Chapter 1 measurements
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Chapter 1 Measurements. Measured Numbers and Significant Figures. Measured Numbers. When you use a measuring tool to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers . Reading a Meterstick.

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Chapter 1 Measurements

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Chapter 1 measurements

Chapter 1Measurements

Measured Numbers and Significant Figures


Measured numbers

Measured Numbers

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


Reading a meterstick

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

or2.76 cm

or2.77 cm


Known estimated digits

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

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 does your answer compare with your neighbor’s answer? Why or why not?


Solution

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 check1

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


Solution1

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

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

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 check2

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


Solution2

Solution

A. Exact numbers are obtained by

2. counting

3. definition

B. Measured numbers are obtained by

1. Using a measuring tool


Learning check3

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


Solution3

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


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