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Word Problems

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.

Whole Numbers and Multiples [09/11/2001]
My students and I have been trying to figure out what numbers are in the set of "Whole Numbers." Is zero a whole number?

Why Are All Repeating Decimals Classified Rational? [11/12/1997]
Please explain how .6 repeating can be a rational number when expressing it over 10's, 100's, etc.

Why Casting Out Nines Works [10/13/2008]
Can you explain in simple terms why the Casting Out Nines method works?

Why Commas after Every Three Places? [07/10/2001]
Why do we put commas after every three places in a number like 200,000?

Why does 0 factorial equal 1? [03/18/1998]
Why does 0! = 1? Is this like anything to the power of 0 equals 1?

Why Do We Have Leap Year ? [02/25/1998]
Why do we need to have one extra day each 4 years?

Why Do We Need to Study Rational Numbers? [04/22/2008]
My students want to know why they need to know what rational numbers are and what use they have in the real world.

Why Do We Use Order of Operations? [09/18/2008]
Why is it necessary to use order of operations? Why can't you just write a calculation from left to right, so 5+2^3*2 is just 2^3*2+5? Doctor Peterson shows how order of operations makes writing and understanding algebraic expressions quite simple.

Why Estimate? [08/16/2002]
Estimate to the nearest thousand a solution to Dave's subtraction problem. The numbers are: 6,107 - 2,980 = 4,127.

Why Estimate? [09/16/2002]
Why do we use estimation?

Why is 1 Not Considered Prime? [3/20/1995]
Just recently a grade six student asked me, "Why is 1 not considered prime?" I tried to answer, but as usual, could not since I do not understand this either. I thought the answer might lie in the fact that we aren't using the true definition or we are interpreting it wrong.

Why is Zero Not a Natural Number? [03/14/2001]
Can you explain why the natural numbers are {1, 2, 3...}? Also, is there a way to prove that zero is an integer?

Why Not Force Dividing by Zero? [10/22/2002]
Has there ever been an attempt to force dividing by zero just as it has been done so successfully by forcing the square root of -1 to be i?

Why Rules? [08/15/2001]
Why do we need to have rules for order of operations?

Why Study Prime and Composite Numbers? [01/25/2001]
My husband and I wonder why this is taught in school at all. Who uses this in the real world? Why does someone need to know whether a number is a prime number or not?

Why Two Odds Always Sum to an Even [03/21/2002]
Why do two odd numbers always equal an even number but two even numbers never equal an odd number?

Why Use Q and Z? [09/12/2001]
Why is the letter Q used for rational numbers and Z for integers?

Wondrous Numbers [02/07/2001]
What is a wondrous number?

Word for a 225th Birthday [07/10/2001]
This year America is celebrating its 225th birthday. As we celebrated the bicentennial in 1976, is there a term for 225 years?

Working in Base 7 [08/02/2007]
How do I add, subtract, multiply and divide in base 7?

Working with Different Bases [9/7/1995]
Please explain base 10 to me - then base 4.

Working with Sequences [11/14/1998]
Give the next two terms of the sequence: 1, 1, 2, 4, 3, 9, ....

Would Aliens Use Base 10? [05/13/2002]
If aliens had 6 fingers, would they use base 12?

Writing Numbers [11/24/2002]
Which words are okay to capitalize and when are hyphens used between words?

Writing Numbers in Words [09/15/1997]
Write each number in words: 1) 73.78007 2) 2.900087 (3) 34.4939.

Zero and One, Each Unique in Its Own Special Way [04/10/2013]
Zero is neither positive nor negative; 1 is neither prime nor composite. So how do we classify these numbers?

Zero and the Commutative Property of Multiplication [04/18/2003]
If we take 0x1, we get 0, and if we take 0x2, we still get 0, for it is still 0+0+0. But if we do it the other way round, why must it still be 0, if any number to the power of 0 = 1?

Zero Before the Decimal Point? [10/06/2000]
What is the merit of writing the zero before the decimal point in numbers less than one, for example 0.25?

Zero in the Denominator [8/14/1996]
What is the value of 4/0 * 0/4?

Zero Significance [10/27/2013]
Confused about the significance of the zeros on either side of a number such as 0.000, a student expresses doubts about manipulating them, and about representing integers in scientific notation. Doctor Peterson clears the air.


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