Questions on Algebra: Unit Conversion answered by real tutors!

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Convert 2.9g/cm^3 to milligrams per cubic millimeter.
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A millimeter is 1/10 of a centimeter, so a cubic centimeter (cc) is 10 mms on each side. That means a cc is 10x10x10 cubic millimeters, = 1000 cubic millimeters.
If there are 2.9 g in a cc, there is 1/1000 of that in a volume that's 1/1000 of a cm^3. See that?
So, 2.9g/cc is 0.0029g/mm^3.
It might seem difficult, but it's better than inches, feet, and 16ths of inches.
It's just moving the decimal point.

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mr winkle jogs 4 miles and then turns and jogs back to his starting point.the first part of his jog he was going mostly uphill so his speed was 2 miles per hr slower than his speed returning.if the total time he spent was 1 2/3 hour find his rate going and his rate returning
:
Let s = speed returning
then
(s-2) = speed up the hill
:
Write a time equation: Time = dist/speed
;
Time return + time out = 1 & 2/3 hrs
+ = 1
:
+ =
Multiply equation by 3s(s-2) to get rid of the denominators, results
4*3(s-2) + 4*3s = 5s(s-2)
:
12s - 24 + 12s = 5s^2 - 10s
:
24s - 24 = 5s^2 - 10s
:
0 = 5s^2 - 10s - 24s + 24
:
A quadratic equation, solve for s
5s^2 - 34s + 24 = 0
Factors to:
(5s - 4)(s - 6) = 0
:
5s = 4
s = ; this solution makes no sense.
and
s = 6 mph is his return speed, then obviously 4 mph is his up-hill speed
:
:
Check solution by find the times
4/6 + 4/4 = 1 hrs

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.
38cm --------> feet

, ANSWER
Thank you,
Jojo

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1 ft=(1/5280)mi
44 ft=(44/5280)mi
1 sec=(1/60)*(1/60)=(1/3600)hr
(1 sec=1/60 min and 1 min=1/60 hr, so 1 sec=1/3600 hr)
Now lets put it togethr
44 ft/sec=(44/5280)mi/(1/3600)hr
(44/5280)/(1/3600)=(multiply numerator and denominator by (3600/1) to get rid of the complex fraction:
(44/5280)*(3600/1)/(1/3600)*(3600/1) mi/hr=
(44*3600)/5280 mi/hr=
158400/5280 mi/hr= 30 mi/hr
CK my Math----I didn't come up with 38 mi/hr but hopefully you see the approach.
P.S. I think that 30 mi/hr is correct.
Hope this helps---ptaylor

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the easiest way is to think about which unit is smaller or larger
__ with fractional quantities (like ft/sec or dollars/gal), do the numerator and denominator seperately

miles are larger than feet, so there will be fewer for the same distance
__ this means multiplying feet by a fraction LESS than one

the same is true for hours and seconds
__ but in this case, the seconds are in the denominator
__ so a smaller denominator means a larger fraction

44ft/sec __ there are 60 sec in a min, so you can go 60 times as far as in a sec
__ 44ft/sec = 2640ft/min
__ there are 60 min in an hr, so you can go 60 times as far as in a min
__ 2640ft/sec = 158400ft/hr

there are 5280ft in a mi __ 158400ft/hr / 5280ft/mi = 30mi/hr


you can also use "conversion factors" incorporating units
__ the units cancel like variables in multiplying fractions

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unit multipliers always have the same measure on opposite sides of the dividing line.
example:
60 seconds = 1 minute is the equation you start with to create the unit multiplier as required.
if you have x per second, you would multiply by 60 seconds per minute.
in equation form, this works out to be:

as you can see the seconds are on opposite sides of the dividing line.
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in your problem you have:
44 feet per seconds = how many miles per hour.
equations you need are:
1 minutes = 60 seconds
1 hour = 60 minutes
1 mile = 5280 feet
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if we work this out piece by piece, we get the following:
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first we convert from feet per second to feet per minute.

-----
next we convert from feet per minute to feet per hour.

-----
next we want to convert from feet to miles.

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the common measure is always on opposite sides of the dividing line.
means the same thing as 30 miles per hour.
you create the fraction that way.
44 feet per second = etc.
always start with the equality, like 1 minute = 60 seconds, and then decide which unit multiplier you want to create from that.
hope this helps.
-----

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1 cubic foot=12*12*12=1,728 cubic in.
273*1,728=471,744 cubic in. in 273 cubic ft.
1 cubic yard=3*3*3=27 cubic ft.
273/27=10.111 cubic yd. in 273 cubic ft.

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you would first convert centimeters to meters using the unit multiplier from the equation 100 centimeters = 1 meter.
you would then convert meters to kilometers using the unit multiplier from the equation 1000 meters = 1 kilometer.
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the unit multiplier is a fraction that is always equal to 1.
this comes from the general equation of a = b.
if a = b, then a/b = 1, and b/a = 1.
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in your problem, you have 365220 centimeters.
it is in centimeters and it is the numerator of the fraction 365220 / 1.
-----
the conversion equation from centimeters to meters is:
100 centimeters = 1 meter.
-----
the unit multiplier can be either:
100 centimeters / 1 meter
or:
1 meter / 100 centimeters
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since your number is the numerator and it is in centimeters, then the unit multiplier you want to use would be 1 meter / 100 centimeters.
this keeps the denominator of the unit multiplier the same measure as the numerator of the number being converted.
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365220 centimeters * (1 meter / 100 centimeters) = 3652.20 meters.
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your number is now 3652.20 meters and you want to convert this to kilometers.
-----
the conversion equation from meters to kilometers is:
1000 meters = 1 kilometer.
-----
the unit multiplier can be either:
1000 meters / 1 kilometer
or:
1 kilometer / 1000 meters
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since your number is in meters and it is the numerator of the fraction 3652.20/1, you want your unit multiplier to have meters as the denominator.
-----
your unit multiplier would be 1 kilometer / 1000 meters.
-----
3652.20 meters * (1 kilometer / 1000 meters) = 3.65220 kilometers.
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conversion is complete.
-----
you started off in centimeters.
you multiplied by 1 meter / 100 centimeters to convert to meters.
you multiplied by 1 kilometer / 1000 meters to convert to kilometers.
-----
your answer is:
365220 centimeters = 3.65220 kilometers
-----

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There are cm in a meter and
meters in a kilometer
cm x (meter / cm) x ( km / meters)
km
km answer

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1/8 + 1/4 + 3/8 + 3/16
2/16 + 4/16 + 6/16 + 3/16 = 15/16
So the 3 CDs are 1/16
3*16=48 CDs were arrainged.
.
Ed

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jazz CDs:
rap CDs:
rock CDs:
popo CDs:

There are 3/16 left and 3 CDs left
Let T = total number of CDs


Tony arranged 16 CDs

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Use six unit multipliers to convert 6 cubic yards to cubic inches

     Start by writing  as  and
     then as , and then put it over , 
     and we start with this:



     We treat a unit just as we would treat a number or
     letter in algebra which is multiplied by a number. So we 
     want to cancel away the three  factors and bring 
     in .  We know that .  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by  three times, one for
     each  factor.  

 

     and then the 's cancel, like this:

 



     Now we want to cancel away the three  factors
     and bring in .  We know that . 
     So there are two possible unit multipliers which we can 
     make with that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by  three times, one for
     each  factor.  

 

     Then the 's cancel:



     So all we have left is:



     Multiply all that out with a calculator,
     and replace the  by 



     or 279936 cubic inches.

     Edwin

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EDWIN'S SOLUTION:
Convert 710m. to inches. (Go from m to cm to in)

     Start by putting  over :



     Now we want to cancel away the  and bring in
     .  We know that .  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by .  

 

     and then the 's cancel, like this




     Now we want to cancel away the  and bring in
     .  We know that .  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by .  


 
     Then the 's cancel:



     So we have left:



     Multiply the numerators and the denominators:









     You probably should round that off. Ask your teacher 
     how he or she wants it rounded.

     Edwin

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I can only tell you how I do it. I had a very good teacher in
high school demonstrate it, and it stuck pretty good in
college.
The best way to learn is do do REALLY long coversions.
Convert cm/sec to miles/hr
OK-I've got to get rid of that cm on top
I can do it like this:
(cm)(miles/cm)
Stop and think- Why can I do this? The only way I can do it
and not change what I started out with is if the (cm/mile)=1,
then (cm)x1 = (cm).
So, as long as I have calculated the EXACT number of cm in 1 mile
or the EXACT fraction of a mile in 1 cm, then I am doing (cm)x1 = (cm)
OK
(cm)(miles/cm) = miles because the cm on top cancels with the
one on the bottom.But what if I don't know the conversion (miles/cm)?
Maybe I should try (meters/cm)
(cm)(meters/cm) = meters. But I want miles. I've got more work to do
(cm)(meters/cm)(miles/meter) = miles
Can you see that cm on top and bottom are the same as (cm/cm)
and meters on top and bottom are the same as (meters/meters)?
Again, what if I don't know the conversion (miles/meter)?
What if I only know (feet/meter)? Then I can do:
(cm)(meters/cm)(feet/meter)(miles/feet) = miles
You can look at it like this:
(cm/cm)(meters/meters)(feet/feet)(miles)
I'm left with miles which is what I want, but
it only works if my conversions are EXACTLY correct
How many miles are in 1 foot?
A very small fraction of a mile: miles to be exact
How many feet are in a meter? Around , but you can look it up.
If you get the idea of units cancelling on the top
and bottom, you're OK. Keep practicing long conversions to get it
right. Remember if somewhere you say (11 inches/1 foot), you'll
be wrong even if your units are correct

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Use the following formula to factor it.

*****************************************

=
=
=

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Note that:
1 kilograms = 100 centigrams
So:
1 centigram = 1/100 kilogram.
Thus 187,625.8 centigrams = 187,625.8/100 kilograms = 1,876.258 kilograms

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400*300=$120,000 Answer.

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1qt/min = (?)gal/week
:
We find the no. of min in 1 week, then change quarts to gallons
2520 gal/week

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0.0450 km to cm?


Thank you,
Jojo

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There is another way of finding your answer. Please know that the answer given previously is correct. Just showing you another way to get your answer.
1 mile = 63360 inches
Therefore, you may multiply 63360 * 0.600 which equals 380160
Hope the examples help you.

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Step 1: Realize that there are 5,280 ft per mile and convert to feet...
0.0600 miles x 5,280 ft per mile = 316.8 FEET
Step 2: Realize that there are 12 inches per foot and convert to inches...
316.8 ft x 12 inches per foot = 3,801.6 inches
So there are 3,801.6 inches in 0.0600 miles.

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.6214 miles=1 kilometer.

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convert to

Begin with



then write the  as 



Now we know that , so we make a
unit fraction (one that equals 1) from that. We
will put the  in the denominator so
it will cancel with the  in the numerator.
So we will multiply by 

×

and, as you see, the grams 's cancel out:

×

Now we know that , so we make a
unit fraction (one that equals 1) from that. We
will put the  in the numerator so
it will cancel with the  in the denominator.
So we will multiply by .
However since there are three factors of ,
we will multiply it three times:

××××

Now you see that the 's all cancel out

××××













Edwin

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Use two unit multipliers to convert 366 centimeters to feet.
-----------------
An inch is 2.54 cm exactly
A foot is 12 inches exactly.
366/2.54 = # of inches
366/(2.54*12) = # of feet
= 12.00787 feet

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3/6=1/2
18/36=1/2

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First, let's convert the denominator of "hour" to "seconds":
72 miles 1 hour 1 min
--------- x ------ x ------
hour 60 min 60 sec
.
Note: notice how the like-units cancel leaving:
72 miles
---------
36 sec
.
Now, let's convert the numerator of "miles" to "meters":
72 mile 5280 ft
-------- x --------- x ------------
36 sec 1 mile 1 ft
.
Again, notice how the units cancel leaving:
(72*5280*0.3048) meters0.3048 meter
-----------------------
36 sec
Resulting in:
115872.768 meters
------------------
36 sec
Finally, we get:
3218.688 meters/sec

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unit rate * time = number of units
the above equation is a necessary starting point.
working from that.....
let unit rate = R.
let number of units = U
let time = T
the algebraic form of the equation is then R*T=U
the unit rate is expressed in units per time
as an example:
let U = 3000
let R = 50 units per hour
let T = total number of hours
putting the values in the formula R*T=U, we get
50*T=3000
solving for T, we get
T=3000/50
T=60 hours
proving the formula is correct, we substitute all values into the original equation.
since R*T=U, and R = 50 units per hour, T = 60 hours, U = 3000 units, we get
50*60=3000 which translates to
50 units per hour * 60 hours produces 3000 units.
since 50*60 = 3000, the equation becomes
3000 = 3000
which proves the formula is correct.

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Two things you are expected to know:
there are 5280 feet per mile (5280 feet/1 mile)
and
there is 1 yard per 3 feet (1 yard/ 3 feet)
.
2.3 miles * (5280 feet/1 mile) * (1 yard/ 3 feet)
Notice the units cancel leaving:
(2.3 * 5280)/3 yards
(2.3 * 1760) yards
4048 yards

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thank you,
Jojo

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my question is use two unit multipliers to conver 10,000 inches to miles i know that 5280 inches equal a mile but im not sure how the skeleton or hot to convert them to get the answer i need help with those problems
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A mile is 5280 feet, not inches.
To do unit conversions, include the units.
10000 inches x 1 ft/12 inches * 1 mile/5280 feet
The inches cancel, the feet cancel, you get the miles.
10000/(12*5280)
= 0.15783... miles

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Another way of solving just use instead of


cubic units (cu.cm)
Thank you,
Jojo

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must determine the volume of a 250mL beaker on two different ways.
Height= 9.03 cm
Diameter=6.73
Raduis= 3.37
use equation V=pieh to calulate the volume in cubic centimeter
-------------
V = PI*r^2*h
V = PI*3.37*3.37*9.03
v = 322.18 cc

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Stanbon answered this question yesterday. Go to our tutors. Look for Stanbon. In his answers you are looking for problem 156643. Good luck.

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Watch your units.
The conversion factor is
(in^3)(1 ft/12 in)^3=1 ft^3/1728 in^3

576 cu. inches = 1/3 cu. ft.

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Consecutive odd integers follow the pattern: , , , , etc...


So if "the sum of 4 consecutive odd integers is 216", then this means that the equation is


Start with the given equation.


Combine like terms on the left side.


Subtract from both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


Go back to the first number (which is the smallest integer of the four)


Plug in


Multiply


Add


----------------------------------------------------------------------

Answer:

So the smallest integer of the group is 51




Check:

51+53+55+57=216

216=216 ... works

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5.7 unks=6.7 tats
47.3 unks=___________tats
Simply,


Thank you,
Jojo

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the average speed is the rate __ rate=distance over time

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30cm (1m /100cm)(1km/1000m) = (30/10^5) = (3/10^4) = 0.0003 km
=====================
Cheers,
Stan H.

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perform the following conversions using unit factoring.
1. 500mL(L/1000mL) = (1/2)L
2. 25cg(g/100cg) = (1/4)g
3. 400mg(g/1000mg)(kg/1000g)= [400/10^6] = (4/10000) = (1/2500)kg
=================
Cheers,
Stan H.

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71K/H*7.5H=532.5K.

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As 1 inch = 25.4 mm, so 1mm = 1/25.4 inch.
1km = 1,000*1m = 1,000*1,000*1mm = 1,000*1,000*(1/25.4)inches = 39,370 inches

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Here's one way to do it:

We know that 1 foot per second = 0.3048 meters per second. So if you want to know how many meters per second there are in 6 feet per second, simply multiply both sides by 6

6*1 foot per second = 6*0.3048 meters per second

6 feet per second = 1.82898 meters per second


So there are approximately 1.82898 meters per second in 6 feet per second.



---------------------------------------------------

Here's another way to do it:

Once again, let's say that we want to find how many meters per second there are in 6 feet per second. So take 6 feet a second and multiply it by the fraction like this




Either way you'll get the same answer. However, I've seen the second method used more since you're able to create more complicated expressions.

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(3-z)(4z^3+6x+2)= (4z^3+6x+2) ganna be (64z+6x+2) ok now 6x+2= 8x+64z= 72xz.
now 3-z = 3-1 coz x=-1 and it's = 2 X 72xz= 144xz..
my answer is 144xz

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(3-z)(4z^3+6x+2)
12z^3+18x+6-3z^4-6xz-2z
-3z^4+12z^3-2z-6xz+18x+6

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1.) 2km to feet
Ans: 2km(0.62 mile/1 km)(5280 ft/1 mi) = [2*0.62*5280]/[1*1*1] = 65472 ft.
--------------------------------------
2.) 375 yards to meters
Ans: 375 yds(3 ft/1 yd)(12 inches/1 ft)(1 meter/39.37inches) =
[375*3*12*1] / [1*1*1*39.36] = 39.36 meters
-----------------------------
3.) 25,200 mm to meter
Ans: 25,200 mm(1 meter/1000 mm) = 25.2 meters
------------------------------------
4.) 85 revolutions over 2 hours to rev over sec
Ans: 85 rev/2 hrs (1 hr/3600 seconds) = 0.0118 rev/sec
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5.) 12 kms. to yards
I'll leave this one to you.
------------------------------
Cheers,
Stan H.