Significant Figures(HOW TO KNOW WHICH DIGITS OF A NUMBER ARE IMPORTANT)

How Accurately Can You Measure with This?

Could you find measurements like this? 1 inch

2.5 inches

3.1 inches

4.6348 inches

Accuracy

We want our numbers to convey the level of accuracy we had when measuring

Math operations can lead to problems with this: 1.0/3.0 = 0.33333333333333333333333

(The answer looks a lot more precise than the numbers we started with)

So, we keep track of the number of significant digits we start with, and use it to round our answer. 1.0/3.0 = 0.33

Rules for Significant Digits

Count the number of digits: 45.1 = 3 sig figs

612 = 3 sig figs

9.12345 = 6 sig figs

Zeroes are tricky: .0000005 NOT significant

6300 NOT Significant

6300. Significant

705 Significant

(Try putting the number in scientific notation, if the zeroes go away, they’re not significant)

Practice with Zeroes

How many significant figures do each of these numbers have?

5437.2

890

650.0

85

80

.0098

6.004

0.008

602

More Practice:

5,067

4,080

9.01

.01

.00302

10.004

6.120

Math With Significant Figures

Adding / Subtracting

Look at all the numbers you started with.

Find the one with the least number of digits after the decimal place.

Round your answer to that number of decimal places.

Multiplying / Dividing

Look at the numbers you started with.

Find the one with the least number of significant digits.

Round your answer to that number of significant digits

Adding/Subtracting

Example: 42.0 + .13 = 42.13

42.0 has one digit after the decimal, .13 has two, so I’ll round the answer to 1 digit after the decimal.

Answer: 42.1

That means this is true: 5 + .4 = 5

Why?

Keep in mind that ‘5’ doesn’t mean 5 anymore

When we write ‘5’ now, what we really mean is that our number is somewhere between 4.5 and 5.4.

Adding and Subtracting Practice

4.12 + .1 =

520 + .02 =

12 + 5.1 =

36.8 – 4 =

5.34 - .2 =

Multiplying and Dividing

Example:

5.2 x 7 = 36.4

5.2 has 2 sig figs, 7 has 1, so we’ll round it to 1 sig fig

5.2 x 7 = 40

Practice:

.03 x 5.21

6.2 x 10

5.780 x 2.0617

6 x .1

92 / .03

12 / 4.01