Ask Dr. Math

Elementary Archive

Browse Elementary 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.

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Decoding Place Value [09/14/2003]

What do the different digits in a base 10 number mean?

Distributive Property over Addition vs. Multiplication [12/11/2002]

Why can't you use the distributive property when the integers in the parenthesis are being multiplied?

Dividing by Zero [05/18/2001]

I cannot comprehend that a human being is not able to divide a number by zero...

Dividing by Zero and Dividing Zero by Something [11/14/2006]

I am trying to understand the difference between dividing by zero and dividing zero by something. I know that one of them is zero and the other is 'can't be done'. Which is which and why?

Does 2k4 Mean 2004 or 2400? [01/10/2004]

On internet communities it is common to reduce figures using 'k' as a shortcut; for example 2k is used instead of 2000. I was under the impression that a number after the k (such as 2k4) meant 2400, and that to get 2004 in this system you'd need to write 2k004. But I've also seen 2k4 used for 2004. Which is correct? Does 2k4 mean 2004 or 2400?

Do Natural Numbers Start with 0 or 1? [7/4/1996]

What arguments would you give 10-year-olds to convince them that natural numbers used for counting start with 0, not 1?

Don't Use Calculators [12/18/2000]

When children should not use calculators to do math.

Do Numbers Go On Forever? [04/08/2002]

Do numbers go on forever, or do they stop? What is the largest number that has a name? What's the best way to explain infinity to a kindergartener?

Egg Doubling Problem; UK & US: Naming Large Numbers [5/6/1996]

The sixtieth time you double them, you have a lot of eggs! How many rectangles would they fill if each egg is one unit?

Egyptian Numerals [10/14/1998]

Can you give me some information or references on Egyptian numerals?

Equals Sign with a Dot or a ~ Over It [01/25/2001]

What does an equals sign with a dot (.) over it mean?

Estimating Quotients [08/29/2001]

What is a valid estimation? Alternate ways of rounding off; significant digits.

Estimating Sums and Differences [10/11/2006]

When estimating sums and differences, I was taught to round each number to the greatest place value position of the smallest number. Is that correct, and can you show me how that works?

Estimation vs. Rounding [01/08/2002]

On our testing we have questions about estimating answers and rounding answers. The two methods give different answers. How are the two methods different?

Etymology of Odd and Even [10/08/2002]

Why are odd numbers named 'odd' and even numbers named 'even'?

Evaluating Absolute Values [02/05/1999]

How do you answer a question that looks like |-6 + 5| ?

Even and Odd Fractions? [01/12/1999]

What rules would we have to have to be able to define a fraction as even or odd?

Even and Odd Numbers [6/13/1996]

Why do we have odd and even numbers?

Even More on Order of Operations [10/26/2017]

How can 8/4(3-1) have two answers? Doctor Peterson unpacks the ambiguities that have made the order of operations a persistent lightning rod for controversy — and misunderstanding.

Evens and Odds in the Multiplication Table [09/11/2005]

In the multiplication table, are there the same number of even numbers as odd numbers, or is there more of one kind than the other?

Expanded and Standard Forms [09/06/1998]

What does it mean to write numbers in 'standard form' and 'expanded form'?

Explaining Order of Operations [09/06/2001]

How would you explain the order of operations to a 5th or 6th grader who has not yet studied the subject?

Explanation of Significant Figures [09/11/2007]

I'm confused about how to determine how many significant digits a given number has. Can you explain it?

Exploring Estimation [08/29/2003]

If a rare truffle is $13.20 for 0.44 oz, estimate the cost of a whole pound.

Fact Families [09/21/2000]

What is a "fact family"?

Fact Family vs. Number Family [09/24/2001]

What is a number family?

Factors and Multiples [01/27/1998]

My son is in 4th grade and needs help naming a common multiple of a pair of numbers.

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 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?

Finding the Operation [06/21/1999]

How can I find the operation '?' given 3?4 = 5, 4?7 = 1, 8?4 = 0, and 1?2 = 9?

Finite Numbers [05/13/2003]

What are finite numbers?

The First Number of the Fibonacci Sequence [10/17/1995]

What is the first number in the Fibonacci sequence, 1 or 0?

Formula for Triangular Numbers [08/29/1998]

Is there a formula to figure out triangular numbers?

A Four-year-old Thinks About Even and Odd Numbers [07/22/1999]

"Half" means 2 parts, and some numbers are not that way. Mom says they're "odd." It's not fair letting 2 be even all by itself!

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.

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.

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