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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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.

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.

Abundant and Deficient Numbers [10/14/1997]

What are abundant and deficient numbers, and what are they used for?

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 an Even and an Odd Number [03/26/2003]

Can you think of any two numbers, one even and the other odd, whose sum is even?

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?

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?

Are There Numbers Greater than Infinity? [10/23/1995]

Are there any numbers past infinity ?

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?

Base 3 [10/24/2001]

What is 2 + 2 in base three?

The Biggest Number [8/7/1996]

What is the largest number we know of?

Binary Notation [8/28/1996]

What is the smallest five digit number in decimal notation?

Calculators and e+ [09/27/1998]

What does the "e+" mean on a calculator?

Can Even and Odd Numbers Be Negative? [04/11/2006]

Can even and odd numbers be non-positive? For example, is 0 even? Is -4 even? Is -5 odd? I've heard both sides of this question. Who's right?

Casting out Nines: How Is 9 the Same As 0? Why Bother? [09/25/2009]

Doctor Peterson makes a case for this old technique in the calculator age -- and makes a connection between digital roots and remainders in base ten division.

Casting Out Nines to Check Arithmetic [08/26/1999]

Can you explain how to use the 'casting out 9's' technique in a way that a 6th grader can understand?

Checking When Rounding [12/10/2002]

Why is it important to check by estimating?

Classifying the Number One [11/27/1998]

My students have learned about prime and composite numbers. What classification fits the number 1?

Coin Recognition [11/20/2002]

My son is working on money in class and I am looking for something that shows what each coin looks like.

Commas in Numbers [09/13/2001]

Do commas change the value of a number?

Comparing Sums of Odd and Even Integers [03/31/2004]

Which is greater, the sum of all of the even numbers that are less than 100, or the sum of all of the odd numbers that are less than 100? It takes too long to add them all up!

Compatible Number Estimating [01/31/2002]

My homework is on compatible numbers to estimate quotients - for example, 1,625 divided by 38.

Compatible Number Method for Estimating [09/10/2001]

We are supposed to estimate using compatible numbers. How does one estimate something like 574/8?

Compensatory Number [01/29/2002]

Is there a math definition for the term "compensatory number"?

Consecutive Numbers [12/13/1997]

I don't understand what consecutive numbers are. Can you please explain them?

Counting a Span Versus Finding a Difference between Two Numbers [06/03/2004]

Why is it that the difference between year 2012 and year 2003 equals 10 years but the difference between the numbers 2012 and 2003 equals 9?

Counting Days of the Week [02/02/1999]

If today is Thursday, what day would it be 120 days from now?

Counting in the Teens [09/10/1998]

Why do we count ten eleven twelve thirteen, instead of ten eleventeen twelveteen thirteen?

Counting to One Billion [12/7/1995]

How long does it take to count to one billion counting one number per second?

Counting to Ten in Foreign Languages [05/16/2000]

What are the names for the numbers one through ten in Spanish?

Current Number System [6/13/1996]

Do you think our number system nowadays is sufficient for its uses?

Decimals and Roman Numerals [10/22/1998]

Is there any notation for fractions in Roman numerals?

Decimal System [08/12/2003]

Why the decimal system? Why not 12 as the base number?

Decoding Place Value [09/14/2003]

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

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