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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Multiples of Four [03/01/1999]

Is zero a multiple of four?

Multiplicand, Multiplier [07/05/2001]

Do you agree with me that in the following mathematical sentence: 456x10, 456 is called the multiplicand and 10 is called the multiplier?

Multiplying by 1 [09/01/1998]

Why doesn't a number change when you multiply it by 1?

Multiplying by Nine [01/10/1997]

Why is the sum of the two digits 9 when you multiply 9 times any number between 1 and 10?

Multiplying by Zero [03/01/2002]

Why does any number times zero equal zero?

Multiplying by Zero [10/19/2002]

I know that zero's value is nothing, but why is it that it turns other numbers that clearly have a greater value to zero when multiplied?

Naming Large Numbers [06/05/2002]

In Rowlett's site for naming large numbers, he seems to take every American prefix and bump its meaning by one to get the corresponding Greek-based prefix. Why?

Naming Nine Things [01/15/2003]

What is the correct name for nine things collectively? I can only find the answer up to 7, septuplet, which has been highly publicized with the McCoy babies.

Naming N-Tuples (Single, Double, etc.) [05/15/2000]

If one is single, two is double, three is triple, etc., what are the names for seven, eight, nine, and ten?

Naming Numbers [09/26/2002]

I have a student who insists that 2400 (twenty-four hundred) is not a number.

Napier's Bones [01/20/1997]

How do you use Napier's Bones to do multiplication?

The Number 6 [07/24/1997]

I need some information on the number 6.

Number Palindromes? [5/17/1996]

What is a number like 62626 that can be read the same frontwards and backwards called?

Numbers and Digits [09/21/2000]

What is a digit? Why can't we call a digit a number?

Numbers and Numerals [09/06/1997]

What's the difference between a number and a numeral?

Numbers and Numerals [08/29/2002]

15/5 and sqrt(9) both reduce to 3, but is it proper to say that they are integers?

Numbers and Numerals [11/20/1998]

What is the difference between numbers and numerals?

Numbers in a Fraction [05/20/2001]

Is a fraction one number or is it two numbers?

Number-Spelling Puzzle [07/08/2002]

What number in English, when spelled out, has its letters in alphabetical order?

Numbers that are Equal [8/20/1995]

Why does 1.999999999...equal 2?

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?

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?

One, Two, ... Infinity, ... Infinities? [11/04/2010]

A teacher recalls two year-olds playing out a simple thought experiment about divisibility, which led them all to wonder if more than one infinity might exist. Doctor Vogler explains two different senses of infinity, one of which confirms their surprising discovery -- and mentions two more contexts of the concept.

Ordering Digits [08/15/1998]

Using the digits 6 1 4 8 3 9, write the largest counting number that is smaller than 5,000 and the smallest counting number that is greater than 5,000...

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. Associative Property [10/10/2002]

Is the associative property an exception to the order of operations, a corollary, or something totally unrelated?

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.

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?

Pattern of Squares [1/08/1998]

Do squares of integers have a pattern? I believe that they do, but I don't know what it is.

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?

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