Question

Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10n where 1 ≤ a < 10 and is a one-digit number.(1 point) Responses 3 × 10−9 3 times 10 superscript negative 9 baseline 3 × 10−8 3 times 10 superscript negative 8 baseline 3 × 109 3 times 10 superscript 9 baseline 3 × 108

Answer 1

To express the number 0.000000003 in the form of \( a \times 10^n \), we need to write it as a value between 1 and 10 multiplied by a power of 10.

The number \( 0.000000003 \) can be converted as follows:

1. Identify the decimal point: \( 0.000000003 \).
2. Move the decimal point to the right until we have a number between 1 and 10. Moving the decimal point 9 places to the right gives us \( 3 \).
3. Each time we move the decimal point to the right, we decrease the exponent of 10 by 1. Since we moved it 9 places, we have \( 3 \times 10^{-9} \).

Thus, the number can be expressed as:

\[ 3 \times 10^{-9} \]

So the correct response is:

3 × 10⁻⁹