Return to the Purplemath home page

 

Try a demo lesson Join Purplemath Plus Login to Purplemath Plus

 

Index of free lessons | PM's free lessons in offline form | Forums | Search free lessons | Print this page | Local tutors

X

Rounding and Significant Digits (page 2 of 3)

Sections: General rounding, Rounding and significant digits


Another consideration in rounding is when you have to round to "an appropriate number of significant digits". What are significant digits? Well, they're sort of the "interesting" or "important" digits. For example,

    3.14159 has six significant digits (all the numbers give you useful information)

    1000 has one significant digit (only the 1 is interesting; you don't know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders; they may have rounded something off to get this value)

    1000.0 has five significant digits (the ".0" tells us something interesting about the presumed accuracy of the measurement being made: that the measurement is accurate to the tenths place, but that there happen to be zero tenths)

    0.00035 has two significant digits (only the 3 and 5 tell us something; the other zeroes are placeholders, only providing information about relative size)

     

    ADVERTISEMENT

     

    0.000350 has three significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to have a value of zero)

    1006 has four significant digits (the 1 and 6 are interesting, and we have to count the zeroes, because they're between the two interesting numbers)

    560 has two significant digits (the last zero is just a placeholder)

    560. (notice the "point" after the zero) has three significant digits (the decimal point tells us that the measurement was made to the nearest unit, so the zero is not just a placeholder)

    560.0 has four significant digits (the zero in the tenths place means that the measurement was made accurate to the tenths place, and that there just happen to be zero tenths; the 5 and 6 give useful information, and the other zero is between significant digits, and must therefore also be counted)

If you need to express your answer as being "accurate to" a certain place, here's how the language works with the above examples: Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved

    3.14159 is accurate to the hundred-thousandths place

    1000 is accurate to the thousands place

    1000.0 is accurate to the tenths place

    0.00035 is accurate to the hundred-thousandths place

    0.000350 is accurate to the millionths place (note the extra zero)

    1006 is accurate to the units place

    560 is accurate to the tens place

    560. is accurate to the units place (note the decimal point)

    560.0 is accurate to the tenths place

Here are the basic rules for significant digits:

    1)  All nonzero digits are significant.
    2)  All zeroes between significant digits are significant.
    3)  All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant.

Here are some rounding examples; each number is rounded to four, three, and two significant digits.

  • Round 742,396 to four, three, and two significant digits:
    • 742,400 (four significant digits)
      742,000 (three significant digits)
      740,000 (two significant digits)

  • Round 0.07284 to four, three, and two significant digits:
    • 0.07284 (four significant digits)
      0.0728   (three significant digits)
      0.073     (two significant digits)

  • Round 231.45 to four, three, and two significant digits:
    • 231.5 (four significant digits)
      231    (three significant digits)
      230    (two significant digits)

<< Previous  Top  |  1 | 2 | 3  |  Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "Rounding and Significant Digits." Purplemath. Available from
    http://www.purplemath.com/modules/rounding2.htm. Accessed
 

 

 

 

FIND YOUR LESSON
This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2000-2014  Elizabeth Stapel   |   About   |   Terms of Use   |   Linking   |   Site Licensing

 

 Feedback   |   Error?