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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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? Why?

Russian Peasant Method of Multiplication [10/07/1998]

I understand the 'Russian peasant' method of multiplication, but not why it works.

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?

19 Odd Number Puzzle [10/22/2001]

What four odd numbers add up to 19?

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 its vertices.

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 50.

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 history?

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?

Are All Digit Strings in Pi? [08/06/1999]

Do all possible digit combinations appear in pi? For example, is it possible that somewhere in the decimal expansion there are a million 2's in a row?

Are these numbers odd or even? [4/27/1995]

Would 2.5 be an even number, odd number, neither or both? Also, what about zero's evenness and/or oddness. Infinity's?

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