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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Facts about e [11/09/1998]

Where does the number "e" come from and what uses does it have in the real world?

Figurate and Polygonal Numbers [11/21/1998]

I need to know everything about figurate numbers.

Figurate Numbers [12/31/1997]

Questions about figurate numbers (triangular, square, pentagonal)...

Finding Input-Output Rules [10/08/2003]

My 3rd grader is having trouble finding rules to change one list of numbers (the inputs) into another (the outputs)...

Finding n(n-1)/2 in the Real World [09/14/2002]

How can n(n-1)/2 be explained in common everyday language? When is it used?

Finding Pi [11/14/1997]

What is the quickest algorithm for finding pi?

Finding the Digit of a Decimal Expansion [11/14/1998]

What digit will appear in the 534th place after the decimal point in the decimal representation of 5/13?

First 100 Irrational Numbers [10/26/2002]

Could you please tell me the first 100 irrational numbers?

Forming Palindromic Numbers [12/04/1998]

Can you give me some examples of forming palindromic numbers with different operations? How many steps would it take?

Formula for Triangular Numbers [08/29/1998]

Is there a formula to figure out triangular numbers?

Formula to Compute One's Exact Age [05/31/2000]

Is there an equation to find a person's exact age on a given date, taking into account leap years?

Four-Digit Palindromes [10/21/1998]

Why is every four-digit palindrome divisible by 11?

Fourth Highest Perfect Number [08/21/1997]

What is the fourth (4th) highest perfect number?

From Binary to Octal, Base 4 to Base 16 [01/20/2003]

How do I convert numbers from one base to another without converting to a base 10 equivalent first?

Front End Estimation of Addition Problems [09/06/2005]

An introduction to "front end estimation" and ideas on how to become a good estimator.

Front End Estimation with Adjustment [02/17/2004]

A discussion of front end estimation with adjustment, its limitations, and ways to teach kids how to estimate.

Getting 0.99999... [04/15/1998]

Is there any mathematical way to get 0.99999999999......?

Graham's Number [06/01/1999]

What is the world's largest significant number?

Greater Than and Less Than Symbols [05/30/2000]

What does it mean when a greater than or less than symbol appears before a number, with nothing to the left of the symbol?

Greatest Possible Error [02/11/1999]

I need an elementary-level answer to what is the greatest possible error.

Guess and Check [06/17/2002]

The sum of two numbers is 15. The difference is 3. What is the product?

Happy Numbers [06/21/1998]

What are happy numbers?

Happy Numbers [01/05/2006]

What is a "happy" number? What are all the two-digit "happy" numbers between one and one hundred that are multiples of four?

Hebrew Mathematics [09/21/2000]

I need to write a one-page article on the Hebrew mathematics system.

Hexadecimal Division and Addition [07/06/2003]

Could you provide a few examples of how to solve hexadecimal addition and division problems?

The History of Numbers and Numerals [12/08/1998]

Can you give me some information on the history of numbers? How were they developed and where are they used?

History of Numerals and Counting: Bibliography [11/18/1996]

Where do I find information on different systems of measurements?

History of Writing Decimals and Number Lines [10/28/1998]

Why, on a number line, are the negative numbers are on the left? When you deal with decimals, why are the whole numbers are on the left?

Hit-and-Run Prime Number Problem [12/10/2002]

Did you get his license number?

'Honest' Numbers [11/11/2002]

My teacher asked the class: What is the only 'honest' number?

How Can the Product of Two Radicals Be Finite? [06/27/2006]

How is it possible that sqrt(5) * sqrt(20), each of which is by itself an infinite number, can make exactly 10 when they are multiplied?

How Does Base 4 Work? [11/06/2003]

How does base 4 work?

How Does This Multiplication Method Work? [11/12/2003]

I've just learned a new way to multiply, where all you have to do is double, split in half, and add. Why does this work? Could you extend this to division, where all you have to do is double, halve, and add?

How Long Does It Take to Count to a Billion? [03/28/2003]

Why people who need to deal precisely with long intervals (like astronomers and computer scientists) avoid using 'years' as a unit of time.

How Old at $4,000? [10/15/2002]

Aunt Isabella gives each niece and nephew $10 on his or her first birthday, and on each birthday thereafter the children get $20.00 more than on the birthday before. How old will a child be when he or she receives a total of $4,000.00?

How Pi Was Derived and Relates to Area of a Circle [03/04/1998]

Using inscribed and circumscribed polygons to derive Pi and circle area.

Identity Element [10/12/2001]

What is an "identity element"?

The Imaginary Number [1/5/1995]

A student questions the meaning of the imaginary number, i.

Imaginary Numbers [02/28/1999]

What jobs and professions use imaginary numbers?

The Importance of Number Sense and Estimating Answers [04/28/2004]

I don't understand how to solve problems using number sense. For example, if an employee at the deli counter slices a 2 foot long salami, about how many slices will he get? How can I figure that out? Why is it important?

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