NOTES: 3.1, part 2 -

Significant Figures

Significant Figures:

The “sig figs” in a measurement include all of

the digits that are known, plus a last digit that

is estimated

The # of sig figs in a measurement depends

on the precision of the instrument being used

How do we determine which digits are

significant?

THE “RULES” FOR

SIG FIGS!!

1) All non-zero numbers are

significant.

EXAMPLES:

672 -

34 -

1,245 -

24,346 -

1) All non-zero numbers are

significant.

EXAMPLES:

672 - 3 sig figs

34 - 2 sig figs

1,245 - 4 sig figs

24,346 - 5 sig figs

2) Zeroes between two non zero

numbers are significant.

EXAMPLES:

202 -

1.01 -

1,305 -

10,001 -

3,002 -

62,004 -

2) Zeroes between two non zero

numbers are significant.

EXAMPLES:

202 - 3 sig figs

1.01 - 3 sig figs

1,305 - 4 sig figs

10,001 - 5 sig figs

3,002 - 4 sig figs

62,004 - 5 sig figs

3) “Leading” zeroes are not

significant (just placeholders)

EXAMPLES:

0.0012 -

0.000231 -

0.00855 -

0.0022 -

0.0006469 -

3) “Leading” zeroes are not

significant (just placeholders)

EXAMPLES:

0.0012 - 2 sig figs

0.000231 - 3 sig figs

0.00855 - 3 sig figs

0.0022 - 2 sig figs

0.0006469 - 4 sig figs

4) Final or trailing zeroes are not

significant UNLESS there is a

decimal point in the number.

EXAMPLES:

150 -

22.0 -

12,500 -

0.00240 -

5,250 -

0.02300 -

0.000350 -

4) Final or trailing zeroes are not

significant UNLESS there is a

decimal point in the number.

EXAMPLES:

150 - 2 sig figs

22.0 - 3 sig figs

12,500 - 3 sig figs

0.00240 - 3 sig figs

5,250 - 3 sig figs

0.02300 - 4 sig figs

0.000350 - 3 sig figs

5) Powers of ten are not

significant

EXAMPLES:

1.50 X 102 -

8.890 x 104 -

7.0 x 108 -

4.010500 x 1010 -

6.35 x 10-12 -

5) Powers of ten are not

significant

EXAMPLES:

1.50 X 102 - 3 sig figs

8.890 x 104 - 4 sig figs

7.0 x 108 - 2 sig figs

4.010500 x 1010 - 7 sig figs

6.35 x 10-12 - 3 sig figs

PRACTICE: Determine how many

significant figures are in each of the

following measurements

1) 0.0034050 L ___________

2) 33.600 m ___________

3) 7500.0 g ___________

4) 47,900 mm ___________

5) 7,000,000,001 miles ___________

6) 8.07 Hz ___________

PRACTICE: Determine how many

significant figures are in each of the

following measurements

1) 0.0034050 L ___________

2) 33.600 m ___________

3) 7500.0 g ___________

4) 47,900 mm ___________

5) 7,000,000,001 miles ___________

6) 8.07 Hz ___________

5

553103

Sig Figs in Calculations:

Find the area of a floor that measures

7.7 meters by 5.4 meters:

AREA =

Sig Figs in Calculations:

Find the area of a floor that measures

7.7 meters by 5.4 meters:

AREA = 41.58 m2

But wait!...

The calculated answer has 4 sig figs, but

each measurement used in the calculation

only had 2!

The calculated area cannot be more precise

than the measured values used to obtain it!

SO…we “round” the answer to the

appropriate # of sig figs

ROUNDING:

After you have determined how many sig figs

the answer can have, round to that many

digits:

If the last significant digit is less than 5: leave

the last sig fig as is;

If the last significant digit is 5 or greater:

round up!

Practice Problems:

How many sig figs in each of the following?

1) 123 meters -

2) 40,506 meters -

3) 9.8000 x 104 m -

4) 0.07080 m -

5) 98,000 m -

Practice Problems:

How many sig figs in each of the following?

1) 123 meters - 3 sig figs

2) 40,506 meters - 5 sig figs

3) 9.8000 x 104 m - 5 sig figs

4) 0.07080 m - 4 sig figs

5) 98,000 m - 2 sig figs

More practice…Round the following

measurements off so that they each

contain 3 significant figures.

1) 366.2 L ___________

2) 9,047,022 mg ___________

3) 12.76 g ___________

4) 999.9 J ___________

More practice…Round the following

measurements off so that they each

contain 3 significant figures.

1) 366.2 L ___________

2) 9,047,022 mg ___________

3) 12.76 g ___________

4) 999.9 J ___________

366 L

9,050,000 mg

12.8 g

1.00 x 103 J

Notice this one must be in scientific

notation to have 3 sig. figs.

NOTES: 3.1, part 2 –

Operations With

Significant Figures!!

ADDITION AND SUBTRACTION

First add or subtract, then round the answer to

the last decimal place they have in common.

25.46 1.6251

+ 221.3 -0.543

= = = =

ADDITION AND SUBTRACTION

First add or subtract, then round the answer

to the last decimal place they have in

common.

25.46 1.6251

+ 221.3 -0.543

= 246.76 = 246.8 = 1.0821 = 1.082

Example:

123.25 + 46.0 + 86.257 =

=

Example:

123.25 + 46.0 + 86.257 = 255.507

= 255.5

The answer is expressed as

255.5 since 46.0 has only one

decimal place.

Examples:

a. 15.2 b. 10.8164

+ 5.0892 - 8.22

= = = =

c. 17.1 d. 2.1 + 4.235 + 3.92

- 0.77

= = = =

Examples:

a. 15.2 b. 10.8164

+ 5.0892 - 8.22

= 20.2892 = 20.3 = 2.5964 = 2.60

c. 17.1 d. 2.1 + 4.235 + 3.92

- 0.77

= 16.33 = 16.3 = 10.255 = 10.3

MULTIPLICATION AND

DIVISION

Multiply or divide first, then round the answer

to the same number of sig figs as the

smallest number you started with.

1.311 x 2.20 = =

6.884 / 2 = =

MULTIPLICATION AND

DIVISION

Multiply or divide first, then round the answer

to the same number of sig figs as the

smallest number you started with.

1.311 x 2.20 = 2.8842 = 2.88

6.884 / 2 = 3.441 = 3

Example:

23.0 x 432 x 19 =

=

Example:

23.0 x 432 x 19 = 188,784

= 190,000

The answer is expressed as 190,000 or 1.9 x 105 since 19 has only two sig. figs.

Examples:

a. 3.214 x 4.24 =

b. 6.8 x 3.145 =

c. 122.82 / 2.00 =

d. 0.072 / 4.36 =

e. (5.82 x 760 x 325) =

(723 x 273)

Examples:

a. 3.214 x 4.24 = 13.6

b. 6.8 x 3.145 = 21

c. 122.82 / 2.0 = 61.4

d. 0.072 / 4.36 = 0.17

e. (5.82 x 760 x 325) = 7.3

(723 x 273)

1) 36.57 m / 3.21 s =

2) 41.376g + 13.3g + 42.9g =

3) 5.67 m x 13.44 m =

4) (5.83 m / 2.67 s) / 2.1 s =

5) 9.374 V x 6.0 =

Perform the following calculations. Round your

answers to the proper # of sig. figs.

1) 36.57 m / 3.21 s = 11.4 m/s

2) 41.376g + 13.3g + 42.9g = 97.6 g

3) 5.67 m x 13.44 m = 76.2 m2

4) (5.83 m / 2.67 s) / 2.1 s = 1.0 m/s2

5) 9.374 V x 6.0 = 56 V

Perform the following calculations. Round your

answers to the proper # of sig. figs.

From now on, we will round all our answers

to the correct # of significant figures!