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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Product-Perfect Numbers [02/26/2001]

Is there a statement that describes product-perfect numbers?

Products of Integers (Even or Odd) [03/23/2002]

How can I prove that the product of two even integers is an even integer and the product of two odd integers is an odd integer?

Pronumerals [05/14/2002]

What is a 'pronumeral'?

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.

Proving Irrational Numbers [05/10/2000]

How do you prove that non-terminating and non-repeating decimals are irrational?

Proving Something is Always So [04/01/1998]

Why is the result always 1089 in the following process? Take a three digit number and reverse its digits...

Pyramidal Numbers [07/04/2001]

Can I make a square pyramid with 1000 tennis balls?

Questions About .999... [11/13/1995]

Is 0.999... a rational number? Can .999... ever be equal to one?

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?

Rearranging Variables [10/01/1998]

Why when you use a variable in a problem does the answer sometimes still have a variable, so you can't get an actual number answer?

Repeating Decimals [5/31/1996]

I claim that 0.9 repeating is equal to 1...

Representing a Number [10/29/2001]

How can you represent the number three without using any letters or variables or the digits 1 through 9?

Representing Positive Integers in an Irrational Base [08/13/2007]

I know that 3 in base 2 is written as 11. But how would I express 3 in terms of an irrational base, like base square root of 2?

Reversal of Age Digits Every Eleven Years [11/06/2007]

Every 11 years, my age is the exact reverse of my mother's age. When I was 13 she was 31, when I was 24 she was 42, and so on. Why does this work?

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

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

Reversing the Digits [07/28/1999]

Why do you always get 9 when you take a 2-digit number; reverse the digits; subtract this from the original number; and divide the result by the difference between the two digits?

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?

Same Day Off? [12/08/2002]

One person has every ninth day off and started on Sunday, and another person has every sixth day off and started on Monday. When will they both be off on the same day?

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 and Engineering Notation [10/22/2003]

What is the difference between Scientific Notation and Engineering Notation?

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?

Significance of Irrational Numbers [08/23/1999]

What exactly is the meaning of .333... or pi? What's the difference between point three repeating and point three to the 105th decimal place?

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?

Simple Example of Ramanujan's Work [03/28/1999]

Ramanujan's contributions to the divisibility properties of partitions of whole numbers.

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?

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 and Composite Numbers [9/5/1996]

Is it possible for a number to be a square number and a composite number?

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?

Square Roots and Irrational Numbers [10/08/1997]

Will every square root of a positive number that is not a perfect square be an irrational number?

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