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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Counting to One Million [10/25/1999]

How long would it take to count to one million?

Counting Up Three Digit Numbers [10/27/1998]

How many possible 3-digit numbers are there with a middle zero? How many possible 4-digit numbers are there with two middle zeros?

Current Number System [6/13/1996]

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

Cute Numbers [06/03/2001]

How can I show that 2001 is a cute number? How can I show that every integer greater than 5 is a cute number?

Cute Numbers [08/29/2003]

I have found two definitions of a cute number. Which is correct?

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?

Defining Numerals, Numbers, and Digits [05/20/2004]

There seems to be a lot of ambiguity about the definitions of the words "numeral", "number", and "digit". It seems like I see them used somewhat interchangeably. What are their proper math definitions?

Definition of Interpolate [10/27/1995]

Could you please define interpolate and give me an example?

Definition of Mixed Number [11/22/2004]

Is 5 a mixed number? Why or why not? I think it is, because you can write 5 0/3, can't you?

Different Approach to a Set of Equations [11/13/2002]

The sum of four numbers is 22. The first number is twice the difference of the second and the fourth. The second number is five times the difference of the third and the fourth. The third number is twice the difference of the first and the fourth. What are the four numbers?

Different Types of Numbers [4/13/1996]

I don't understand how to tell the difference between the different kinds of numbers. i.e. reals, integers...

Digit Patterns of the Powers of 5 [09/14/1998]

Why is there a pattern in the last digits of the powers of 5?

Digit Reversal Trick Explained [03/23/2001]

Take a 3-digit number and subtract its reverse. Then, take the result and add its reverse. Why is the answer is always 1089, no matter what the initial numbers were?

Distance between Points on a Line [10/02/2002]

When the 10 distances between 5 pairs of points on a line are listed from smallest to largest, the list reads: 2,4,5,7,8,k,13,15,17,19. What is the value of k?

Dividing by Zero [05/18/2001]

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

Dividing Radicals [02/15/1999]

How do you simplify 7 sqrt32 / (5 sqrt63) ?

Divisibility and Subtraction in Other Bases [07/28/1999]

How can you tell if a number is even in bases other than base 10? How do you borrow when subtracting in other bases?

Divisibility Tests in Different Bases [11/16/2008]

How do divisibility tests work in other bases? For example, is there a test to tell if a number in base 9 is divisible by 7?

Division by Zero: Indeterminate or Undefined? [02/23/2002]

I'm having some trouble understanding division by zero.

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?

Doesn't Pi Ever Repeat? [7/8/1996]

How do people know that pi goes on forever without repeating?

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

When children should not use calculators to do math.

Duotrigintillion or Dotrigintillion? [03/14/2002]

What number is right - duotrigintillion or dotrigintillion?

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?

Equations with Infinity [07/29/1998]

How can you use infinity in maths equations? Is it like other numbers?

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?

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?

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.

Factors and Multiples [01/27/1998]

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

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