Significant figures, also called significant digits, are those digits that carry meaning
contributing to its precision. The concept of significant figures is used in rounding numbers into much precise answers.
Rules
for Significant Figures
1. Digits from 1-9 are always significant.
2. Zeros between two other significant digits are always
significant
3. One or more additional zeros to the right of both the
decimal point and another significant digit or nonzero digits are significant.
4. Zeros used solely for spacing the decimal point
(placeholder) are not significant.
|
EXAMPLES
|
# OF SIG. DIG.
|
COMMENT
|
|
453 kg
|
3
|
All non-zero digits are always significant.
|
|
5057 L
|
4
|
Zeros between 2 sig. dig. are significant.
|
|
5.00
|
3
|
Additional zeros to the right of decimal and a sig. dig.
are significant.
|
|
0.007
|
1
|
Placeholders are not sig
|
Adding and Subtracting
RULE: When adding or subtracting
your answer can only show as many decimal places as the measurement having the
fewest number of decimal places.
Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g
We look to the original problem to see the number of decimal
places shown in each of the original measurements. 2.1 shows the least number
of decimal places. We must round our answer, 20.69, to one decimal place (the
tenth place). Our final answer is 20.7 g
Try: a.
(1.650 m) + (3.0 m) =
b. (3.0 x104
g) -(6.889 x103g) =
Multiplying and Dividing
RULE: When multiplying or dividing,
your answer may only show as many significant digits as the multiplied or
divided measurement showing the least number of significant digits.
Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm =
5946.50525 cm3
We look to the original problem and check the number of
significant digits in each of the original measurements:
22.37
shows 4 significant digits.
3.10
shows 3 significant digits.
85.75
shows 4 significant digits.
Our answer can only show 3 significant digits because that
is the least number of significant digits in the original problem.
5946.50525 shows 9 significant digits, we must round to the
tens place in order to show only 3 significant digits. Our final answer becomes
5950 cm3.
Try: a.
(1.650 m) (3.0 m) =
b. (6.0 x104
g) (2.5 x103g) =
No comments:
Post a Comment