Question

The speed of light is 3.00x10^8m/s. How fast is this in mph? Use the conversion 1mile = 1610m.

Answer 1

Use the conversion factors: 1 mile = 1610 meters, 1 min = 60 seconds, 1 hour = 60 minutes. Using these factors,
       (3.00 x 10^8 m/s) x (1 mile / 1610 meter) x (60 s/ 1 min) x (60 min/ 1 h)
                           = 6.7x10^8 mph
Therefore, the speed of light in mph is approximately 6.7x10^8 mph. 

Answer 2

6.71 x 10⁸ mph.

Further explanation

Given:

The speed of light is 3.00 x 10⁸ m/s

Question:

How fast is this in mph?

Use the conversion 1 mile = 1,610 m.

Problem solving:

We will solve the problem here about the conversion of length and time units.

To solve our case, consider the following unit length and time conversions.

Lenght (or Distance)

• $\boxed{ \ 1 \ km = 1,000 \ m \ }$
• $\boxed{ \ 1 \ mile = 1,610 \ m \ }$ especially in our case this time.

Time

• $\boxed{ \ 1 \ hour = 60 \ minutes \ }$
• $\boxed{ \ 1 \ minute = 60 \ seconds \ }$
• $\boxed{ \ 1 \ hour = 3,600 \ seconds \ }$

Convert m/s to mph

$\boxed{ \ 3.00 \times 10^8 \ \frac{m}{s} \times \frac{1 \ mile}{1,610 \ m} \times \frac{3,600 \ s}{1 \ hour} \ }$

$\boxed{ \ 3.00 \times 10^8 \times 2.2360 \ \frac{mi}{hr} \ }$

$\boxed{ \ 6.708 \times 10^8 \ mph \ }$

After rounding to 2 decimal places, the result is $\boxed{\boxed{ \ 6.71 \times 10^8 \ mph \ }}$

Convert m/s to km/hr (this is extra, as an exercise for you)

$\boxed{ \ 3.00 \times 10^8 \ \frac{m}{s} \times \frac{1 \ km}{1,000 \ m} \times \frac{3,600 \ s}{1 \ hr} \ }$

$\boxed{ \ 3.00 \times 10^8 \times 3.6 \ \frac{km}{hr} \ }$

$\boxed{ \ 10.8 \times 10^8 \ \frac{km}{hr} \ }$

Adjust it again to fit the scientific notation.

$\boxed{ \ 1.08 \times 10^9 \ \frac{km}{hr} \ }$

The result is $\boxed{\boxed{ \ 1.08 \times 10^9 \ \frac{km}{hr} \ }}$

Learn more

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Keywords: the speed of light is 3.00 x 10⁸ m/s, in vacuum, how fast, is this in mph? mile per hour, conversion, length, time, 1 mile = 1,610 m, the scientific notation