QuestionHow far does sound travel in $3 \times 10^{10}$ seconds at $3.4 \times 10^{2}$ m/s? Show the calculator's answer.

Studdy Solution

STEP 1

Assumptions1. The speed of sound is $3.4 \times10^{}$ meters per second. The time for which we need to calculate the distance is $3 \times10^{10}$ seconds3. The distance is calculated by multiplying the speed of sound by the time

STEP 2

We need to find the distance travelled by sound. We can do this by multiplying the speed of sound by the time.
$Distance = Speed\, of\, sound \times Time$

STEP 3

Now, plug in the given values for the speed of sound and time to calculate the distance.
$Distance =3. \times10^{2}\, m/s \times3 \times10^{10}\, s$

STEP 4

To simplify the multiplication of numbers in scientific notation, we can multiply the coefficients (the numbers before the exponent) and add the exponents.
$Distance = (3.4 \times3) \times10^{(2+10)}\, m$

STEP 5

Calculate the distance.
$Distance =10.2 \times10^{12}\, m$

STEP 6

The calculator will show the answer in scientific notation. To convert the above result into scientific notation, we need to have only one digit before the decimal point. So, we move the decimal point one place to the left, and add one to the exponent.
$Distance =1.02 \times10^{13}\, m$ The calculator will show the answer as $1.02 \times10^{13}$ meters.

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