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.
- Rounding to Specific Number of Significant Figures [05/30/2003]
How do I round to five significant figures?
- Rules for Significant Figures and Decimal Places [03/23/1999]
Accurate measurement: What are significant digits? When do we use them?
- Russian Peasant Method of Multiplication [10/07/1998]
I understand the 'Russian peasant' method of multiplication, but not why
- Scientific Notation: Exponents [8/29/1996]
What do you call 0.000000000000000000000002?
- Signs: Rules, Number Line [07/13/2001]
What is (-) - (+) = ? or (+) + (-) = ?
- Square Root of a Negative Number [01/25/1997]
Is it possible to find the square root of a negative number and, if so,
to what number system do these square roots belong?
- Types of Real Numbers [8/16/1996]
What are all the types of real numbers?
- Venn Diagram of Our Number System [12/13/2002]
I don't know how to include complex numbers that consist of a real
part and an imaginary part. Can you please diagram this for me?
- What Does 'n' Mean? [09/25/2001]
In a pair of numbers, if n is the first number, what is the second?
- What is Log? [2/26/1995]
What is 4 to the half power, and what is log?
- Why does PEMDAS work? [7/9/1996]
Why does the PEMDAS (Parentheses, Exponents, Multiplication, Division,
Addition, Subtraction) order of operations really work?
- Why Do We Round? [12/18/2002]
What's the whole point of rounding?
- Working with Integers [01/12/1999]
Could you explain how to divide, multiply, add, and subtract integers?
- Writing Commas in Numbers [07/11/2003]
Is it true that in France where we in America use decimals in math,
they use commas, and where we use commas they use decimals?
- 0.999... and Infinity [09/17/2003]
How does x = 0.9999... forever turn into x = 1?
- 0.99... Repeating Can't Really Equal One, Can It? [08/14/2008]
Doesn't 0.999... repeating simply get infinitely close to 1, but never
quite get there? Each 9 that is added simply makes the number more
precise, closer to 1. But the number will only become MORE precise, it
will never become, well, PRECISE.
- 0-Based Counting [07/05/2003]
I am trying to convince people that you should count from 0.
- 1000 $1 Bills in 10 Envelopes [12/11/2002]
Put 1000 $1 bills into 10 envelopes in such a way that someone can ask
you for any amount of money from $1 to $1000 and you can give it to
him through a combination of the envelopes.
- 1 + 1 Doesn't Equal 2 [06/04/1998]
1 + 1 does not equal 2. What is the math equation that proves this?
- 1, 2, 3, ... as Varied as Arabic, Roman, ... Yoruban? [10/08/2011]
A researcher familiar with an African language's words for its counting numbers wants
to know what symbols its native speakers use to write them. Through analogies to Latin and French -- and English etymologies -- which show the distinction between speech and writing, Doctor Peterson explains why a numbering system unique to the Yoruban language likely does not exist.
- 19 Odd Number Puzzle [10/22/2001]
What four odd numbers add up to 19?
- 2421 and Only One [01/10/2017]
A teen sees valid representations in the 2421 coding system go unused. Doctor
Peterson draws on complementarity to makes sense of how the system copes with
- 2421 Decimal Code [11/08/2004]
Can you explain why some bit combinations for 2421 are invalid? For
example, to represent decimal 5 (five) in 2421, the correct code is
1011. But why can't we represent decimal 5 in 2421 as 0101, because
if we add the weights as 0*2 + 1*4 + 0*2 + 1*1, we get 5 in decimal.
- About Base Five [10/22/2001]
I don't understand anything about bases.
- Absolute Value as a Grouping Symbol? [07/25/2002]
Should absolute value bars be considered grouping symbols, along with
parentheses, brackets, braces, and the fraction bar?
- Absolute Value Graphs [11/16/2002]
Graphing inequalities: finding an equation, graphing it, and finding
- Abundant and Deficient Numbers [10/14/1997]
What are abundant and deficient numbers, and what are they used for?
- Abundant Numbers [03/27/1999]
I need to find all the perfect, abundant, and deficient numbers from 1 to
- Adding and Subtracting Units of Time [12/11/1998]
How do you subtract units of time? In particular, how do you borrow from
hours to make the minutes bigger?
- Adding a Negative Number [3/19/1996]
How do you solve 123 + (-43) ?
- Adding Odd and Even Numbers [05/28/2003]
Can you add any two numbers (one odd and one even) to total an even
number? Can you add any two odd numbers to total an odd number?
- Adding Odd Numbers [02/22/2002]
Why do you get an even number when adding odd numbers?
- Addition Facts [6/29/1995]
I'd like to understand the reason for the "fact" that 2+2 = 4.
- Additive Identity and Other Properties [01/03/1999]
Can you explain the identity of zero and the commutative and
multiplicative properties? Why are they special?
- Alabama legislature and pi [04/15/1998]
Did Alabama really vote that pi should have its biblical value of 3?
- Algebra as a Metaphor for Life [06/11/2002]
I've been given 'proofs' that -1 = 1, and that 2 > 4. Can you show me
why they aren't true?
- An Algorithm for Converting Bases [2/2/1996]
I would like a formula for base conversions. My math teacher said that he
had one, but now he can't find it.
- Alien Fingers and Bases [12/07/1998]
Scientists observe a class of young aliens through a telescope. These
equations are on their blackboard: 13 + 15 = 31, ... How many fingers do
the aliens have?
- Amicable Numbers [11/12/1998]
What are amicable numbers? Can you give me examples? What's their
- Applying the Distributive Property to Division or Subtraction [12/29/2006]
The distributive property is easily shown with multiplication and
addition. Can it be used with subtraction or division?