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 where
and is a onedigit number. (1 point)
a × 10
n
1 ≤ a < 10
3 × 10
8
3 × 10
−8
3 × 10
9
3 × 10
−9

Answer 1

Oh come on. We all know c= about 3*10^8 meters/ second
now here:
0.000000003 of a second / meter = 3 * 10^-9 seconds/ meter
which is 1/ (3*10^-9) = (1/3)*10^9 = 0.333333.... * 10^9 = 3 * 10^8 meters / second, which of course you knew.

Answer 2

To express the number \( 0.000000003 \) in the form \( a \times 10^n \) where \( 1 \leq a < 10 \), we can rewrite this number.

First, we notice that \( 0.000000003 \) can be rewritten in scientific notation:

\[
0.000000003 = 3 \times 10^{-9}
\]

Now, here \( a = 3 \) and \( n = -9 \), which satisfies the condition \( 1 \leq a < 10 \).

Thus, the correct expression is:

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

So the answer from the given options is:

**\( 3 \times 10^{-9} \)**.

Answer 3

You're correct! The speed of light \( c \) is approximately \( 3 \times 10^8 \) meters per second.

If it takes light \( 0.000000003 \) seconds (or \( 3 \times 10^{-9} \) seconds) to travel a distance of 1 meter, then the speed can be calculated as follows:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ meter}}{3 \times 10^{-9} \text{ seconds}} = \frac{1}{3 \times 10^{-9}} \text{ meters/second}
\]

This simplifies to:

\[
\frac{1}{3} \times 10^{9} \text{ meters/second} \approx 0.3333 \times 10^{9} \text{ meters/second}
\]

This brings us back to:

\[
3 \times 10^{8} \text{ meters/second}
\]

You have accurately translated the time taken for light to travel 1 meter into speed, demonstrating that light indeed travels at this incredible speed. Thank you for your insightful observation!