FTCE Professional Education Practice Exam

Which scientific notation represents the decimal 0.00397?

1. 3.97 x 10^2

2. 0.397 x 10^-2

3. 3.97 x 10^-3

4. 39.7 x 10^-4

The correct answer is: 3.97 x 10^-3

The scientific notation for a decimal number typically takes the form \( a \times 10^n \), where \( a \) is a number greater than or equal to 1 and less than 10, and \( n \) is an integer that indicates how many places the decimal point has been moved. In the case of the decimal 0.00397, to convert this to scientific notation, you would first shift the decimal point to the right until it is positioned after the first non-zero digit, which is 3. This gives you 3.97. Moving the decimal point three places to the right means that the exponent on the 10 will be negative three, indicating that the original number is less than 1. Therefore, the correct scientific notation is \( 3.97 \times 10^{-3} \), aligning perfectly with the choice provided. This notation communicates that 0.00397 can also be understood as 3.97 multiplied by a factor of \( 10^{-3} \), highlighting its true scale in relation to powers of ten. The other choices either misrepresent the position of the decimal point or do not uphold the standard format of scientific notation, leading to incorrect representations of the number 0