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. . 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?

cm

Solution . l8. . . . I . . . . I9. . . .I . . . . I10. .

cm

Estimate 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. . What is the length of the line?

1) 6.0 cm 2) 6.06 cm 3) 6.60 cm

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 objects 2 soccer balls 1 watch 4 pizzas

Obtained from a defined relationship 1 foot = 12 inches 1 meters = 100 cm

Not obtained with measuring tools

Learning Check A. Exact numbers are obtained by 1. measuring 2. counting 3. 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