2.998x10^8 m/s is how many kilometers per hour

QUESTION POSTED AT 02/06/2020 - 01:19 AM

Answered by admin AT 02/06/2020 - 01:19 AM

1.079 x 10⁹ km/h

Further explanation

2.998 x 10⁸ m/s has been known as the speed of light.

Let us convert the unit m/s to km/hour.

Change in unit length:

If 1 km = 1,000 cm, then \boxed{ \ 1 \ cm = 0.001 \ km \ } \rightarrow \boxed{ \ 1 \ cm = 10^{-3} \ km \ }

Change in unit time:

If \boxed{ \ 1 \ hour = 60 \ minutes = 3,600 \ seconds \ }, then \boxed{ \ 1 \ second = \frac{1}{3,600} \ hours \ }

The Process:

\boxed{ \ 2.998 \times 10^8 \ \frac{m}{s} \times \frac{10^{-3} \ km}{1 \ m} \times \frac{1 \ s}{\frac{1}{3,600} \ hours} \ }

\boxed{ \ 2.998 \times 10^8 \times 10^{-3} \ km \times \frac{3,600}{hours} \ }

\boxed{ \ 10,792.8 \10 \times 10^5 \ \frac{km}{hour} \ }

Remember, we must write the results in scientific notation, i.e.,

\boxed{\ a \times 10^b \ } \rightarrow \boxed{ \ 1 \leq a < 10 \ } \rightarrow \boxed{ \ b \ must \ be \ an \ integer \ }

Thus the result of unit conversion is

\boxed{ \ \boxed{ \ 2.998 \times 10^8 \ m/s \ } \rightarrow \boxed{ \ 1.079 \times 10^9 \ km/h} \ }

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Keywords: speed of light, convert, m/s to km/h, unit length, time, hours, minutes, second, scientific notation

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