See also the
Dr. Math FAQ:
place value help
3D and higher
Browse Elementary Place Value
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Selected answers to common questions:
Place value questions.
- 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 [08/08/2005]
My math class is working on front end estimation, and I just don't get
it. Can you explain it to me?
- Front End Estimation (FEE) [08/23/2001]
My son was asked to estimate 1088 minus 399. His answer was 700. Wrong -
the "correct" answer was 600. The explanation given was 1000 minus 400
equals 600. Does this make sense?
- Front End Estimation of Addition Problems [09/06/2005]
An introduction to "front end estimation" and ideas on how to become a
- 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.
- Greatest Possible Error [02/11/1999]
I need an elementary-level answer to what is the greatest possible error.
- Hexadecimal Division and Addition [07/06/2003]
Could you provide a few examples of how to solve hexadecimal addition
and division problems?
- History of Zero and Place Value [02/17/1999]
Where were zero and place value invented or discovered?
- How Does the Crystal Ball Know What Number I Chose? [01/05/2010]
Doctor Ian reveals how a mind-reading crystal ball "knows" the number
you've chosen: represent any two-digit number 'ab' as 10*a + b....
- How Does This Multiplication Method Work? [11/12/2003]
I've just learned a new way to multiply, where all you have to do is
double, split in half, and add. Why does this work? Could you extend
this to division, where all you have to do is double, halve, and add?
- How Many Significant Digits? [10/17/2001]
Why does 5030 have three significant digits and 5030. four?
- How to Use a Chinese Abacus [06/24/2004]
An introduction to how the abacus works and examples of entering,
reading and adding numbers using it.
- Interpreting What "Rounding Up" Means [11/25/2006]
If I'm rounding up to the nearest 100, does 400 round up to 500 or
stay at 400? Why?
- Introducing Place Value to Children [10/01/2007]
Do you have any ideas on how to introduce children to the concept of
place value? I'm working with my son and finding it hard to explain.
- Moving the Decimal Point to Divide [02/28/2009]
Why do we move the decimal point over when doing decimal division? For
example, in the problem 100/0.4, why do we move the decimal and make
- Multiplying Decimal Numbers and Placing the Decimal Point [09/20/2007]
Why does counting up the total decimal places when multiplying decimal
- Number of Places in Products of Decimals [09/19/2002]
When you multiply decimals, why is there always the same number of
decimal places in the answer as in the problem?
- Operations in Scientific Notation [08/30/2001]
How do you add, multiply, and divide in scientific notation?
- Order of Digits in Multiplication [03/27/2001]
Why do we learn to multiply starting with the least significant digits in
the ones place, instead of starting with the larger place values?
- Placement of Commas in Writing Numbers [10/22/2003]
Why is the ones period named for the ones place value and why is the
thousands period named for the thousands place? Why is there not a
- Place Value and Roman Numerals [10/23/2001]
What is the importance of place value in relation to the value of a
- Place Value and the Number Nine [08/31/2002]
Why is 9 the largest number you can put into any place value spot?
- Reversing Digits When Reading Numbers [07/04/2004]
My young son reads the number 15 as fifty-one. What can I do to
ensure his language and understandings are corrected?
- Rounding 3.445 to the Tenths Place [05/24/2001]
In order to round 3.445 to the tenths place, shouldn't it first be
rounded to 3.45, then to 3.5? In my daughter's 6th grade math class, they
are told to round it directly to 3.5. Is that the preferred way?
- Rounding Decimals [10/19/1998]
Can you explain how to round decimals?
- Rounding Decimals: Even/Odd Issues [05/08/2001]
When do you round down, and when do you round up?
- Rounding Down to Nothing [10/23/2000]
If you had to round numbers from 0-4 to the nearest 10, would you round
them down to 0? Wouldn't that be inaccurate, since your answer would be
"nothing" when you do have "some"?
- Rounding Logic [12/11/1996]
When you have 5.5 why do you always round UP, instead of down?
- Rounding Millions [08/24/1997]
I know that 5 or greater rounds up and 4 or less rounds down, but how
many significant digits does this affect?
- Rounding Negative and-a-Half Up or Down [11/10/2010]
A class of students entertains several conflicting notions about which direction on the
number line to round negative halves. Doctor Peterson explains why no one convention
- Rounding Numbers [9/24/1995]
I want to ask about rounding numbers. Let's say we have to round to the
nearest 10's. 11,12,13,14,15,16,17,18,19... What do we do with 15?
- Rounding numbers [8/4/1996]
The children ask, "What is round?"
- Rounding to Nearest Multiple [07/31/2001]
I can't figure out how to round to the nearest multiple of 10, 100, or
- Rounding to Nearest Thousand [09/07/2001]
What is 46 rounded to the nearest thousand?
- Rounding to Specific Number of Significant Figures [05/30/2003]
How do I round to five significant figures?
- Rounding to the Nearest... [10/15/1997]
I don't know if I'm supposed to round a number (say 451.7576) to 451 or
451.7 or 451.8 when my teacher tells me to round to the nearest tenth.
- Rounding to the Nearest Tenth [8/29/1998]
Would 6.96 be 7.0 or 6.9?
- Rounding to Whole Numbers [04/01/2001]
How do you round to the nearest whole number?
- Rounding Up or Down on a 5 [06/13/1999]
If the digit following the one to be rounded is a 5, is rounding up or
rounding down determined by whether the original digit is even or odd?
- Round to Nearest Non-Zero Number [11/13/2001]
How do you round 47,859,600 to the nearest one non-zero number?