The equivalent of 10095 m/s is 6.2728 mi/s.
Further Explanation
To get the answer to this problem we use the conversion factor for meters to miles: 1609.34 m = 1 mi.
Setting up the dimensional analysis:
[tex]speed \ = 10095 \frac{m}{s} \times \frac{1 \ mi}{1609.34 \ m}\\[/tex]
We put the number of meters in the numerator so that the unit (meter) may be cancelled.
By multiplying the given by the number of meters in mile, we arrive at the answer:
[tex]\boxed {\boxed {speed = 6.2728 \ \frac{mi}{s}}}[/tex]
Since the given has 5 significant figures, the final answer must also have five significant figures.
Additional Example:
Sometimes the problem requires the conversion of both numerator and denominator. Below is a worked example for these kinds of question.
The conversion factor relating miles to meters is 1mile=1610m. The speed of light is 3.00×108 m/s. How fast is this in miles per hour (miles/h)?
The problem gives the conversion factor for miles to meter:
1 mi =1610 m
To convert the speed of light into the desired unit the following steps must be carried out:
These conversion may be done individually or simultaneously in a single dimensional analysis equation. The equation below shows the simultaneous conversion in one equation:
[tex]speed \ of \ light = 3.00 \times 10^8 \ \frac{m}{s} \times \frac{1 \ mi}{1610 \ m} \times \frac{60 \ s}{1 \ min} \times \frac{60 \ min}{1 \ h}\\\\\boxed {speed \ of \ light = 6.71 \times 10^8 \ \frac{mi}{h}}[/tex]
Since the answer must be expressed with only 3 significant figures, the final answer is:
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Keywords: miles, meters, conversion
