By the end of this tutorial you will understand:
- What sig figs are.
- The fastest way to find to the sig figs.
- How to place your answer in sig figs after arithmetic.
What are sig figs?
Simply put, sig figs is the degree of reliability for a measurement. Calculations done on a measurement are as accurate as the least reliable measurement. You will encounter sig figs in chemistry, when dealing with atomic structures, and molecular. It’s worth noting that Sig Figs are commonly called Significant Figures, or Significant Digits. But I prefer Sig Figs.
The fastest way to finding sig figs.
The traditional way of teaching sig figs contains too many conditions. List of rules here. So, I found a way to simplify the approach into the following statement.
Sig figs are the number of digits from the “first nonzero” to the “last position”.
The “Last Position” is the last number’s position if the measurement has a decimal. Otherwise, the “Last Position” is the last non-zero’s position.
The “First NonZero” is the position of the first non-zero.
Another way of writing this is below.
Number of sig figs = ( “Last Position” – “First NonZero” ) + 1
NOTE: If the measurement is defined, then all the numbers are sig figs.
Now let’s do a few examples.
Note that “method 1” is done by counting. While method 2 is done by using the algorithm.
Question 1: 1200 has how many sig figs?
Answer: 2 sig figs.
Method 1: The first is 1, and the last is 2. There are two digts from digit 1 to digit 2. Therefore 2 sig figs.
Method 2: ( “Last Position” – “First NonZero” ) + 1 ) = (2 – 1) + 1 = 1 + 1 = 2 sig figs
Question 2: 1200.25 has how many sig figs?
Answer: 6 sig figs
Method 1: The first is digit 1 and the last is digit 5 because there is a decimal. There are 6 digits from 1 to 5. Therefore 6 sig figs.
Method 2: ( “Last Position” – “First NonZero” ) + 1 ) = (6 – 1) + 1 = 5 + 1 = 6 sig figs
Question 3: 0.0025 has how many sig figs?
Answer: 2 sig figs
Method 1: The first is digit 2 and the last is digit 5. There are 2 digits from 2-5. Therefore 2 sig figs.
Method 2: ( “Last Position” – “First NonZero” ) + 1 ) = (5 – 4) + 1 = 1 + 1 = 2 sig figs
Question 4: 1.0010 has how many sig figs?
Answer: 5 sig figs.
Operations then sig figs:
When multiplying and dividing measurements, the result must have the same sig figs as the term with the least. However, you should ignore sig figs for unitless numbers.
When adding and subtracting, the result must have the same number of decimal places as the term with the least.
Question 5: What is the average of 130 in and 122.14 in
Answer: 76 in
Average is sum of the terms divided by 2.
130 in + 122.14 in = 152.14, only worry about sig figs after your calculation are done.
152 in / 2 = 76 in. 2 is unit-less, so you should consider sig figs in this operation.
Question 6: What is the 8,000 ft / 20 ft
Answer: 4 x 103
8,000 ft / 20 ft = 4 x 103. Not 400 because you must use the sig figs from the term with the least.
That concludes this tutorial.
Like always I appreciate feedback.