Ask Dr. Math

Elementary Archive

Browse Elementary Number Sense/About Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    About zero.
    Multiplying by zero.
    Casting out nines.
    Classifying numbers.
    Googol, googolplex.
    Number facts from the Web.

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The Highest Exponent [10/23/1995]

What is the highest exponent ever known?

History of Numerals and Counting: Bibliography [11/18/1996]

Where do I find information on different systems of measurements?

History of Writing Decimals and Number Lines [10/28/1998]

Why, on a number line, are the negative numbers are on the left? When you deal with decimals, why are the whole numbers are on the left?

'Honest' Numbers [11/11/2002]

My teacher asked the class: What is the only 'honest' number?

How Does This Multiplication Method Work? [11/12/2003]

I've just learned a new way to multiply, where all you have to do is double, split in half, and add. Why does this work? Could you extend this to division, where all you have to do is double, halve, and add?

How Far Can You Count? [1/6/1995]

How far can you count after millions, billions, and trillions? In other words, what is the highest point you can count to?

How Long is 1000 Seconds? [02/18/2005]

How long does it take to count to one thousand counting one number per second?

How many prime numbers are squares? [01/09/1997]

Can a prime number be a square?

How Pi Was Derived and Relates to Area of a Circle [03/04/1998]

Using inscribed and circumscribed polygons to derive Pi and circle area.

Identity Element [10/12/2001]

What is an "identity element"?

The Importance of Number Sense and Estimating Answers [04/28/2004]

I don't understand how to solve problems using number sense. For example, if an employee at the deli counter slices a 2 foot long salami, about how many slices will he get? How can I figure that out? Why is it important?

Importance of Zero [12/19/1995]

Has anyone developed an inquiry-based activity for the classroom in which students in grade 5 can explore the importance of zero?

Infinity [5/24/1996]

Is infinity positive or negative?

Infinity times Infinity [10/15/1998]

What is infinity multiplied by infinity?

Integers in Everyday Life [01/16/2002]

How do we use integers in everyday life?

Invented Strategies for Subtraction [09/18/2002]

I need some help understanding two students' ways of understanding math.

Is 0 a whole number? [7/17/1996]

Is 0 a whole number?

Is K a Roman numeral? [07/19/1998]

A car ad shows 40K miles. Is this equal to a thousand?

Is Pi Infinite? [01/29/1998]

How can we know that pi is infinite? Does it ever turn into a pattern of zeros and ones, like a computer code?

Is Zero a Digit? [9/3/1995]

Is zero considered a digit? I think so, but there has been much discussion in my class!

Is Zero a Multiple of Every Number? [07/06/2002]

Is zero a multiple of every number? I have some books that say it is, and others that say it isn't.

Is Zero a Number? [07/05/2003]

If infinity is not a number, then is zero really a number?

Is Zero a Square Number? [02/16/2000]

Is zero considered to be a square number? I have found some sources that say it is, and others that say it isn't.

Is Zero Even? [03/28/2001]

The justification that 0 is an even number is based on the fact that 0 is divisible by 2. But how many times does 2 go into 0? Answer: no times; or to rephrase, 2 doesn't go into 0. Can you explain this?

Is Zero Even, Odd, or Neither? [03/31/1997]

Two students bet on whether zero is even, or neither even nor odd.

Is Zero Odd or Even? [06/17/1998]

My 4th grade students are not satisfied with any explanation I can offer.

Is Zero Positive or Negative? [01/26/2001]

Is zero a positive or a negative number?

The Last Finite Number? [02/01/2004]

I just read an article about the "last finite number", and I was wondering whether such a number could possibly exist.

Letters Used to Name Integers and Irrational Numbers [1/13/1996]

My students wonder why the set of integers is referred to as J, and what letter is used to name the set of irrational numbers.

Line under Greater or Less Than Symbol [01/26/2001]

What does it mean when there is a line under the greater or less than symbol?

Mathematical Palindromes [01/17/1997]

Can you tell me about number palindromes?

MathLands [6/18/1996]

I'm trying to find information about a math program called MathLands.

Meaning of Greater Than, Less Than Symbols [11/07/2002]

Does the meaning of less than and greater than signs depend on location?

The Meaning of Powers, such as Squares and Cubes [3/14/1996]

What does the power mean? Like 5 to the power of 2?

Memory Aid for Roman Numerals [05/10/2000]

What number is XLIII? Do you have a way of remembering what letter equals what number?

Mental Math [07/25/2003]

I would like to find a trick for multiplying by 3367.

Meters Squared vs. Square Meters [11/18/2001]

Is 12 m^2 better read as 12 square meters or 12 meters squared?

Mnemonic for Less Than and Greater Than [08/11/1999]

What was the old adage for telling how to read the less than and greater than symbols correctly?

Most Frequently Used Digit [6/13/1996]

Which is the most frequent digit in our number system?

Multiples of Four [03/01/1999]

Is zero a multiple of four?

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