Measurements

1. Measurements

2. Measurement You are making a measurement when you • Check you weight • Read your watch • Take your temperature • Weigh a cantaloupe What kinds of measurements did you make today?

3. What is a Measurement? • Measurement: a comparison of an the dimension of object or substance to a known standard. • Dimension: a physical property of an object, any measureable property of an object • Standard: a known quantity that is universally accepted • Tool: an artificial object used to aid the senses in determining known standards for measurements

4. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard.

5. Some Tools for Measurement

6. Solution From the previous slide, state the tool (s) you would use to measure A. temperature thermometer B. volume measuring cup,graduated cylinder C. time watch D. weight scale

7. Stating a Measurement In every measurement there is a • Number followed by a • Unitfrom measuring device

8. What Universal System Do We Use? • SI- Systeme Internationale • Metric System- a system of measurement based on multiples or divisions of of 10 • Why? • It is convenient • It is universally used amongst scientists, doctors, mathematicians, etc.

9. Metric System • The metric system is based on a base unit that corresponds to a certain kind of measurement • Length = meter • Volume = liter • Weight (Mass) = gram • Prefixes plus base units make up the metric system • Example: • Centi + meter = Centimeter • Kilo + liter = Kiloliter

10. The Metric System • The metric system is a measurement system based on our decimal (base 10) number system. • Other countries and all scientists and engineers use the metric system for measurement.

11. Common Dimensions and Their Given Units of Measure

12. What is the Length? • We can see the markings between 1.6-1.7cm • We can’t see the markings between the .6-.7 • We must guess between .6 & .7 • We record 1.67 cm as our measurement • The last digit an 7 was our guess...stop there

13. Learning Check What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm

14. Meters • One centimeter is about the width of a large paper clip • or your fingernail.

15. Meters • A meter is about the width of a doorway

16. Gram • Grams are used to measure mass or the weight of an object.

17. Grams • A milligram weighs about as much as a grain of salt.

18. Liters • Liters measure liquids or capacity. 2 Liter Soda

19. Liter • 1 milliliter is about the amount of one drop

20. Changing Metric Units • To change from one unit to another in the metric system you simply multiply or divide by a power of 10.

21. Metric System • So if you needed to measure length you would choose meter as your base unit • Length of a tree branch • 1.5 meters • Length of a room • 5 meters • Length of a ball of twine stretched out • 25 meters

22. Metric System • But what if you need to measure a longer distance, like from your house to school? • Let’s say you live approximately 10 miles from school • 10 miles = 16093 meters • 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: • 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

23. Metric Prefixes • Metric Units • The metric system has prefix modifiers that are multiples of 10.

24. To change from a larger unit to a smaller unit, you need to multiply. 1 km x 1000 = 1000 m 1 m x 100 = 100 cm 1 cm x 10 = 10mm

25. To change from smaller units to larger units you divide by a power of ten. 1000mm ÷ 10 = 100cm 100cm ÷ 10 = 10dm 10dm ÷ 10 = 1m

26. Metric System • The three prefixes that we will use the most are: • kilo • centi • milli

27. Metric System • These prefixes are based on powers of 10. What does this mean? • From each prefix every “step” is either: • 10 times larger or • 10 times smaller • For example • Centimeters are 10 times larger than millimeters • 1 centimeter = 10 millimeters

28. Metric System • Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 40 41 40 41 1 cm

29. Metric System • For each “step” to right, you are multiplying by 10 • For example, let’s go from a base unit to centi 1 liter = 10 deciliters = 100 centiliters 2 grams = 20 decigrams = 200 centigrams ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200)

30. Metric System • Now let’s try our previous example from meters to kilometers: 16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers • So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)

31. Metric System • If you move to the leftin the diagram, move the decimal to the left • If you move to the rightin the diagram, move the decimal to the right

32. Metric System • Summary • Base units in the metric system are meter, liter, gram • Metric system is based on powers of 10 • For conversions within the metric system, each “step” is 1 decimal place to the right or left • Using the diagram below, converting to the right, moves the decimal to the right and vice versa

33. Place Values of Metric Prefixes

34. Place Values of Metric Prefixes Movethe decimal point to the right to multiply.

35. Place Values of Metric Prefixes

36. Place Values of Metric Prefixes Movethe decimal point to the left to divide.

37. Place Values of Metric Prefixes

38. Accuracy and Precision