Question

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

Answer 1

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

Answer 2

The conversion of $2.998 \times {10^8}{\text{ m/s}}$ into km/hr is $\boxed{1.079 \times {{10}^9}{\text{ km/hr}}}$.

Further Explanation:

Measurements are compared by using some standards called units. These can be fundamental or derived. Fundamental units do not require any other unit to describe them whereas derived units need fundamental units to express themselves. Units like mass and temperature are fundamental ones while density, area, and volume are derived units.

One unit can be converted into another desired unit by multiplying it with a ratio known as the conversion factor. These are the ratios described in the form of fractions.

The given quantity is $2.998 \times {10^8}{\text{ m/s}}$. This is a unit of speed that is defined as the distance travelled per unit time. It implies $2.998 \times {10^8}{\text{ m}}$ of distance is travelled in 1 second.

The distance is to be converted from m to km. The conversion factor for this is,

$1{\text{ m}} = {10^{ - 3}}{\text{ km}}$

Therefore the distance can be calculated as follows:

$\begin{aligned}{\text{Distance}} &= \left( {2.998 \times {{10}^8}{\text{ m}}} \right)\left( {\frac{{{{10}^{ - 3}}{\text{ km}}}}{{1{\text{ m}}}}} \right)\\&= 2.998 \times {10^5}{\text{ km}}\\\end{aligned}$  

The time is to be converted from s to hr. The conversion factor for this is,

 $1{\text{ s}} = \dfrac{1}{{3600}}{\text{ hr}}$

Therefore the time can be calculated as follows:

 $\begin{aligned}{\text{Time}}&= \left( {1{\text{ s}}} \right)\left( {\frac{{1\;{\text{hr}}}}{{3600{\text{ s}}}}} \right)\\&= 0.000278\,{\text{hr}}\\\end{aligned}$

The speed from m/s to km/hr can be converted as follows:

 $\begin{aligned}{\text{Speed}}\left( {{\text{km/hr}}} \right) &= \frac{{2.998 \times {{10}^5}{\text{ km}}}}{{0.000278{\text{ hr}}}}\\&= 1.07928 \times {10^9}{\text{ km/hr}} \\ &\approx 1.079 \times {10^9}{\text{ km/hr}}\\\end{aligned}$

Therefore $2.998 \times {10^8}{\text{ m/s}}$ is equivalent to $1.079 \times {10^9}{\text{ km/hr}}$.

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Answer details:

Grade: Senior School

Chapter: Basic concepts of chemistry

Subject: Chemistry

Keywords: unit, conversion factor, fundamental, derived units, m, km, $2.998*10^8 m/s$, speed, distance, time, 1.079*10^9 km/hr.