Measured And Exact Numbers

Chapter 1

Measurements

Measured Numbers and Significant Figures

Measured Numbers

When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

Reading a Meterstick

. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm

First digit (known) = 2 2.?? cm

Second digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.07

Length reported = 2.75 cm

or 2.76 cm

or 2.77 cm

Known + Estimated Digits

Known digits 2 and 7 are 100% certain

The third digit 6 is estimated (uncertain)

In the reported length, all three digits

(2.76 cm) are significant including the

estimated one

Learning Check

. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?

1) 9.2 cm

2) 9.22 cm

3) 9.23 cm

How your answer compare with your

neighbor’s answer? Why or why not?

Solution

. l8. . . . I . . . . I9. . . .I . . . . I10. . cmEstimate to the hundreth’s place (0.01 cm)

2) 9.22 cm

3) 9.23 cm

The estimated digit may be slightly different.

Both readings are acceptable.

Learning Check

l5. . . . I . . . . I6. . . .I . . . . I7. . cm

What is the length of the line?

1) 6.0 cm

2) 6.06 cm

3) 6.60 cm

Solution

l5. . . . I . . . . I6. . . .I . . . . I7. . cm

Estimate to the hundreth’s place (0.01 cm). The reading is between 6.0 and 6.1. You may have estimated 6.07 cm as well.

2) 6.06 cm

Zero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?

First digit 4.?? cm

Second digit 4.5? cm

Last (estimated) digit is 4.50 cm

(not to the left or right of .5)

Exact Numbers

Obtained when you count objects2 soccer balls

1 watch

4 pizzas

Obtained from a defined relationship1 foot = 12 inches

1 meters = 100 cm

Not obtained with measuring tools

Learning Check

A. Exact numbers are obtained by

1. measuring

2. counting3. definition

B. Measured numbers are obtained by

1. measuring

2. counting

3. definition

Solution

A. Exact numbers are obtained by

2. counting

3. definition

B. Measured numbers are obtained by

1. Using a measuring tool

Learning Check

Classify each of the following as an exact (1)

or a measured (2) number.

A.___Gold melts at 1064°C

B.___1 yard = 3 feet

C.___A red blood cell with diameter 6 x 10-4 cm

D.___There were 6 hats on the shelf

E.___A can of soda contains 355 mL of soda

Solution

Classify each of the following as an exact (1) or a measured(2) number. Give reason.

A. 2 Requires a thermometer(measuring tool)

B. 1 From a definition in U.S. system

C. 2 Need measuring tool to determine

D. 1 Counted the hats

E. 2 Measured

% Yield

• Actual/Theoretical x 100%

• If you are attempting an experiment and the theoretical yield is 100g and your group’s yield is 79g, determine the % error.

Variables

• Independent Variable:

• A variable that stands alone and is not changed. Not changed by what we measure.

• Dependent Variable:

• Depends on other factors. This is what changes in the experiment.