See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Number Sense/About Numbers
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Multiplying by zero.
Casting out nines.
Number facts from the Web.
- 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.
- Line under Greater or Less Than Symbol [01/26/2001]
What does it mean when there is a line under the greater or less than
- Locating Pi on a Number Line [08/23/2000]
How can I locate pi on a number line? What number for pi should I use?
Should I just use 3.14, or should I go farther?
- Mathematical Palindromes [01/17/1997]
Can you tell me about number palindromes?
- Mathematics As Analogy [12/16/2003]
How can the ratio of a finite circumference to a finite diameter give
an infinite value for pi?
- Math Symbols [03/11/2002]
What do these symbols mean in math? ' ~ ! @ # $ % ^ & * ( ) - _ + = /
- Meaning of Greater Than, Less Than Symbols [11/07/2002]
Does the meaning of less than and greater than signs depend on
- The Meaning of Powers, such as Squares and Cubes [3/14/1996]
What does the power mean? Like 5 to the power of 2?
- Meaning of the Phrase: Divide by Zero. [01/02/1998]
I want to use 'divide by zero' to indicate a physically impossible task.
What does the phrase actually mean?
- Memory Aid for Roman Numerals [05/10/2000]
What number is XLIII? Do you have a way of remembering what letter equals
- Mental Math [07/25/2003]
I would like to find a trick for multiplying by 3367.
- Meters Squared vs. Square Meters [11/18/2001]
Is 12 m^2 better read as 12 square meters or 12 meters squared?
- Mnemonic for Less Than and Greater Than [08/11/1999]
What was the old adage for telling how to read the less than and greater
than symbols correctly?
- 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?
- Multiplication's Multiple Meanings: Unified by the Distributive [01/01/2015]
Area? Matrix multiplication? Scaling and rotation? A parent seeks a global
understanding — or at least some internal consistency — as to what ties
together all the operations called "multiplication." Building up from the natural
numbers, where multiplication is repeated addition (MIRA), Doctor Peterson teases out two
- Multiplying a Number by 4 [01/11/1999]
Can you help me find a few numbers that when you multiply them by 4, you
will get the original number backwards?
- 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 in Bases Greater Than 10 [10/13/2002]
I need to know how to multiply and divide by bases greater than 10.
- My Calculator Gives Wrong Answers for Large Values of x ... [01/20/2010]
Doctor Vogler reveals how a calculator's imprecision leads to
increasingly large rounding errors -- and misleads a student trying to
make sense of the formula for the base of natural logarithms.
- 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.
- Napier's Bones [01/20/1997]
How do you use Napier's Bones to do multiplication?
- Natural Numbers [6/25/1996]
There are "natural" numbers, but are there "artificial" numbers?
- Natural Numbers Problem [5/12/1995]
How would you prove that one added to the product of four consecutive
natural numbers is a perfect square?
- Negative Absolute Value [6/28/1996]
Is -|8| -8 or 8?
- Negative Numbers in Base 2, 16, etc. [01/24/2003]
Are there negative numbers in alternate bases? Our calculator says
that 1-2 in base16 is FFFFFFFFFF. This can't be right!
- New Rule for Divisibility by 7 [11/01/1997]
Multiply the integer excluding the one's digit by 3, and add the one's
- Non-terminating Decimal Representations of Fractions [11/10/1997]
Why when you take a finite, limited quantity like one-third and turn it
into a decimal do you get .333... on into infinity?
- Not Enough Information about ... Ellipses [12/01/2010]
A student wonders how to interpret the "dot dot dot" notation in decimal expansions.
While acknowledging the ambiguity of the ellipsis symbol, Doctor Peterson explains that
context often helps.
- Nth Term in a Sequence [01/11/2003]
Here is the sequence: 1, 2, 5, 14 ... Find the following 2 terms and a
formula for the nth term.
- Null Sets [8/23/1996]
Is the null set a proper subset of every set?
- The Number Line and Its Contents, Rational and Irrational [07/13/2015]
A teen wonders how to plot irrational numbers on a number line, and why a segment would
fail to represent the set of rational numbers. Doctor Peterson draws on several choice
examples to get the points across.
- 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