

Verification

Secondly, verify if the part of the number that is between 1 and 10 (inclusive) contains not more than one digit before the decimal point and any numbers of digits after it. In the example \( 1.23 * 10^4 \), there is only one digit (1) before the decimal point and two digits (23) after it in 1.23.
03

Agreement

Lastly, confirm if the format of the number fits into the condition for scientific notation. Both conditions (from Step 1 and Step 2) must meet for the number to be in scientific notation. By checking both conditions, the number \( 1.23 * 10^4 \) can be determined as being written in scientific notation

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