What is 7.8×10^5 m/h in kilometers per day?

3.240×10^10 km/day

3.240×10^8 km/day

1.872×10^6 km/day

1.872×10^4 km/day

Question

What is  7.8×10^5 m/h in kilometers per day?

3.240×10^10 km/day

3.240×10^8 ​ km/day ​

1.872×10^6 ​ km/day ​

1.872×10^4 km/day ​

mathstudent55 · Answer

You need to convert meters into kilometers, and hours into days.
Do you know the conversion factors for theses conversions?

blackops2_143 · Answer

not really I'm still learning

blackops2_143 · Answer

@mathstudent55

mathstudent55 · Answer

Ok. Let's start with m and km.
The prefix k in SI means 1000.
1 km = 1000 m

When you divide a number by itself, it equals 1.
For example, 2/2 = 1
5/5 = 1
1000/1000 = 1

Since 1000 m = 1 km, if you divide one side by the other you will get 1 since the two sides are equal.

You can write the conversion as a fraction

$\dfrac{1~km}{1000~m} = \dfrac{1000~m }{1~km} = 1$

Ok so far?

blackops2_143 · Answer

yes

mathstudent55 · Answer

Ok.
We have m and we want km.
We have two conversion fractions to choose from.
We know which one to choose because we need to cancel out m and keep km.
Since m is in the numerator, we need a conversion fraction that has m in the denominator and km in the numerator.

$7.8×10^5 ~\dfrac{m}{h}  \times \dfrac{1~km}{1000~m} $

Do you see how m in the numerator will cancel out m in the denominator, leaving you kn in the numerator?

$7.8×10^5 ~\dfrac{\cancel{m}}{h}  \times \dfrac{1~km}{1000~\cancel{m}} $

mathstudent55 · Answer

^km in the numerator

mathstudent55 · Answer

Now if you look at the units, you will see that we have km/h.
We want km/day, so we still have some conversions to do.

mathstudent55 · Answer

We need this conversion:

24 h = 1 day

Once again, we write it as a fraction.
There are two fractions possible.

$\dfrac{1~day}{24~h} = \dfrac{24~h}{1~day} = 1$

mathstudent55 · Answer

We need to pick the fraction that will cancel out h from the denominator and will gives us day in the denominator.

$7.8×10^5 ~\dfrac{\cancel{m}}{h}  \times \dfrac{1~km}{1000~\cancel{m}} \times \dfrac{24~h}{1~day}$

We chose this fraction on purpose because then the hours will cancel out, and we get day.

$7.8×10^5 ~\dfrac{\cancel{m}}{\cancel h}  \times \dfrac{1~km}{1000~\cancel{m}} \times \dfrac{24~\cancel h}{1~day}$

The only units left are km/day.

Now all you need to do is the arithmetic.

blackops2_143 · Answer

so 1.872×10^4 km/day ​ is the answer right? @mathstudent55

mathstudent55 · Answer

Exactly.
Good job.

mathstudent55 · Answer

This method of converting units is called "dimensional analysis."
It is well worth learning because it makes conversions easy to do.
Because you are always minding the units, you always know whether you need to multiply by the conversion factor or divide by the conversion factor.

blackops2_143 · Answer

okay, thank you so much for your help ^.^

mathstudent55 · Answer

Here is a trivial example.

We know well that 12 in. = 1 ft.

What is 12 ft in inches?
You know the conversion number is 12, but do you multiply the given 12 by 12, or do you divide the given 12 by 12?

This method takes away the guessing

$12~\cancel{ft} \times \dfrac{12~in.}{1~\cancel{ft}} = 144 ~in.$

The only way to cancel out ft and get in. is by multiplying, so you always get the correct answer.

mathstudent55 · Answer

You're welcome.