Question

Roughly it takes light less than 0.000000003 are they second to travel a 1 m distance express this number in the form of times 10 power of n where one is less than a and less than 10 and is a one digit number with the answer be 3×10 negative power of 83×10 power of 93×10 power of eight or 3×10 negative power of nine

Answer 1

To express the time it takes for light to travel 1 meter in the form of \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer, we need to first understand the value you provided: "it takes light less than 0.000000003 seconds."

This number can be rewritten in scientific notation.

1. Convert 0.000000003 seconds into scientific notation:
   • Move the decimal point 9 places to the right: \[ 0.000000003 = 3.0 \times 10^{-9} \text{ seconds} \]

So, the travel time for light to cover 1 meter is approximately \( 3 \times 10^{-9} \) seconds.

Now let's check your provided options:

1. \( 3 \times 10^{-8} \)
2. \( 3 \times 10^{-9} \)
3. \( 3 \times 10^{8} \)
4. \( 3 \times 10^{9} \)

The correct representation for the time it takes light to travel 1 meter is: \[ \text{Answer: } 3 \times 10^{-9} \]

Thus, the correct option is \( 3 \times 10^{-9} \).