Significant Figures in Physics
| rules | practice |
- For counted numbers (no units):
- they are exact and therefore have an infinite number of significant figures
(i.e. 2 pencils = 2.00...0 pencils)
Numbers with units
are measured and used the following rules:
- For given values:
- All non-zero digits are significant
- All zeroes between non-zero digits are significant
- A zero to the left of the decimal and to the right
of the last non-zero digit can be significant if it is underlined or overstruck.
(i.e.
) Special case:if
the last significant figure is in units place the decimal point can be
written to show the significance. (i.e. 
)
- All zeroes to the right of the decimal and to the right
of the last non-zero digit are significant.
- For arithmetic:
- Addition and Subtraction
- Find the last significant figure in each value.
- Which last-significant-figure is farthest to the left (least precise?
- Round your answer to the position of that digit.
OR Find the value that is least precise and round your answer to that same precision (see below).
- Multiplication and Division
- Find the number of significant figures in each value
- Determine which value has the least number of significant figures
- Round your answer to the number of significant figures in that value
OR Find the value with the least accuracy and round off answer to that accuracy (see below).
Answers should always have a minimum of two significant figures.
You are allowed to have one significant figure beyond what the rules define.
- Rounding:
Find the digit you are rounding to. If the next digit is to the right of the decimal and greater than 4 then round the preceding digit up, otherwise leave the preceding digit alone. Replace the rest of the digits to the left of the decimal with zeroes. Digits to the right of the decimal are not replaced.
- Bottomlines
- 5.1 = 5.2 if the uncertainty is ±0.1, so 1 = 2
- 2.0 ≠ 2.000
- most times you can round to 3 sig figs, in spite of all of the rules, to get an acceptable answer
| rules | practice | Click here to go to a file that is easier to print.
Give the number of significant figures in each number. Do at least half of the problems. Do as many more as you need to practice, but * indicates a required problem.
*a) 5000 |
b) 1.56 |
c) 92 |
*d) 630 |
e) 90100 |
f) 40.7 |
| *g) 0.0001 |
*h) 0.0250 |
i) 0.0607 |
j) 300.5 |
*k) 0.0450 |
*l) 20.690 |
| *m) 140700 |
n) 2300 |
*o) 0.008900 |
*p) 6.020 |
q) 20030 |
r) 40 |
*s)  |
*t)  |
u) 4001 |
*v) 800.0 |
*w) 0.012 |
x) 0.0100 |
Round off each of the following values to three significant figures
| *aa) 72.65 |
*ab) 14736 |
ac) 0.00257 |
*ad) 0.0030555 |
ae) 647249 |
*af) 2.9999 |
| *ag) 6 |
ah) 14.96 |
*ai) 2996374 |
|
|
|
Do the following arithmetic
ba) add (in m)
|
*bb) add (in g)
|
*bc) add (in s)
 |
| *bd) 67.6 x 1.30 = |
*be) 41320/9.36 = |
*bf) 0.0572 x 1563 = |
| *bg) 9.36/3.12 = |
*bh) 0.030 x 5208 = |
bi) 4.300/132.7 = |
last modified 5-30-10