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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Perfect Numbers [9/15/1996]

What is a "perfect number"?

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?

Placement of Commas in Writing Numbers [10/22/2003]

Why is the ones period named for the ones place value and why is the thousands period named for the thousands place? Why is there not a hundreds period?

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?

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.

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?

Proof: 2 = 1? [10/03/1997]

a = b is factored to a^2 = ab by multiplying both sides by a...

Proof that 1 + 1 = 1? [09/04/1997]

Can you shed any light on this subject?

Properties, Defined and Illustrated [10/10/2001]

I need a page of information on the commutative, associative, and F.O.I.L. properties.

Rational Numbers and Square Roots [10/07/1998]

Our teacher told us to find all the rational numbers we could containing a sqrt symbol...

The Real Number System in a Venn Diagram [09/08/1998]

How do you construct a Venn diagram that illustrates the real number system?

Reverse Polish Notation in Calculators [09/17/2005]

An introduction to "reverse Polish notation" and the terms "stack", "push", and "pop" in that context.

Roman Numerals [11/13/1997]

What are three ways Roman numerals are used today?

Roman Numerals on Clocks [06/04/2001]

Is the Roman numeral on a clock written as IV, or IIII?

Rounding to the Nearest Multiple of 5 [01/08/2005]

How do you round to the nearest 5? Would 27 round down to 25 while 28 would round up to 30?

Rounding to the Nearest Tenth [8/29/1998]

Would 6.96 be 7.0 or 6.9?

Saying Numbers Out Loud [03/06/2002]

I have recently been told that the use of "and" is incorrect. Is it "one hundred one" or "one hundred and one"?

Scientific Notation [09/16/1997]

I don't understand how you get the answer: 5x10 to the 3rd power = 5,000; 5x10 to the -3rd power = -5,000.

Scientific Notation of Zero [09/09/2002]

What is the scientic notation of zero?

Short Word Form [10/15/2002]

How is 474,136 written in short word form vs. standard form?

Significant Digits [09/07/1998]

What are significant digits?

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 and Zero [05/19/1999]

When are zeros significant and when are they not significant?

The Size of Infinity [09/03/1998]

What is infinity times 2? Can we measure infinity?

Sizes of Infinities [01/31/1997]

How can you prove that one infinity is larger than another?

Smallest 5-Digit Number [02/05/2002]

My dad says the smallest 5-digit number is 00000, but my teacher says it is 10000. The dictionary says that zero is a digit. What's the right answer?

Spaces and the Number Line [02/26/2003]

If you say, 'How many degrees are there between -2 and 4?' would you count the 0 degrees and answer 7 degrees or would you not count the nought and answer 6 degrees?

Square Numbers End in 0 1 4 5 6 9 [10/15/2002]

Why do all square numbers end in 0 1 4 5 6 9?

Teaching Children Other Bases [02/20/2002]

Why teach children number systems other than the base 10 number system?

Teaching Elementary Concepts [04/04/1997]

How can I teach rational counting, prime and composite numbers, and square roots at a grade-school level?

Three Consecutive Natural Numbers [09/17/2001]

Why is it that the product of any three consecutive natural numbers is always divisible by six?

Trick for Numbers Divisible by 3 or 9 [02/24/1998]

Proof of a trick for numbers that are divisible by 3 or 9.

Trilogy, Tetralogy... [05/28/2003]

Why isn't there a numbering system for groups like trilogies?

Use and Meaning of 'And' in Naming Decimals [12/01/2004]

Can you please tell me what the word "and" means in the word form of a decimal number?

Use of Plural with Decimal Numbers [02/27/2002]

What are the rules for 1.0001, 1.1, 1.5 or 1.999 ? Should we write 1.0001, 1.1, 1.5, 1.999 point or 1.0001, 1.1, 1.5, 1.999 points ? Differences between plurals in English and French.

Using Integers [01/05/1999]

I need some real-life examples of integers to show my students that they need to be able to use them in math class.

What is 0? [5/21/1996]

Is 0 a positive or a negative integer, or neither?

What is a Number Base? [04/19/2003]

The base eight number 7n3 is equal to the base 7 number 1n35. What digit does n stand for?

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