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Word Problems

Browse Middle School Measurement
Stars indicate particularly interesting answers or good places to begin browsing.

See also:
      Terms/Units of Measurement

Selected answers to common questions:
    A million/billion seconds.
    Significant figures/digits.
    Unit conversions, unit cancellation.
    Using a protractor, reading a ruler.

4- and 9-liter Pails: How to Measure 7 Liters [05/07/2002]
How can you measure 7 liters using only 4-liter and 9-liter pails? A strategy for solving this kind of problem.

Administering Insulin [07/09/2003]
If a doctor prescribes 30 units of insulin in 500 ml to be administered over 2 hours, how many drops per minute should be administered if the set is calibrated to deliver 20 drops per ml?

Groups and Units: Multiply or Divide? [04/15/2003]
Changing units to other units.

Measurement: Precision vs. Accuracy [01/07/2003]
Using a metric ruler student A measured the length of an object to the nearest tenth (0.1) of a centimeter, while student D measured its length to the nearest centimeter. Which measurement is more accurate?

Measuring Material [07/04/2003]
I need 225 4-inch squares cut from cotton material. If the material is 30 inches wide, how many yards of material will I need?

Operations on Measurement Units [08/21/1998]
Why can we divide distance by time, but not add distance to time?

Reading a Ruler [09/18/1997]
I need to read a ruler, and I can't. Can you help me?

Unit Analysis and Conversion Factors [02/01/2003]
How to convert the following? 7.5 x 10^4 nm to kilometers; 3.9 x 10^5 mg to decigrams; 2.21 x 10^-4 dL to microliters.

Volume to be Infused by Drip Factor [07/02/2003]
A patient is to receive 1440 milliliters of fluid in 24 hours. The drip factor is 15 drops per milliliter. How many drops per minute should the patient receive?

What is a Significant Digit? [12/25/2001]
I came across a question asking for an answer with no more than "2 significant digits" - can you please explain what a significant digit is?

What is a slide rule? [07/27/1997]
What does a slide rule do and how does it work?

2 Square Feet vs. 2 Feet Square [11/22/1998]
What is the difference between 2 square feet and 2 feet square?

About Measurements and Unit Conversion [02/03/2002]
I don't understand measurements.

Accuracy in Measurement [02/08/2002]
Since pi is irrational, either the circumference or the diameter of a circle must be irrational. How is that possible?

Accuracy in Measurement [01/09/2007]
I've heard that it's impossible to measure things exactly, and I don't understand that. How can our world be based on estimations?

Analyzing a Prescription for the Correct Dose [04/27/2005]
A 46 lb child is prescribed 1 Tsp of medicinal syrup three times a day. There are 2 mg of medicine per 5 ml of syrup, and a safe dose is 0.1 mg per kg of body weight. Is the prescribed dose safe?

Benchmarks [03/25/2001]
What is a benchmark? Could you please give me an example?

Calculating Errors in Measurement [08/06/2002]
Suppose you are told that a digital scale measures to the nearest 0.2kg and asked to find the absolute error involved in using the scale to weigh a cat that weighs 7.4 kg.

Changing Units ... and Significant Figures? [08/22/2011]
A student seeks clarity with the significant digits required after converting a measurement from US customary units to metric. Reinforcing how precision applies to measured data, Doctor Peterson walks through an example.

Choosing a Unit of Measurement [05/06/2002]
What's the proper unit of measurement for measuring butterflies?

Comparing Volume and Surface Area [05/01/2002]
Why is it that the surface area of a given rectangular solid can sometimes be greater than the volume of that solid?

Complementary or Supplementary? [04/02/2001]
I keep getting complementary and supplementary mixed up. How can I remember which is which?

Converting Grams to Milliliters [05/12/2006]
How many milliliters would 35 grams of flour fill?

Converting Metric Measurements [11/03/2005]
I don't understand how to convert 50 millimeters into centimeters. Do I multiply 50 by 10 or divide it by 10? How do I decide?

Converting Millimeters to Inches and Back [03/14/2003]
I would like to see how to calculate without a chart.

Converting Units across Measurements [08/31/2010]
How do you convert units to a different measurement? And how do you know how many decimal places to move as a result? Doctor Ian suggests making the multiplication of units explicit, and introduces ratios of two quantities equal to each other.

Converting Units of Measure [7/17/1996]
Find the unit of measure for (3 pounds over 1 square inch) * (144 square inches over 1 square foot)....

Cutting Equal Strips [09/08/2005]
Given five 4 ft by 8 ft rectangular sheets of plywood, how many strips that are 7 1/2 inches wide and 8 feet long could you cut? Each saw cut eliminates 1/16 inch of the plywood as sawdust, and you are not able to glue any strips together.

Dimensional Analysis and Unit Conversions [09/15/2002]
Using dimensional analysis, convert 8 feet/second to kilometers/hour.

Does Pi Equal 3.14? [01/27/1998]
We use pi as 3.14. How can this be right?

Exact Numbers and Conversion Statements [07/25/2005]
I'm confused about how to decide if a number is exact or inexact. I know that in general measurements are considered inexact, but how about conversion factors such as 1 inch = 2.54 cm? The exactness of the number plays a role in the number of significant digits to keep. What other kinds of numbers are considered exact and inexact?

Explanation of Significant Figures [09/11/2007]
I'm confused about how to determine how many significant digits a given number has. Can you explain it?

Feet Per Second [02/22/2003]
Determine the velocity in a pipe in ft. per second... Where does the constant term in the formula come from?

Fraction or Decimal? [06/23/1998]
Which is more precise, a fraction or a decimal - for instance, 1/3 or 0.33?

Fundamental Idea of Division [03/24/2000]
My 8-year-old daughter had 12 bracelets which she arranged into 4 piles of 3. Did she divide 12 by 3 or by 4?

How Many Blocks in a Mile? [11/24/2005]
How many city blocks are there in a mile?

How to Calculate Greatest Possible Error [04/12/2004]
I'm an 8th grade student working on greatest possible error and it just doesn't seem to make any sense. I know that GPE is half of the smallest unit of measure, but I don't understand how to decide what the smallest unit of measure is.

Inches and Feet and Miles, Oh My! [04/14/2008]
Why are English measures inconsistent in conversions? The metric system works in the meter and power of tens, but English units are kind of crazy (1 ft = 12 in, 3 ft = 1 yd, 1 mi = 1760 yd or 5280 ft, etc.).

Indirect Measurements and Hubble's Constant [01/31/2003]
How are indirect measurements used in astronomy? For example, how can scientists tell how far the Earth is from Pluto?

Instruments for Measuring Angles [09/28/2001]
I need the name, picture, or description of five devices used to measure angles.

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