Ask Dr. Math

Middle School Archive

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

See also:
      Calendars/Dates/Time
      Temperature
      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.

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Instruments for Measuring Angles [09/28/2001]

I need the name, picture, or description of five devices used to measure angles.

Learning Fractions in the Metric System [11/27/2003]

Since the metric system doesn't use fractions, are math students in metric countries able to skip fractions and work on more useful things?

Limits to Paper Folding [05/09/2002]

What is the limit to the number of times that a piece of paper can be folded, and how is it established?

Measurement and Comparison [04/30/1999]

Why is comparison the key to measurement?

Measurement: Raindrops, the Weight of the Earth [05/02/2001]

How many raindrops have fallen from the sky to the earth since the Big Bang? Has anyone ever tried to calculate the weight of the Earth?

Measurements on a Logarithmic Scale [11/21/1998]

What kinds of measurements are done on a logarithmic scale? What physical properties make a logarithmic scale more appropriate?

Measuring Angles with a Protractor [02/28/2002]

I want to know how to measure acute, reflex and obtuse angles with a protractor.

Measuring a Puddle [09/05/2002]

How many different ways can you measure a puddle?

Measuring by Shadows [05/22/2001]

How can I measure a tree using its shadow and mine?

Measuring Distances in Space [06/02/2008]

How can we measure the distance from Earth to Mars accurately? Space is infinite--how can you measure something that is always moving?

Measuring: Greatest Possible Error [04/18/1998]

How can you find the greatest possible error for a measurement?

Measuring the Circumference of the Earth [08/16/1999]

How did Eratosthenes use a mathematical formula to prove the earth is round?

Measuring the Height of a Building Using Shadows [05/24/2000]

What time of day is best to use a shadow to measure the height of a building by using triangles?

Measuring the Speed of a Pitch [06/11/2002]

Our school doesn't have a radar gun for determining how fast a pitcher can throw a baseball. How can I estimate this using a stopwatch?

Metric and Standard Rulers [04/20/2001]

In the United States we only use a customary (standard) ruler, and in other parts of the world they use the metric side. Why do we just use the standard side?

Metric vs. Standard System [08/19/2001]

Compare and contrast the advantages and disadvantages of the metric system and the standard system using weights and measures.

Pennies in a Mile [04/23/1999]

How many pennies are there in a mile?

Precision in Measurement: Perfect Protractor? [10/16/2001]

Given that protractors are expected to be accurate to the degree, and in some instances the minute or second, how are angles accurately constructed and marked?

Reaction Time: Softball, Baseball [04/26/2003]

A baseball pitcher throws at 90mph from 60 feet, and a softball pitcher throws at 60mph from 40 ft. How can I measure reaction time for the batters?

Reading a Protractor [9/8/1996]

Which side of a protractor scale do you use?

Reading a Ruler II [11/08/2000]

What do the little lines on a ruler stand for?

Reading a Ruler III [03/03/2005]

I am looking for simple, basic instructions to teach a child how to read a ruler. I remember that we used to count the lines--where the line falls on the ruler is the top number of the fraction and how many lines in between 0 to 1 inch represents the bottom number (the whole). Is this correct?

Recipes and Adjusting Ingredient Amounts [04/20/2005]

In a recipe, 5 1/2 cups of coconut uses 14 ounces of milk, but I only have 4 cups of coconut, so how many ounces of milk do I use?

Serving Size, Calories, Daily Values, and Food Labels [05/26/2005]

How do they determine the percent of daily value, calories, and other information shown on food labels?

Significant Digits and Irrational Numbers [09/24/2005]

How can you determine the signifigant digits of a non-terminating or irrational number like pi?

Significant Digits in Numbers Written in Scientific Notation [06/20/2005]

A discussion between Dr. Peterson and a student who is struggling with how to determine significant digits in general and with regard to numbers in scientific notation in particular.

Size of the Universe [10/31/2001]

Is it possible to measure the size of the universe?

Some Conversions are Impossible [08/07/2006]

How do I convert 567 square inches to cubic inches?

Subtracting with Mixed Units [02/10/2009]

How would you subtract 1 ton, 12 lb, 6 oz from 4 tons?

Tape Measure Markings [8/11/1997]

What is the small diamond on all tape measures that occurs every 19.2 inches for?

Teaching the Metric System [08/18/2000]

How can I teach my second grader about the metric system? I have no idea how to read a metric ruler or how to convert inches into the metric system or vice versa.

Using Scale Drawings [05/24/2002]

Use a scale drawing to determine the actual size of an object.

Visualizing the Metric System [08/02/1997]

What are some common things that could be used to approximate lengths for a visual picture of the different lengths in the metric system?

Volume and Surface Area of a Box [04/06/2008]

How can two cardboard boxes that have the same surface area have different volumes? Wouldn't the volume be constant no matter how you configure the cardboard if each box has the same amount of cardboard?

Which Grasshopper Wins the Race? [06/11/2003]

The larger grasshopper covers 10 inches per jump, while the smaller one covers 5 inches. The smaller grasshopper takes 2 jumps for every jump of the larger grasshopper. Which one wins, and why?

Which is More? [05/21/2002]

Given a choice between nickels stacked to your height, or quarters placed end to end to your height, which should you choose?

Why Pi? [07/19/2002]

Instead of using pi, why don't we measure the radius and circumference of a given circle, and use that ratio to find the area? Wouldn't that be more accurate?

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