Tutors Answer Your Questions about Unit Conversion Word Problems (FREE)
Question 1165584: Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Explain the rules for multiplication and division to convert units.
How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let's imagine that we measure some quantity 'A', and we find that this quantity is 'a' units, measured in the scale P.
(so, one unit in this scale is P, which we consider as a standard).
We want to express this quantity in the scale Q
(one unit in this scale is Q, which we consider as another standard).
We know that the ratio of quantities P and Q,  , is 'k' (non-dimensional value).
Then the measure of the quantity 'A' in the scale Q (in terms of Q) is
conversion: 'a' units P ---> of units Q, or 'k*a' units Q. (1)
It is how conversion of units works.
Example.
Let 'A' be the quantity '3 hours', so it is a time interval.
The unit (= the scale) which we use for it now is P = 'one hour'.
We want to convert it to minutes.
So, the other scale is Q = 'one minute'.
We know that the ratio =  = 60.
So, in this case 'k' = 60.
You know intuitively that 3 hours = 3*60 = 180 minutes.
Formula (1) converts in this case 3 hours into 3*60 = 180 minutes,
i.e. works in accordance with your intuition, precisely in a way as you expect it.
Usually, for simple units and simple everyday quantities, people make conversion
'in their mind' mentally without any problems.
For more complicated cases/quantities/conceptions, people use their professional expertise.
When they have enough expertise, they make conversion "without thinking"
and practically without errors even in complicated cases.
Exercises to check your understanding
(a) Convert $3.25 to cents.
(b) Convert 425 cents to dollars.
Question 1210377: If you have to mix 1 gallon of water with 1/4 cup of mixing solution, how would you figure out how much you would need if you only use 1 quart of water.
Found 2 solutions by timofer, ikleyn:
Answer by timofer(104) (Show Source):
You can put this solution on YOUR website! "to mix 1 gallon of water with 1/4 cup of mixing solution, how would you figure out how much you would need if you only use 1 quart of water?"
Using 4 quarts of water needs 1/4 cup of "mixing solution".
Using 1 quart of water needs 1/4 of 1/4 cup of "mixing solution".
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
If you have to mix 1 gallon of water with 1/4 cup of mixing solution,
how would you figure out how much you would need if you only use 1 quart of water.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
One gallon is 4 quarts.
Or, in other words, one quart is 1/4 of a gallon.
So, following to your recipe, if you have 1/4 of a gallon of water, you need to mix it
with  =  of a cup of mixing solution, to keep the assigned proportion.
Question 1210150: solve the equation 3x+2/5-2x+3/3=3
Found 3 solutions by mccravyedwin, josgarithmetic, greenestamps:
Answer by mccravyedwin(407)  (Show Source):
Answer by josgarithmetic(39617) (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Without parentheses, we have no idea what the equation really is. Exactly as you show it....
It is possible, but not very likely, that that is what you really wanted.
Proper use of parentheses is important in mathematics....
Re-post, making it clear what the real equation is.
Question 1208693: If x spoons full of spice are needed for y ounces, then how many spoons full of spice are needed for one pound?
Answer by ikleyn(52781) (Show Source):
Question 1205677: A business based in the U.S. pays a consultant based in China 112,000 dollars per year. Assume that the conversion is 1 yuan to 0.14 dollars. What is the consultant's salary in yuan per month?
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
Convert 112,000 dollars to yuan using the conversion factor 1 dollar =  = 7.142857143 yuan.
Then divide the obtained annual compensation in yuan by 12 to get the monthly salary in yuan.
Happy calculations (!)
Question 1203495: A new Community Sports Complex is being built in Alston. The perimeter of the rectangular playing field is 456 yards. The length of the field is 4 yards less than triple the width. What are the dimensions of the playing field?
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
A TWIN problem was just solved today under this link
https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1203492.html
Use it as your TEMPLATE and solve this current problem in the same way.
Question 1203374: a pollen sample weighs 12 grams
and contains 1:5 × 10 to the power nine pollen grains.
calculate the weight of one pollen grain in grams.
give your answer in scientific notation.
Found 3 solutions by ikleyn, math_tutor2020, MathLover1:
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
As I (and other tutors) see this format in your post " 1:5 × 10 to the power nine ", it seems strange.
A normal writing is (probably) " 1.5 × 10 to the power nine ". It is how me (and other tutors) read it.
So, we all read it differently from what we see.
It is just bordering with a crime.
(By the way, it is you who pushes us to this crime)
But what your writing actually means, we do not know and can not know, since you use non-standard format.
(It is the same as if you use chines' hieroglyphs)
We can only guess.
In Math, every word, every symbol and every punctuation sign does matter.
And if some post contains non-standard formatting,
it should be rejected, strictly saying, and reported up to the instance.
So, my question is: from which source did you re-write your number
and what, ACTUALLY, is written in that source ?
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
12 = 1.2 * 10^1
1.5*10^9 = 1.5 billion = 1,500,000,000
There are 8 zeros after the "1,5" portion.
x = weight, in grams, of 1 pollen grain
(1.5*10^9)x = weight of 1.5*10^9 grains = weight of 1.5 billion grains
(1.5*10^9)x = 12 grams
(1.5*10^9)x = (1.2*10^1) grams
(1.5*10^9)x = 1.2*10^1
x = (1.2*10^1)/(1.5*10^9)
x = (1.2/1.5)*10^(1-9)
x = 0.8*10^(-8)
x = (8.0*10^(-1))*10^(-8)
x = 8.0*( 10^(-1)*10^(-8) )
x = 8.0*10^( -1+(-8) )
x = 8.0*10^( -9 )
This is 8 billionths of a gram.
Be sure to not mix up the place value "billions" with "billionths".
How can we interpret such a small number?
If the single pollen grain was 1 billionth of a gram, then we'd need 1 billion grains to get 1 gram collectively.
It's similar to how we need 1000 millimeter pieces to make up a full meter.
Side note: many calculators offer the ability to switch to scientific notation mode.
-------------------------------------------------------------
-------------------------------------------------------------
Answer: 8.0 * 10^(-9) grams
Answer by MathLover1(20849)  (Show Source):
Question 1201723: In 2015, there were approximately 3,741,000 births in a country. Find the birth rate in births per minute. Assuming a population of 388 million, what was the annual birth rate in units of births per 1000 people?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! --------------------------------------------------
2015, there were approximately 3,741,000 births in a country. Find the birth rate in births per minute.
--------------------------------------------------
That starts as 3741000 births per 1 year.
Use whatever you need from these:
1 year = 365.25 days
1 day =24 hours
1 hour = 60 minutes
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website!
In 2015, there were approximately 3,741,000 births in a country. Find the birth rate in births per minute. Assuming a population of 388 million, what was the annual birth rate in units of births per 1000 people?
In 2015, there were approximately 3,741,000 births in year 2015 (Not a leap year)
1 year 365days *24 hours *60 = 525600 minutes
n 525600 minutes ----3,741,000 births
1 minute 3,741,000/525600 =7.11 births
population of 388 million ------------3,741,000 births
for 1000 people how many?
1000*3741000/388,000,000.=9.641 biths /1000
Question 1201446: If the daycare you are working in has 4 one year olds, 7 two year olds, 12 three year olds and 4 four year olds, what is the minimum number of staff which must work there?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52781) (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! If the daycare you are working in has 4 one year olds, 7 two year olds, 12 three year olds and 4 four year olds, what is the minimum number of staff which must work there?
--------------
Probably depends on local laws.
Question 1201377: On a balance scale, a bag of flour on the left side balances with a 5/6 kg weight and 2/7 of a bag of flour
on the right side. The weight, in kg, of a bag of flour is
a) 1/2 b) 25/42 c) 6/7 d) 1 1/6 e) 1 17/25
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
On a balance scale, a bag of flour on the left side balances with a 5/6 kg weight and 2/7 of a bag of flour
on the right side. The weight, in kg, of a bag of flour is
a) 1/2 b) 25/42 c) 6/7 d) 1 1/6 e) 1 17/25
~~~~~~~~~~~~~~~~
Let's assume that "a bag of floor" is a standard weight ( like a "world constant" ).
Then the problem says that 5/7 of a bag of floor weights 5/6 kg.
Hence, 1/7 of a bag of floor weights 1/6 kg
and then a whole bag of floor weights 7/6 kg = 1  kg. ANSWER (option d).
Solved.
Question 1199186: You receive the following prescription order:
Humulin R 33 units/1L
Using a 10mL vial with a concentration of 100units/mL, how many mL will you need to add to a 1000ml bag?
Select one:
Oa. 0.33mLs
Ob. 33mLs
Oc. 3.3mLs
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your concentration available is 33 units to 1 liter.
1 liter = 1000 milliliters.
therefore, the order is for 33 units to 1000 milliliters.
you have a 10 milliliter vial with a concentration of 100 units per milliliter.
you want to add 33 units to 1000 milliliters.
since your vial contains 100 units to 1 milliliter, you need to add .33 milliliters from the vial to the bag.
your ratio is 100/1 = 33 / x
x is the number of milliliters you have to add.
cross multiply to get:
100 * x = 1 * 33
solve for x to get:
x = 33/100 = .33 milliliters
you need to add .33 milliliters from the vial to add 33 units to the bag..
that would be selection Oa.
Question 1199187: If you add 30mL of 1:400 of Solution A to 270mL of water, what is the resulting concentration?
Select one:
Оа. 0.3%
Ob. 0.025%
Oc. 0.35%
Od. 0.15%
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
If you add 30mL of 1:400 of Solution A to 270mL of water, what is the resulting concentration?
Select one:
Оа. 0.3%
Ob. 0.025%
Oc. 0.35%
Od. 0.15%
~~~~~~~~~~~~~~~~~~
30 mL of 1:400 of solution A contain  mL = 0.0748 (rounded) mL of the pure substance A.
When we add 270 mL of water, the total volume becomes 30 + 270 = 300 mL,
with the same amount 0.0748 mL of the pure substance A.
Hence, the final concentration is  = 0.000249333 = 0.00025 (rounded) = 0.025%.
Solved and fully explained.
Question 1199094: An air traffic controller is tracking two planes. To start, Plane A is at an altitude of2609feet and Plane B is at an altitude of3500 feetPlane A is gaining altitude at 60.5 feetper second and Plane B is gaining altitude at40.25feet per second.
Answer by math_tutor2020(3817) (Show Source):
Question 1198077: How many moles of chromium(III) ( Cr3+(aq) ) are present in 0.850 L of 0.0130 M Cr3+(aq) ?
Answer by josgarithmetic(39617) (Show Source):
Question 1197834: Fahrenheit and Kelvin temperature scales are related by the formula K = 5/9 (F - 32) + 273. Solve this equation for F.
A. F = K - 273
B. F = 5/9 (K - 273)
C. F = 5/9 (K - 273) - 33
D. F = 5/9 (K - 273) - 32
E. F = 9/5 (K + 273) + 32
F. F = 9/5 (K - 273) + 32
Answer by ikleyn(52781) (Show Source):
Question 1197727: jA car accelerated from 25 km/hr to 55 km/hr in 30 seconds. What is its acceleration?
Found 3 solutions by Alan3354, MathLover1, ikleyn:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! jA car accelerated from 25 km/hr to 55 km/hr in 30 seconds. What is its acceleration?
----------------------
It's (55 - 25)/30 km/hr per second.
-----
If you want to spec units, then say that.
Answer by MathLover1(20849) (Show Source):
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
A car accelerated from 25 km/hr to 55 km/hr in 30 seconds. What is its acceleration?
~~~~~~~~~~~~
By the definition, an acceleration is the change of speed related to the change of time
a =  = 30*120 = 3600 km/hr^2.
Here 1/120 represents 30 seconds, that comprise 1/120 of an hour.
Solved.
Question 1197592: Gold is selling for $1917 per ounce. How many milligrams of gold can you purchase for one cent?
(16 ounces = 1 lb, and 1 lb = 454 g)
Answer by MathLover1(20849) (Show Source):
Question 1197503: 1. A string is 3 ft. long. How much remains if
a. i inches b. (i-5) inches is cut off?
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
D U P L I C A T E
I just responded once.
Below is the copy of that response.
//////////////////////
(a) remains (3-i) inches, if i < 3;
if i = 3, remains 0 (same as nothing);
if i > 3 or i < 0, then the problem makes no sense.
(b) remains 3 - (i-5) = 8-i inches, if 5 < i < 8;
remains 3 inches, if i = 5;
remains 0 inches, if i = 8;
if i < 5 OR i > 8, then the problem makes no sense.
Solved, with giving you full answers.
Question 1197499: A string is 3 ft. long. How much remains if:
a. i inches
b. (i-5) inches is cut off?
Answer by ikleyn(52781) (Show Source):
Question 1197498: A string is 3 ft. long. How much remains if:
a. i inches
b. (i-5) inches is cut off?
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
(a) remains (3-i) inches, if i < 3;
if i = 3, remains 0 (same as nothing);
if i > 3 or i < 0, then the problem makes no sense.
(b) remains 3 - (i-5) = 8-i inches, if 5 < i < 8;
remains 3 inches, if i = 5;
remains 0 inches, if i = 8;
if i < 5 OR i > 8, then the problem makes no sense.
Solved, with giving you full answers.
Question 1196040: From the Master Formula determine the quantities of ingredients to complete the mixtures.
Ingredient...........Formula Quantity...........Amount Used
Tablets 100mg...........3000...................._____?___tabs
Levigating Agent........10mL .................. _____?___mL
Vehicles...................qs 1L .................. qs 75mL
Answer by ikleyn(52781) (Show Source):
Question 1196007: Convert 52°F to degrees Celsius.round to the nearest tenth of a degree.Here are the formulas.
C = (5/9)*(F-32)
F = (9/5)*C+32
Found 4 solutions by ikleyn, Alan3354, josgarithmetic, math_tutor2020:
Answer by ikleyn(52781) (Show Source):
Answer by Alan3354(69443) (Show Source):
Answer by josgarithmetic(39617) (Show Source):
Answer by math_tutor2020(3817) (Show Source):
Question 1195653: If you randomly select
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
comment from student: i don't need u to teach me anything for a temporary class
just answer the questions u a werido don't nobody care about yo personal opinions!!!
My response: This forum does exist for only one goal: to teach students/visitors.
If you don't need learning, then look for another site.
Question 1194086: Hi!
i am the student of class 6th doing cambridge . i have problem in d1 maths chapter 15 "Statistical Data Handling" and its exercises..
can u explain me some......................................................
Answer by josgarithmetic(39617) (Show Source):
Question 1193642: A piece of Capillary tubing was Calibrated in the Following Manner. A clean Sample of Mass 3.247 g . A thread of Mercury, drawn into the tube a length of 23.75 mm as observed under microscope . The mass of Tube and Mercury was 3.489 g. The Density of Mercury is 13.60 g/cm^3 .Assuming that the capillary bore is a uniform cylinder, find the diameter of the bore if the volume of a cylindrical object is V= pie r^2 h
Answer by ikleyn(52781) (Show Source):
Question 1192665: Use two unit multipliers to write the expression needed to convert 95,000 square feet to square miles. ( do not carry out the actual multiplication)
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52781) (Show Source):
Answer by Boreal(15235)  (Show Source):
Question 1191324: Explain how understanding transformations can help you figure out the domain and range of f(x).
Answer by MathLover1(20849) (Show Source):
Question 1191108: Fifteen millimeters of alcohol is mixed with 3.5 L of water.How many millimeters are there in the mixture?
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
Fifteen millimeters of alcohol is mixed with 3.5 L of water. How many millimeters are there in the mixture?
~~~~~~~~~~~~~~~~
Double check your post.
The volume is not measured in millimeters.
Revise your dimensions; then re-post to the forum.
Please do not post it to me personally.
Question 1189917: The square paper that Yuki is using to make an origami frog has an area of 165 cm2. Find the side length of the paper to the nearest centimeter. (answer with units)
Answer by Boreal(15235) (Show Source):
Question 1189590: In the city of San Miguel on the island of Cozumel, Mexico, there is a museum with a room devoted to pirates and sailing ships. One of the displays shows a log chip - a small triangular, weighted device used by fifteenth- and sixteenth-century sailors to measure speed. The log chip was tied to a rope that was wound up on a reel. The sailors tied evenly spaced knots in the rope. They would then throw the rope overboard and the weight of the log chip would allow the rope to unreel as the boat moved along. The sailors would allow it to unreel for 30 seconds, timed with a sand hourglass. They would then haul the rope in and count the number of knots that had been reeled out. This number was the speed of the boat in knots (nautical miles per hour). If one nautical mile is 6076.10333 feet (one minute of arc of the earth’s circumference), how many feet apart are the knots?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the boat drops anchor at point A.
one end of the rope stays at that point.
the other end of the rope is where the rope is grabbed. this is at point B.
this happens after 30 seconds have elapsed.
the length of the rope from point A to point B is measured.
if the boat was traveling at 1 knot, then the boat was traveling at a speed of 1 nautical mile per hour.
1 nautical mile is 6076.10333 feet.
1 hour is 3600 seconds.
if the boat was traveling at 1 knot, then it would have traveled 6076.10333 feet in 3600 seconds.
since the boat was traveling for 30 seconds then the boat traveled 30 * 6076.10333 / 3600 = 50.63419442 feet.
that would be the length of the rope after 30 seconds.
consequently, each knot on the rope would have to be 50.63419442 feet from another knot on the rope.
assuming that is good, then the number of knots on the rope should be giving the sailors a good idea of how fast they were going.
assuming the boat was traveling at 4 knots, then the boat was traveling at 4 nautical miles per hour.
4 nautical miles per hour is 4 * 6076.10333 feet = 24304.41332 feet.
multiply that by 30/3600 to get 202.5367777 feet.
divide that by 50.63419442 and you get 4 knots.
i used internally stored numbers.
these are rounded to maybe 15 decimal places.
if you use display numbers, they are rounded to maybe 8 decimal places.
my numbers came right on because i used internally stored numbers.
if you tried it with displayed numbers, you might be a little off, but not by much.
most likely the sailors weren't able to get the accuracy shown here, so their speeds were approximate based on how accurately they could measure the distance between knots on the rope.
since the sailing ships of the day probably couldn't do more than 4 or 5 knots, then the maximum length of the rope was probably something less than 300 feet.
let me know if you have any questions.
theo
Question 1189565: Smoking has long been connected to all sorts of horrible diseases such as lung cancer, emphysema, heart disease, and others. It has been estimated that for every cigarette a person smokes, he or she loses anywhere from 10 to 15 minute of his or her life. Assuming the worst (15 minutes of life lost for each cigarette), how much shorter would the life span be of someone who smoked two packs a day for 35 years? (Each pack contains 20 cigarettes.) Assume that there are 365 days in a year and give your answer in years, days, hours, and minutes. (For example: 42 years, 152 days, 7 hours, and 28 minutes.)
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) (Show Source):
Answer by josgarithmetic(39617) (Show Source):
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710
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