FTCE General Knowledge Math Practice Test

What is the scientific notation for 0.00397?

1. 3.97 x 10³

2. 3.97 x 10²

3. 3.97 x 10^-3

4. 39.7 x 10^-4

The correct answer is: 3.97 x 10^-3

The correct choice is the one that properly expresses the decimal number 0.00397 in scientific notation. In scientific notation, a number is written in the form of \(a \times 10^n\), where \(a\) is a number greater than or equal to 1 and less than 10, and \(n\) is an integer. To convert 0.00397 to scientific notation, you need to shift the decimal point to the right until you have a number between 1 and 10. In this case, moving the decimal point to the right three places transforms 0.00397 into 3.97. Since you moved the decimal three places to the right, you represent this adjustment by using a negative exponent of 10. Therefore, it becomes \(3.97 \times 10^{-3}\). This notation indicates that 0.00397 is equivalent to multiplying 3.97 by \(10^{-3}\), which is a way of expressing that you have a small number. Thus, the representation accurately captures the original value in a concise format.