Introduction: Matter and Measurement Chapter 1. Uncertainty in Measurement The term significant figures refers to digits that were measured. When rounding.

Introduction:Matter and Measurement

Chapter 1

Uncertainty in Measurement

•The term significant figures refers to digits that were measured.

•When rounding calculated numbers, we pay attention to

significant figures so we do not overstate

the accuracy of our answers.

Determining Significant Figures

• Any digit that is not zero is significant

1.234 kg 4 significant figures

• Zeros between nonzero digits are significant

606 m 3 significant figures

• Zeros to the left of the first nonzero digit are not significant

0.08 L 1 significant figure

• If a number is greater than 1, then all zeros to the right of the decimal point are significant

2.0 mg 2 significant figures

• If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant

0.00420 g 3 significant figures

Rules for Significant Figures

Addition or Subtraction

The answer cannot have more digits to the right of the decimalpoint than any of the original numbers.

89.3321.1+

90.432 round off to 90.4

one significant figure after decimal point

3.70-2.91330.7867

two significant figures after decimal point

round off to 0.79

Rules for Significant Figures

Multiplication or Division

The number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Significant Figures

Exact Numbers

Numbers from definitions or numbers of objects are consideredto have an infinite number of significant figures

The average of three measured lengths; 6.64, 6.68 and 6.70?

Because 3 is an exact number

6.64 + 6.68 + 6.703

= 6.67333 = 6.67 = 7

Dimensional Analysis

• We use dimensional analysis to convert one quantity to another.

• Most commonly dimensional analysis utilizes conversion factors (e.g., 1 in. = 2.54 cm)

1 in.

2.54 cm

2.54 cm

1 in.or

Dimensional Analysis

Use the form of the conversion factor that puts the desired unit in the numerator.

given unit desired unitdesired unit

given unit

Conversion factor

Dimensional Analysis Method of Solving Problems1. What data with units are we given in the problem?

2. What quantity and units do we wish to obtain?

3. What conversion factors do we need to take given quantity to desired quantity?

4. If all units cancel except for the desired unit(s), then the problem was solved correctly.

1 L = 1000 mL

How many mL are in 1.63 L?

1L

1000 mL1.63 L x = 1630 mL

1L1000 mL

1.63 L x = 0.001630L2

mL

The speed of sound in air is about 343 m/s. What is this speed in miles per hour?

1 mi = 1609 m 1 min = 60 s 1 hour = 60 min

343ms

x1 mi

1609 m

60 s

1 minx

60 min

1 hourx = 767

mihour

meters to miles

seconds to hours

Exercise 1.44 (d) p 33

An individual has 232 mg of cholesterol per 100. mL of

blood. If the total blood volume of the individual is

5.2 L, how many total grams of cholesterol does the

Individual’s body contain?

Exercise 1.50 p 33

The concentration of carbon monoxide in an urban

apartment is 48 μg/m3. What mass in grams of CO

is present in a room measuring 9.0 x 14.5 x 18.8 ft?

In class exercises:

Kenyan Daniel Yego won the 2007 Rock ‘N’ Roll

Marathon, a 26-mile, 385 yard race, with a time of

2:09:04. At this rate, how long would it take him to

run 3.00 miles?

A solid sphere of plutonium has a diameter of 10.5 inches. Given that the density of Pu is 19.84 g/cm3, what is the mass in kg of the Pu?