Chapter 1 Measurements Measured and Exact Numbers

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. l I.... I 3....I.... I 4.. cm First digit (known)= 2 2.?? cm Second digit (known)= ? cm Third digit (estimated) between Length reported=2.75 cm or2.76 cm or2.77 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 MN1. l I.... I 9....I.... I 10.. 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 MN1. l I.... I 9....I.... I 10.. 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 MN2 l I.... I 6....I.... I 7.. cm What is the length of the line? 1) 6.0 cm 2) 6.06 cm 3) 6.60 cm

Solution MN2 l I.... I 6....I.... I 7.. 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. l I.... I I.... I 5.. 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 MN3 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 MN3 A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. Using a measuring tool

Learning Check MN4 Classify each of the following as an exact (1) or a measured (2) number. A.___Gold melts at 1947°F B.___1 yard = 3 feet C.___A red blood cell with diameter 6 x cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda

Solution MN4 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

True(1) or False(2) 1. ___All measuring tools have limitations 2. ___Some measurements can be exact 3. ___Every measurement has some error 4. ___Every measurement has uncertainty Learning Check MN5

True(1) or False(2) 1. _1_All measuring tools have limitations 2. _2_Some measurements can be exact 3. _1_Every measurement has some error 4. _1_Every measurement has uncertainty Solution MN5