Significant FiguresSignificant FiguresSignificant FiguresSignificant Figures

The Four RulesThe Four Rules

Rule #1:All non-zero numbers are

always…

4 3

2

1

6

78

9

5

SIGNIFICANT!!!

So, the only number So, the only number to worry about is…to worry about is…

So, the only number So, the only number to worry about is…to worry about is…

0

Using Othello to understand Rule #2Zeros between non-zero numbers

are always significant

Using Othello to understand Rule #2Zeros between non-zero numbers

are always significant

The Other Zero Rules

All final zeros to the ______ of a decimal point are significant.

right

Zeros that act as ____________ are NOT significant.

placeholders

0.0000340000

Rule #3:

Rule #4:

For rule #3 and #4, it can be summarized by these two questions:

1) Is there a decimal point?2) Is there a number in front of the

zero?Answering yes to both of these questions means that the zeros are significant figures.

1000000.0

Significant?

Another note: if a number is Another note: if a number is written in scientific notation, written in scientific notation, all numbers all numbers beforebefore the x 10 the x 10 are significant, all numbers are significant, all numbers

afterafter are not significant. are not significant.

Another note: if a number is Another note: if a number is written in scientific notation, written in scientific notation, all numbers all numbers beforebefore the x 10 the x 10 are significant, all numbers are significant, all numbers

afterafter are not significant. are not significant.

Is ItIs ItSignificant?Significant?

Is ItIs ItSignificant?Significant?

16407.100

0.00010080

904008000

Significant Non-Significant

8 sig figs

5 sig figs

6 sig figs

Let’s look at some examples

a. 508.0 L

b. 820 400.0 L

c. 1.0200 x 105 kg

d. 807 000 kg

4 significant figures

7 significant figures

5 significant figures

3 significant figures

Let’s look at some examples

a. 0.049 450 s

b. 0.000 482 mL

c. 3.1587 x 10-8 g

d. 0.0084 mL

5 significant figures

3 significant figures

5 significant figures

2 significant figures

So, why are So, why are significant figures significant figures

important?important?

So, why are So, why are significant figures significant figures

important?important?

Significant figures and mathSignificant figures and math

Addition and Subtraction

• When adding or subtracting—the answer has the least number of decimal places

• Hint: Before adding and subtracting, line up all the numbers so the decimal points align.

187.6+ 2.303

189.903

189.9

961.95- 943

18.95

19

Multiplication and Division

• When multiplying or dividing—the product has the least number of significant figures

21.6x 0.067

1.4472

1.4

7216÷ 0.034

212235.294118

210000

(3 sig figs)

(2 sig figs)

(2 sig figs)

(2 sig figs)

(4 sig figs)

(2 sig figs)

Or 2.1 x 105

Now, try some of Now, try some of these on your ownthese on your ownNow, try some of Now, try some of

these on your ownthese on your own

Addition

a) 43.2 cm

51.0 cm

+ 48.7 cm

b) 258.3 kg

257.1 1 kg

+ 253 kg

c) 0.0487 mg

0.05834 mg

+ 0.00483 mg

142.9 cm 0.1 1 1 87 mg768.41 kg

768 kg 0.1119 mg

Multiplication

a) 24 m x 3.26 m

b) 120 m x 0.10 m

c) 1.23 m x 2.0 m

d) 53.0 m x 1.53 m

= 78.24 m

= 78 m

= 12 m

= 2.46 m= 81.09 m

= 2.5 m

= 81.1 m

Why do we have them?

When we measure things, we want to measure to the place we are sure of and guess one more space.

So, they show the uncertainty in our

measurements

Since the marks on this Since the marks on this ruler are subdivided as ruler are subdivided as they are, our answer for they are, our answer for

the length of this nail has the length of this nail has 33 significant figures. significant figures.

Since the marks on this Since the marks on this ruler are subdivided as ruler are subdivided as they are, our answer for they are, our answer for

the length of this nail has the length of this nail has 33 significant figures. significant figures.

However, we only have However, we only have significant figures when significant figures when

we are we are measuringmeasuring something. something. CountingCounting will give you an exact will give you an exact

number.number.

However, we only have However, we only have significant figures when significant figures when

we are we are measuringmeasuring something. something. CountingCounting will give you an exact will give you an exact

number.number.