FTCE General Knowledge Math Practice Test

What is the scientific notation for the number 0.000000975?

1. 9.75 x 10⁻⁷

2. 9.75 x 10⁶

3. 97.5 x 10⁻⁹

4. 0.975 x 10⁻⁶

The correct answer is: 9.75 x 10⁻⁷

The correct scientific notation for the number 0.000000975 is expressed as 9.75 x 10⁻⁷. In scientific notation, a number is represented as a product of a coefficient and a power of ten. The coefficient must be a number greater than or equal to 1 and less than 10. In this case, to convert 0.000000975 into scientific notation, you first shift the decimal point to the right until you have a number between 1 and 10. Moving the decimal point 7 places to the right gives you 9.75. Since you moved the decimal to the right, the exponent for the power of ten is negative, indicating a value less than one. Thus, you get 9.75 x 10 to the power of negative seven. The other options do not properly represent the number in scientific notation. The second choice involves an exponent that does not accurately reflect the original value, while the third choice incorrectly shifts the decimal to yield a coefficient greater than 10. The last choice also misplaces the decimal and the exponent in a way that does not correspond to the initial numerical value.