What is the density of a solid that has a mass of 60.27 g and a volume of 711 mL?

D = M/V = 0.084767932 g/mL

How do we know how to express (where to round off) this answer?

Evaluating Zero as a Significant Digit

All nonzero digits are significant.

Significant (Measured) Digits in Calculations

A zero is significant when it is :

1. Between nonzero digits:205 61.09

2. At the end of a number that includes a decimal point:

0.500 25.160

3.00 20.

A zero is not significant when it is :

1. Before the first nonzero digit. (These zeros are used to locate a decimal point.):

0.0025 0.0108

2. At the end of a number without a decimal point: 1000 590

Practice Problem

How many significant figures are in each ofthese numbers?

a) 4.5 inches e) 25.0 grams b) 3.025 feet f) 12.20 liters c) 125.0 meters g) 100,000 people d) 0.001 mile h) 205 birds

2 34

11

34

4

Rounding Off Numbers

Look at the next digit (after those you want to retain for the proper number of significant digits)

If it is 5 or greater → round up.

If it is 4 or less → round down.

Practice Problem

Round off these numbers to the number of significant figures indicated:

a) 42.246 (four)b) 88.015 (three)c) 0.08965 (three)d) 0.08965 (two)e) 225.3 (three)f) 14.150 (three)

42.2588.00.08970.09022514.2

Multiplication or Division

Round off your answer to be no more than the fewest number of significant digits.

Practice Problem

a) (134 in.)(25 in.) = ?

b) 213 miles 4.20 hours = ?

c) (2.2)(273) 760 = ?

3400 in2

Limited to 2 sigs

50.7 mi/hr

.79

Limited to 3 sigs

Limited to 2 sigs

Addition or Subtraction

Round off the answer to no more than the fewest number of places to the right of the decimal.

(i.e greatest level of shared confidence)

Practice Problem

How many significant figures should the answer in each of these calculations contain?

a) (14.0)(5.2)

b) (.1682)(8.2)

c) (160)(33) 4d) 8.2 + 0.125

2 sigs

1 sig

2 sigs

2 sigs - tenths

= 73

0.125 8.2= 8.3

= 1000

= 1.4

How many significant figures should the answer in each of these calculations contain?

e) 119.1 – 3.44

f) 94.5 1.2

g) 1200 + 6.34

h) 1.6 + 23 – 0.005

4 sigs - tenths

2 sigs

2 sigs - singles

2 sigs - hundreds

= 115.7

= 79

= 1200

= 25