Metric Measurement

1. Metric Measurement

2. The Metric System Created by French scientists in the late 1700’s Goal of the system was to create a system of measurement that was based on the decimal instead of fractions. Single unifying system used throughout the world. Only country that does not use the metric system as a basic unit of measurement is the United States.

3. Basic Units and Quantities

4. Basic Units and Quantities (cont’d)

5. Precision in Measurement When we measure, we always add one digit BEYOND the last known measurable digit -- That digit is called the first uncertain digit FOR EXAMPLE: 0 1 2 3 4 On the ruler above, the arrow is pointing between 2.4 and 2.5 cm. 2.4 cm is the last known digit. We also must add the first uncertain digit to show that our measurement is greater than 2.4, but less than 2.5 cm. Therefore, the most correct measurement would be something like 2.46 cm

6. Metric Prefixes T tera 1012 1 000 000 000 000 trillion G giga 109 1 000 000 000 billion M mega 106 1 000 000 million k kilo 103 1 000 thousand h hecto 102 100 hundred da (D) deka 101 10 ten 100 1 d deci 10-1 0.1 tenth c centi 10-2 0.01 hundredth m milli 10-3 0.001 thousandth μ micro 10-6 0.000 001 millionth n nano 10-9 0.000 000 001 billionth p pico 10-12 0.000 000 000 001 trillionth

7. Measuring Length, Height, Width, Etc. . . • When measuring length in science, we always use variations of the metric unit of measurement, the meter • If our measurements are too small for the meter, (like the length of a pencil), we use variations of the meter, like centimeter or millimeter • If our measurements are too large for the meter (like distances traveled), we use larger variations of the meter, like kilometer

8. Instruments Used to Measure Length, Height, Width, Etc. . . • In science, there are two basic instruments used to measure length • For large objects, we use meter sticks • For medium-sized objects, we use rulers -- make sure to use the cm side!!!

9. Measuring Mass When we measure mass in science, we always use variations of the metric unit for mass, which is the gram For very large objects with lots of mass (like cars), we would use the kilogram (1000 g). -- A lot of later formulas are based off of the kilogram, so be careful which unit you need!

10. Instruments Used to Measure Mass Normally, triple beambalances are sufficient to find mass of most objects, however, they are NOT very accurate for small objects INSTEAD We prefer to use the electronic balances, which give mass in grams and are very accurate -- You must remember to zero (tare) the electric balance AFTER you have placed the plastic measurement tray on!

11. Measuring Time • Time measurements are the same for both English and Metric Systems • Seconds, minutes, hours, days, etc. • Seconds can be further broken down using our prefixes; milli, micro, nano, femto • There are a variety of timers and stopwatches that we will use to measure the passage of time

12. Measuring Temperature • The metric units of temperature are the Celsius scale and the Kelvin scale • Celsius is the more commonly use • The Kelvin scale is also known as the absolute scale • 0 K is as cold as anything can every be • We will talk about temperature more later in the year • Temperature measurements are made with thermometers

13. Measuring Volume We measure volume in science using variations of the metric unit for volume, the cubic centimeter (cm3) You must remember that 1 cm3 is EXACTLY EQUAL to 1 milliliter (mL). This comes from water’s special definition (more on this later) Usually, when we report volume, we report it in mL, however, for large volumes, we use the liter (1000mL).

14. Instruments Used to Measure Volume of Liquids (and some solids) It’s pretty simple: The ONLY WAY to accurately measure volume is with a graduated cylinder*** Always read the measurement from the bottom of the meniscus -- DO NOT use a beaker -- DO NOT use an Erlenmeyer flask

15. Meniscus

16. Other Ways to Measure Volume If an object is a perfect cube, we can calculate it’s volume using a simple mathematical formula: Volume = length x width x height, or V = lwh For instance, if we measure a small cube, with sides of 2 cm each, we can easily calculate its volume: L = 2 cm H = 2 cm W = 2 cm V = 2 cm x 2 cm x 2 cm = 8 cm3 2 cm 2 cm 2 cm

17. Measuring Volume of Non-Cube Shaped Solids • If we want to measure volume of unusually-shaped solids, we use what is called the water displacement method. • Steps to the Water Displacement Method: • Fill a large graduated cylinder with a known volume of water. Write this value down as Volume 1. • Place the object in the graduated cylinder until it is completely submerged. • Record the new volume of water in the graduated cylinder. Write down this value at Volume 2. • Volume 2 – Volume 1 = Volume of the solid, since you didn’t add any water to the cylinder! Try It!

18. What is the volume of the stone? • Measure the initial volume Click for volume 200 mL Click to place the stone in the graduated cylinder -Now measure the new volume Click for volume 280 mL The volume of the stone is the difference between the 2 280 mL – 200 mL = 80 mL stone! Click for the answer

19. Metric Conversions Because the metric system is decimal-based, it is very easy to convert between similar metric amounts (like from centimeters to kilometers) The only trick in moving from one metric level of measurement is knowing which way to move the decimal point (right or left) REMEMBER, when going from bigger units to smaller units, your number should always increase (you need more smaller units to fit into one bigger unit) The easiest method to remember is to use the METRIC STAIRS

20. The Metric Stairs kilo hecto deka deci centi milli When moving from bigger to smaller units (left to right), we move our decimal one space to the right for each step down (our amount will get bigger!) When moving from smaller to bigger units (right to left), we move our decimal one space to the left for each step up (our amount will get smaller!)

21. Convert 12 kg to decigrams 1 2 0 0 0 0 Dg kg hg dg g Click to convert

22. Convert 350 cm to meters 3 5 0 cm dm m Click to convert

23. Practice Using the Metric Stairs How many millimeters are in 24 decimeters? How many kilograms are in 1734.26 centigrams? How many liters are in 59 hectoliters? How many kilometers will you have run if you run 550000 mm? Click for answer 2400 mm Click for answer .0173426 kg Click for answer 5900 L Click for answer .55 km

24. Things to remember • The short forms for metric units are called symbols, NOT abbreviations • Metric symbols never end with a period unless they are the last word in a sentence. • RIGHT: 20 mm, 10 kg • WRONG: 20 mm., 10 kg. • Metric symbols should be preceded by digits and a space must separate the digits from the symbols • RIGHT: the box was 2 m wide • WRONG: the box was 2m wide

25. Things to remember • Symbols are always written in the singular form • RIGHT: 500 hL, 43 kg • WRONG: 500 hLs, 43 kgs • BUT: It is correct to pluralize the written out metric unit names: 500 hectoliters, 43 kilograms • The compound symbols must be written out with the appropriate mathematical sign included • RIGHT: 30 km/h, 12 cm/s • WRONG: 30 kmph, 30 kph (do NOT use a p to symbolize “per”) • BUT: It is ok to write out “kilometers per hour”

26. Things to remember • The meaning of a metric symbol is different depending on if it is lowercase or capitalized • mm is millimeters (1/1000 meters) • Mm is Megameters (1 million meters) Final Questions

27. Question 1 • What would the best units be to measure the mass of a horse? • What about a paperclip? Answer Kilograms Answer grams

28. Question 2 • Why would it be better to measure the volume of a sphere with water displacement rather than with a calculation? You would be able to get a more accurate reading using water displacement than if you tried to find the diameter of the sphere and calculate the volume Answer