Ask Dr. Math

Middle School Archive

Browse Middle School 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.
    Significant figures/digits.

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Inequalities on a Number Line [05/07/2003]

How do you graph inequalities on a number line?

Infinite Number of Primes [04/14/1998]

Prove there are an infinite number of primes. What is the largest prime number known?

Infinity [5/24/1996]

Is infinity positive or negative?

Infinity and Inequalities [06/05/2002]

I'm supposed to use positive and negative infinity to solve problems like 2x - 3 < 7.

Infinity minus Infinity [10/26/1995]

Infinity - Infinity = ?

Infinity Plus One [12/26/1995]

What is infinity plus one?

Infinity times Infinity [10/15/1998]

What is infinity multiplied by infinity?

Integers and Rational Numbers [5/25/1995]

Can you explain the difference between SET Q (rational numbers) and SET Z (integers)?

Integers in Everyday Life [01/16/2002]

How do we use integers in everyday life?

Introduction to Rational Numbers for Middle School Students [12/06/2006]

Why do we need to know about rational numbers? Aren't all fractions rational numbers? What's the difference?

Irrational Between Two Rationals [07/19/2002]

How can I find an irrational number that lies between a pair of rational numbers?

Irrational Numbers [08/13/1997]

How can three irrational numbers added together give you a rational number?

Irrational Numbers [01/07/1998]

Are pi and the square root of 2 irrational numbers? Why? What about 1.33333... and 1.181818...?

Irrational Numbers [01/13/1998]

How do you prove that (sqrt)2 is irrational? Given two irrational numbers, a and b, is it possible to get an a^b that is rational?

Irrational Numbers; Rational Square Roots [02/04/1998]

How can you tell whether root 10 is a terminating or repeating decimal, or an irrational number? Are some square roots rational?

Irrational Pi [7/15/1996]

Why is pi considered an irrational number when it's defined as the ratio of the circumference of a circle to its diameter?

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

Is 0 a whole number?

Is Integer Division Associative? [05/14/2002]

Is integer division associative?

Is It Possible That x/0 is Not Really Undefined? [06/14/2004]

Is it possible that 1/0 is not really undefined, but is in fact the key to a whole new class of numbers, much as the imaginary unit i led to the development of complex numbers?

Isn't 1/0 the Biggest Number? [02/28/1998]

It makes sense that if you add or multiply a number to the biggest number you will get the same biggest number, right?

Is One a Triangular Number? [03/22/2004]

Triangular numbers have that name because if drawn as dots they can form a triangle. But 1 is just a single dot, so it can't be a triangular number, can it?

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 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? [10/23/1995]

Why is 0 classified as a whole number and not a natural number? Natural numbers can be touched, whereas whole numbers cannot - is 0 a whole number strictly by definition?

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

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

Is Zero a Signed Number? [01/09/2002]

What is the sign of zero?

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 Prime or Composite? [10/23/1995]

Is zero prime, composite, or neither?

Is Zero Really a Number or Just a Concept? [09/15/2005]

I've been taught that infinity is just a concept, not an actual number. I'm wondering if the same thing can be said of zero?

Karatsuba Multiplication [10/15/2007]

Can you explain the ideas and steps behind the Karatsuba method of multiplying?

K as an Abbreviation for Thousands [05/29/2002]

I was taught that 30K meant thirty thousand. Is that correct?

Laps and Least Common Multiples [05/24/2002]

Three people are running around a track at different speeds. When will they all return to the starting point at the same time?

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.

Learning Addition and Multiplication with Algebra [3/16/1996]

How do you know what the (a) is in algebra? I saw this on a picture: a(1/a) = 1/a(a) = 1...

Leaving Answers in Terms of Pi [12/11/2006]

My teacher says it's okay to leave an answer like 600pi, but I think it should be multiplied out as 600(3.14) = 1884 or you haven't finished the problem. What do you think?

Length of Pascal's Triangle [6/13/1996]

How long was Pascal's Triangle?

Line Segment Representing Sqrt(3) [10/07/2002]

Draw a line segment that represents radical 3.

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