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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0.9999... equal to 1? [6/28/1996]

One of my teachers insists that the value of 0.9999999999... is one. The other insists that anyone who thinks that 0.9999999... is one is an idiot!

1 and 0: Prime or Composite? [10/06/1997]

Is the number one a prime or a composite number? Why? What about zero?

About Rational Numbers [3/20/1996]

Can you explain "rational numbers" to me? How do you express them? What kind of operations can you perform on them?

Adding and Subtracting Roman Numerals [10/07/1997]

Do you have any suggestions for how to teach adding and subtracting of Roman numerals?

Adding Arithmetic Sequences [07/10/1998]

How do you add the numbers from 1 to 5000 without actually doing it or using a calculator? What if you were adding just the odd numbers?

Adding in Base 9 and Base 5 [10/21/1997]

In 3rd grade my son is learning how to add in bases other than 10.

Ancient Math Symbols [09/07/1997]

I need to know the numerals for 1,10 100, 1000 in Arab, Samarian, Greek, Roman, and Hindu.

Base 2 Subtraction and Clock Arithmetic [01/26/2001]

We know that computers use the "2's complement" method to do subtraction of base 2 numbers, and that this method works every time, but we have no idea why it works.

Base Number [10/07/1998]

What does base number mean?

Cardinal and Ordinal Numbers [01/08/1997]

How can 3 be both a cardinal and ordinal number at the same time?

Concepts of Adding in Base 2 [08/18/1998]

I don't understand the whole concept of base 2.

Converting Fractions to Decimals [01/08/1997]

How do you convert fractions to decimals? How do you turn decimals into ratios?

Converting Repeating Decimals to Fractions [11/19/1997]

I know .333333333333 is 1/3, but what is the trick to it?

Defining Kinds of Numbers [03/21/1997]

Could you please define: perfect numbers, deficient numbers, square numbers, abundant numbers, amicable numbers, and triangular numbers?

Diagram for Math Numbers [10/05/1997]

My daughter is doing a tree diagram using terms related to math "numbers." Could you please explain in lay terms what surds are?

Difference Between Zero and Nothing [12/12/1996]

What is the difference between zero and nothing?

Divide by 0 Undefined? [9/10/1996]

When something is divided by 0, why is the answer undefined?

Explanation of Place Values [05/08/2000]

What is meant when we say that as you progress from the units place to the tens place to the hundreds place, the value is increasing ten times the number on its right?

First Ten Perfect Numbers [12/11/2001]

I have to figure out at least 10 perfect numbers for my homework.

How can .999999.... equal 1? [03/21/2001]

If .99999999.... goes on forever, wouldn't it be just a little below one?

Is 120 a Perfect Number? [10/15/1997]

Is 120 a perfect number? It seems to fit all of the criteria.

Multiplying by 0 [03/09/2001]

Why, when multiplying any number by 0, do you get 0?

Names of Bases (Octal, Hexadecimal, etc.) [04/15/2002]

I don't know the names of the bases after nonadecimal.

Negative Bases [06/10/1999]

Are there such things as negative bases?

Numbers [12/10/1997]

How do integers and whole numbers, rational numbers, transcendental numbers, and counting numbers relate to each other?

Numbers: Cardinal, Ordinal, Nominal? [10/25/1999]

Which group of numbers - cardinal, ordinal or nominal - does "time" fit into? Are there other types of numbers as well?

Order of Operations vs. Associative Property [10/10/2002]

Is the associative property an exception to the order of operations, a corollary, or something totally unrelated?

Perfect Numbers [12/07/1996]

What are the first 10 perfect numbers? Is there a formula for getting a perfect number?

Perfect Numbers [08/14/1997]

What is the highest perfect number that has been found? How many perfect numbers are there? What are they?

Perfect Numbers - Basics, History [11/3/1996]

What is the next perfect number after 28?

Pi in Real Life [7/1/1996]

We have just covered circumference of circles and pi. The children asked how this concept is used in real life and who pi is named after.

Plotting Coordinates on a Graph [07/02/1999]

How can I solve a problem like 3+(-2) = ? using a number line, and how can I plot coordinates like (-4,3) on an X-Y graph?

Prime Numbers vs. Prime Factors [01/13/1997]

What is the difference between a prime number and a prime factor?

Properties of Real Numbers [05/20/1997]

What are the associative, the commutative, and the zero product properties?

Purpose of Zero [11/17/1994]

What is the actual purpose of the number zero?

Rational Numbers [11/24/1997]

Which is greater, the number of rational numbers between 0 and 1 or the number of rational numbers between 0 and 2?

Real and Other Numbers [08/29/2001]

What is a real number? What are the different kinds of real numbers? Are there any more numbers besides real numbers?

Real Number Terminology [12/04/1996]

What does it mean to be non-existent over the reals?

Representing Numbers in Different Bases [08/05/1998]

How did they get the 2 x 3 cubed? Plus some number less than 3 cubed?...

Rounding to One Digit Accuracy [04/16/1998]

Can you explain what it means to round to one digit accuracy?

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