Significant Figures or Significant Digits

Sig Figs/Sig DigitsOr

AAAHHHHHHH!!!!!!

Why do scientists insist upon using Significant Figures in calculations, my math

teacher does not?

Significant figures or Sig Figs are used in science because our numbers are representing how carefully (exactly) a measurement was made.(By the way, we are also REALLY fussy about units too.)Sig fig rules have not always existed. Upon the wide spread adoption the calculator, the rules were developed.

Before the Calculator (even I am too young to have experienced

this period in history)Before the calculator was used, students in math and science used something called a slide ruler.

Due to the way one uses a slide ruler, the number of decimals for an answer were limited.With a calculator, this is not so.A calculator is not aware that the numbers you are using have limited scale (or you only measured to the tenth or hundredth).So your calculator will provided you with all the decimals for an answer (it is just following the mathematical algorithm).

When to use them and when not to?

For anything that is measured such as mass, length, etc… which you could make a finer measurement, you use sig figs.

For anything that is counted such as people, you would not need to use sig figs.

Count me as a whole!

Which of the following are counted numbers?

A. Density of waterB. Eggs in a cartonC. Ribbon lengthD. Temperature of waterE. Swimmers in a race

ESTABLISHING THE FOUNDATIONHow many sig. figs. are in the number?

2000

In the number above, only one of the figures (or digits) is significant.

That is the 2

Your first rule to write down is: all non-zero numbers are significant.The zeros are just place holders letting you know the relative size.

2000.

In this number a decimal has been added. This change is important, because it is communicating to you that the person measuring this quantity measured to the ones place and it was zero.So this number has four significant figures.Rule 2: Any zeros between a non-zero starting number and a decimal is significant.

Practice

a. 34b. 30c. 52.d. 30.

a. 2b. 1c. 2d. 2

2000.0

This number now has a zero after the decimal. It has five sig figs because there is a non-zero number before the decimal and then zeros.

Rule 3: If the zero is after a non-zero number and a decimal point, it is significant.

.02

Here is a different situation. The measured quantity did not have any amount in the tenths place, but started in the hundredths place.So this number only has one significant number.

If you review rules 2 and 3, you will see that the zero must come after a non-zero number to be significant. Here it comes before.

0.020

What do you think?This number has two sig figs.

The last zero comes after the non-zero number (first think to look for) and the decimal point (second thing to look for).

Zeros, such a painSo for zeros, you need to look for a non-zero number before it and the decimal place. If it is sandwiched between or found after both, then it is significant.Another situation, is the zero sandwiched between two non-zero numbers.

Practice

40005034200.340.050842.00.00002750.0200.00402

1434141223

ADDING/SUBTRACTING

One Rule and Only One Rule

For adding or subtracting, look at the numbers to be added together and see which number has the LEAST number of places past the decimal.

Therefore, since one measurement was not as precise as the others, the added or subtracted number is limited to that many places.

Practice

0.087 + 0.0000093 =

How many places may be allowed in the final answer?

3

Individual Practice

How many places may be allowed in the final answer?2 + 3.45 = ________3.6792 + 34.56 = _________20 + 0.1 = ___________

Doing the Calculations

0.876 + 0.745 = ___________12.3+ 0.34 = ____________40002.1 + 45266.75 = ____________

MULTIPLYING AND DIVIDING

The same rules apply for multiplying and dividing

You look at the numbers being multiplied together (or divided) and count how many sig figs are present in each.

The numerical solution can only have as many sig figs as are in the least number in the problem.

Example

6.78 * 5.6 = ___________

The answer on the calculator is: 37.968But, the first number has just 3 sig figs and the second number has just 2 sig figsSo the number, adjusted for sig figs is 38. (rounding occurred because of the 9)

Group Practice

a. 67.23 * 1.22 = _______b. 2.044* 3.4 = _________c. 463 * 0.204 = ________

a. 80.0b. 6.9c. 94.5

Individual Mixed Practice

a. 56.4 + 23 = _________b. 56.4* 23 = _________c. 4.21/3.2 = _________

a. 79b. 1300c. 1.3