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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Numbers with the Digit 3 [10/27/1999]

In how many numbers between 1000 and 9999 does the digit 3 occur?

Number System Advantages, Disadvantages [01/24/2001]

What are the advantages and disadvantages of the present number system?

Number Systems: Two Points of View [06/30/1998]

What are the number systems?

Number Terminology [08/11/1998]

Can you explain some number terminologies: digits, transcendental, algebraic, rational, irrational, and counting numbers?

Number Word Etymologies [05/03/2001]

Who made up the names for numbers?

Numeral Systems and Representing Numbers [10/30/1998]

Can you tell me the different ways the number 8 is represented? For example, what about different numeral systems?

Odd Digits of Square Numbers [02/07/1999]

Why are there no square numbers other than 1 and 9 that consist entirely of odd digits?

One Plus One [04/11/1997]

Are you sure that 1 plus 1 equals 2?

The Oneths Place [09/29/1998]

In decimal numbers, why is there no oneths place?

Ordering Fractions [01/17/2003]

How do I order the fractions 2/3, 3/5, and 2/7?

Ordering Improper Fractions [10/12/2002]

How can I explain ordering improper fractions?

Order of Operations and Fractions [02/22/2002]

Given a+3 and b+5, is 105 / ab 7 or 175?

Order of Operations vs. Distributive Property [02/04/2005]

Does the distributive property contradict the rules of order of operations? When we have a(b + c) order of operations says we should add first in the parentheses, then multiply, but the distributive property says we can multiply first to get ab + ac, then add.

The Origin of Lucas Numbers [10/08/1998]

I need help with Lucas Numbers - how and why they were created.

Other Ways to See That 0.999... = 1 [05/29/2000]

Is there another way of looking at 0.999... = 1 that will help convince me that it's true?

Paint Formulas in Base 48 [08/20/1998]

I work for a paint store where our formulas are based on an ounce being 48 parts...

Palindrome Definition [03/17/2002]

Do mathematicians consider single-digit numbers palindromes?

Palindromic Numbers [08/15/1997]

How many palindromic numbers are there between 10-100, 100-1,000 and 10- 100,000?

Palindromic Numbers to 100,000 [02/05/2000]

Can you list all the palindromic numbers from 0 to 100,000?

Parenthesis [03/09/1999]

Can you help me teach parentheses to a class?

Pennies and Remainders [01/13/2003]

Arnie has between 300 and 400 pennies in his collection. When he divides them into groups of 4, 5, or 9, there is always one penny left over. How many pennies does Arnie's collection contain?

Pentagon Puzzle [09/18/2002]

Write the numbers 1 through 10 so each side of the pentagon has a sum of 14.

Percentage of Votes Cast [06/03/2003]

If you have two percentages, say 25% and 50%, can you do a percent change between the two?

Perfect Number [7/21/1996]

How can I find a perfect number? What are some reference books about number theory?

Perfect Numbers [11/17/1994]

What good are Perfect Numbers?

Perfect Numbers [9/15/1996]

What is a "perfect number"?

Perfect, Triangular, and Hexagonal Numbers [12/18/2001]

How are perfect numbers related to triangular numbers and hexagonal numbers?

The Perils of Predicting Patterns [11/02/2003]

What comes next in 1,3,6,10 ___? Is it 12 or 15?

Pi's Last Digit [7/20/1996]

I know pi is a nonterminating decimal, but if there were a last digit wouldn't the last digit be a 0?

Positive Real and Rational Numbers [09/21/2002]

Is there a positive real number that is smaller than all positive rational numbers?

Practical Applications of Absolute Value [09/19/2000]

My 8th grade students have asked why we need absolute values.

Practical Applications of Imaginary Numbers [11/23/1995]

What are some real life applications that would make imaginary numbers more meaningful to students?

Practical Uses for Pascal's Triangle [2/27/1996]

Some of my students are trying to find practical uses for Pascal's triangle.

Precise Numbers [10/18/2001]

A precise number occurs when its proper divisors multiplied together equal the number: 6 is a precise number because 1*2*3 = 6. Is there another name or formula?

Prefixes in Math [08/21/2001]

What are the prefixes for 7, 8, 9, and 10?

Primality Testing [04/22/1998]

Is there any fomula to find if a number is a prime?

Prime and Composite Numbers, Sieve of Eratosthenes [01/28/1997]

I need a list of all prime numbers and all composite numbers up to 50.

Prime or Composite? [09/30/1997]

Wouldn't every number be composite?

Primes and Repeating Unit Numbers [12/09/1998]

How do you prove this statement: For every prime number there exists a repeated unit number that is a multiple of that prime.

Problem Solving and Mental Process [10/03/2002]

Two numbers add up to 19. The difference between the two numbers is 3. What are the numbers?

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