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Significant Digits!

By: Miriah F. and Kyle M.



Rules of Rounding
:]

1. Mark the rounding location.
Ex.
Round 76.4563 to the thousandth place
76.456
/3
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:]
2. If the digits to the right of the mark are >5 round up.
Ex.
Round 9.8756 to the thousandth place.
9.875
/6
6
>5
9.876
:]
3. If the numbers to the right of the mark are <5 round down.
Ex.
Round 7.7511 to the thousandth place.
7.751
/1
1
<5
7.751
:]

4. If the digit to the right is exactly 5, look to the left.
Ex.
Round 4.1235 to the thousandth place.
4.123
/5
5
=5
4.123
Round 4.1275 to the thousandth place.
4.127
/5
5
=5
4.128

When are Digits Significant?
Non-zero digits are always significant. Thus, 22 has two significant digits, and 22.3 has three significant digits.
With zeroes, the situation is more complicated:

  1. Zeroes placed before other digits are not significant; 0.046 has two significant digits.
  2. Zeroes placed between other digits are always significant; 4009 kg has four significant digits.
  3. Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.
  4. Zeroes at the end of a number are significant only if they are behind a decimal point as in (c). Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point.
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Significant Digits in Multiplication, Division, Trig. functions, etc.

In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc.
Thus in evaluating sin(kx), where k = 0.097 m-1 (two significant digits) and x = 4.73 m (three significant digits), the answer should have two significant digits.
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Significant Digits in Addition and Subtraction
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
Example:
5.67 J (two decimal places)
1.1 J (one decimal place)
0.9378 J (four decimal place)
7.7 J (one decimal place)


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