Converting units in scientific notation to other units.

In summary, the conversation discusses converting units of velocity and energy. The process of converting units is explained using equations and conversion factors. The final answer is obtained by multiplying the given value by the appropriate conversion factors and simplifying the units. The methods used can be applied to other unit conversions.
  • #1
CinderTwig
2
0
I'm having some trouble with a few problems that I'd really appreciate some help with.

1.) The velocity of a space shuttle is 8 x 10^3 meters/seconds

I have to convert this to kilometers/hours. I know there are 1000 meters in a kilometer, and 3600 seconds in an hour.

Next I have to convert meters/seconds to miles per hour!

However, I don't know how to put these into an equation to solve. :( The same goes for the following problem:

2.) 3 x 10^-1 joules/minutes

How many watts is this?

I know 1 watt = 1 joule/seconds, but again don't know how to put it into an equation.

The next part is how many miliwatts is produced?

I am just looking for how to put these into a solvable equation--I can take it from there. :)

Help would be greatly appreciated!
 
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  • #2
It's just a matter of being careful about which way up you have the conversions

8x10^3 m/s = 8000 m/s
There are 1000m in a km = 1000m/km, we want an answer with km on the top - so we need to do

8000 m/s / 1000 m/km = 8 km/s (remember something divided on the bottom goes on the top - just like fractions.
Then there are 1.6km in a mile so divide by 1.6km/mi = 8km/s / 1.6km/mi = 5km/s
 
  • #3
If you have [tex]x .\frac{m}{s}[/tex] then if you want to change anything you need to keep the fraction balanced, as in if the numerator is changed, the denominator needs to be changed in the same way, for e.g. converting to km/s (1km=1000m):

[tex]\frac{x}{1000}. \frac{1000m}{s}[/tex]

[tex]\frac{x}{1000}. \frac{km}{s}[/tex]

Now convert to km/h with 1h=3600s:

[tex]\frac{3600x}{1000}. \frac{km}{3600s}[/tex]

[tex]\frac{3600x}{1000}. \frac{km}{h}[/tex]

Now just simplify and you have [tex]3.6x. \frac{km}{h}[/tex]

This is basically saying that x m/s = 3.6x km/h

Try this for the rest :smile:
 
  • #4
Or use conversion factors/labels :smile:

[tex]\frac{8\times 10^3 ~meters}{1 ~second}\left(\frac{1 ~kilometer}{10^3 ~meters}\right)\left(\frac{3600 ~seconds}{1 ~hour}\right)[/tex]

It's easy to keep track of what units cancels and what you have left to multiply or divide.
 
  • #5
The best explanation I've heard makes use of equations that convert from one unit to another. In your first problem you need to convert meters to miles, and seconds to hours.

The two equations we need are
1 mile = 1609.344 m.
1 hr = 3600 sec

In the first equation we can divide both sides of the equation by "1 mile" to get
1 = 1609.344 m/mi.

Alternatively, we can divide by "1609.344 meters" to get
[tex]\frac{1 mi}{1609.344 m} = 1[/tex]

In the second equation we can proceed similarly to get
1 = 3600 sec/hr or
[tex]\frac{1 hr}{3600 sec} = 1[/tex]

Since these expressions are all equal to 1, we can multiply anything by them without changing its value.

Your original expression is 8 * 103 m/sec. Since we need to convert m/sec to mi/hr, we need to cancel m and sec and end up in units of mi/hr.

To cancel the m (meters) I need the conversion that involves mi/m. To cancel the sec, I need the conversion that involves sec/hr.

[tex]8 * 10^3 \frac{m}{sec} * \frac{1 mi}{1609.344 m} * \frac{3600 sec}{1 hr}[/tex]
[tex]= 8 * 10^3 * \frac{1}{1609.344} * \frac{3600}{1} * \frac{m}{sec} * \frac{mi}{m} * \frac{sec}{hr}[/tex]

As you can see, the m units cancel, and the sec units cancel, and we're left with units of mi/hr. The numbers multiply to 17.89549034 * 103 mi/hr, or 1.789549034 * 104 mi/hr = 17895.49034 mi/hr.
 
  • #6
Ahh, thank you all very much for the help! :) I was able to solve the problems alright.
 

1. How do I convert a number in scientific notation to a different unit?

To convert a number in scientific notation to a different unit, you first need to determine the power of 10 in the original unit. Then, you can use the conversion factor to multiply the original number by the appropriate power of 10 in the new unit.

2. What is the process for converting units in scientific notation?

The process for converting units in scientific notation involves converting the original number to standard form, determining the power of 10 in the original unit, and then using a conversion factor to convert to the desired unit.

3. Can units be converted if they have different powers of 10?

Yes, units with different powers of 10 can be converted using the appropriate conversion factor. The power of 10 in the original unit must be taken into account when determining the conversion factor.

4. How can I check if I have converted units correctly in scientific notation?

To check if units have been converted correctly in scientific notation, you can convert the new unit back to the original unit and compare the result to the original number. The converted number should be the same as the original number in scientific notation.

5. Are there any tips for remembering the conversion process for units in scientific notation?

One tip for remembering the conversion process for units in scientific notation is to practice converting numbers with different powers of 10. It can also be helpful to remember that moving the decimal point to the left increases the power of 10, while moving it to the right decreases the power of 10.

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