1. Measurements Measured and Exact Numbers

2. 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. This type of observation is quantitative because it involves numbers. Words such as “tall” or “heavy” are qualitative observations, and don’t involve measured numbers

3. Reading a Meterstick. l 2.... I.... I 3....I.... I 4.. 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 (All three of the reported lengths are valid !)

4. 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

5. Learning Check MN1. l 8.... 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 does your answer compare with your neighbor’s answer? Who is correct?

6. Solution MN1. l 8.... 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 for different people. Both readings are acceptable. (They have the same amount of certainty and the same degree of estimate)

7. Learning Check MN2 l 5.... 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

8. Solution MN2 l 5.... 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. Another reasonable answer is 6.07 cm. 2) 6.06 cm

9. Zero as a Measured Number. l 3.... I.... I 4.... 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 noticeably to the left or right of.5)

10. 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

11. 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

12. Solution MN3 A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. Using a measuring tool

13. 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’s diameter is 6 x 10 -4 cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda

14. 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

15. 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

16. 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