1 units of measurements 1. a quantity is something that has magnitude, size, or amount. 2. in 1960...

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UNITS OF MEASUREMENTS

1. A quantity is something that has magnitude, size, or amount.

2. In 1960 the General Conference on Weights and Measurements decided all countries would use the International System of Units (Metric) system as the standard units of measurements.

3. Almost every country uses the metric system for daily calculations except the United States and Great Britain.

4. When using the metric system commas are not used with numbers becauseother countries use commas to represent a decimal point.

Ex. 75, 000 is written 75 000 0.001256 is written 0.001 256

5. The metric system (SI system) is based on powers of 10.

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5. There are seven fundamental units in the metric system. All other units are derived from these units.

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6. A derived unit is a combination of fundamental units.

Example: The unit for energy is the Joule = force x length = Nm = kg x m2 / s2

Example: The unit for force is the Newton = N= kg x m / s2

Example: Area is calculated L x W = m x m = m2

7. If a unit is not a fundamental unit, it is a derived unit.

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8. What about volume?

Notice that liter ( the unit for volume) is not a fundamental unit.

To determine the volume of an object a length must be measured. So, volume is derived from length.

Volume = l x w x h = m x m x m = m3

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12. 1000 ml = 1 Liter 1000cm3 = 1 L

11. 1 ml = 1 cm3

A 1 cm x 1 cm x 1cm cube will hold 1 ml of liquid. 1 ml = 1cm3 = 1 cc (cubic centimeter)

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12. 1000 cm3 = 1000 ml 1000 ml = 1 Liter 1000cm3 = 1 L

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Why Metric?

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1.3 Scientists Measure Physical Quantities

1.3 Scientists Measure Physical Quantities

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A physical quantity must include:A physical quantity must include:

A NUMBER + A UNIT A NUMBER + A UNIT

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13. The metric system provides a standard unit of measurements used by all countries. Is the man 92.5 m, 92.5 cm, 92.5 in, or 92.5 ft?

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How many centimeters are in an inch?

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UNCERNTAINTY IN MEASUREMENTS ANDSIGNIFICANT FIGURES

1. Whenever a measurement is taken, the last digit is uncertain and estimated.

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Which clock would be the most accurate?

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RULES FOR COUNTING SIGNIFICANT FIGURES

1. All nonzero digits are significant. Ex. 123 g 3 significant figures. 25 g 2 significant figures 26.42 g 4 significant figures

2. All zeros between non zero digits are significant. Ex. 506 L 3 significant figures 900.43 L 5 significant figures

3. Decimal numbers that begin with zero. The zeros to the left of the first nonzero number are not significant. Ex. 0.205 L 3 significant figures 0.0047 L 2 significant figures

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4. Decimal numbers that end in zero. The last zero is significant.

Ex. 8.00 g 3 significant figures 35.000 g 5 significant figures 8.0 g 2 significant figures

5. Non decimal numbers that end in zero. The zero is significant only when a written decimal is shown. Ex. 480 g 2 significant figures

900 g 1 significant figure 90. g 2 significant figure

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PRACTICE

1. 65.42 g _____2. 385 L _____3. 0.14 ml _____4. 709.2 m _____5. 5006.12 kg _____6. 400 dm _____7. 260. mm _____8. 0.47 cg _____9. 0.0068 km _____10.7.0 cm _____11. 36.00 g _____12.0.0070 kg _____13.100.6040 L _____14.340.00 cm _____

Determine the number of significant figures.

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Rounding Significant Figures

Sample: 205.80 round to 3 significant figures (sf) _______ 0.0583 round to 1 sf ______ 8.159 round to 3 sf ______ 47.374 round to 4 sf ______ 897.48 round to 2 sf ______

Practice

Round to the indicated number of significant figures.

1. 24 km to 2 sf _____2. 0.04851 L to 2 sf _____3. 2.68 g to 2 sf _____ 4. 4.165 L to 3 sf _____5. 2.68 g to 2 sf _____6. 8.35 ml to ml 2 sf _____7. 12 ml to 1 sf _____8. 0.06350 to 2 sf _____

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MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES

1. The arithmetic product or quotient should be rounded off to the same number of significant figures as in the measurement with the fewest significant figures.

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Keep the smallest number of significant figures.

Examples:2.86 g x 2.0 g = 5.72 g the answer is 5.7 g

38 ml / 1.25 ml = 30.4 ml the answer is 30. ml

0.596 g x 0.3450 g = 0.20562 g the answer is 0.206 g

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Adding and Subtracting Significant Figures

1. The arithmetic result should be rounded off so that the final digit is in the same place as the leftmost uncertain digit.

Ex. 213.67 g - 98 g = 115.67 g the answer is 116 g

3127.55 g – 784.2 g = 2343.35 g the answer is 2343.4 g

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PRACTICE

1. 9.40 cm x 2.6 cm = ____________

2. 8.08 dm x 5.3200 dm = ____________

3. 4.07 g + 1.863 g = ____________

4. 36.427 m + 12.5 m + 6.33 m ____________

5. 1.50 g / 2 cm3 = ____________

6. 0.08421 g / 0.640 ml = ____________

7. 21.50 g / 4.06 cm x 1.8 cm x 0.905 cm = ____________

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Scientific Notation

1. Convert 21300000 to scientific notation

2.13 x 10 7

2. Convert 0.0000000020 to scientific notation

2.0 x 10-9

Practice: Convert to scientific notation

1. 9002. 7500003. 930000004. 0.0004035. 0.0000826. 0.0097007. 250000

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CALCULATOR PRACTICE

1. 3 x 1055 x 7.56 x 1015 =

2 x 10 71

2. 3.71 x 10 -26 x 4.00 x 10-45 = 1.48 x 10-70

Practice: Don’t forget to keep the correct number of significant figures.

1. 2.6 x 102 + 4.1 x 102 = 2. 8.3 x 10-5 + 1.2 x 10-5 = 3. 7.43 x 104 - 5.09 x 104 = 4. (3 x 10 5 )( 2 x 107 ) = 5. (7.5 x 106 )/(4 x 10-2) =

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BACK TO ROUNDING SIGNIFICANT FIGURES INVOLVING SCIENTIFIC NOTATION

1. Round 400 g to 3 significant figures.

4.00 x 102

2. Round 0.000003 to 2 significant figures

3.0 x 10-6

Simply change the number to scientific notation when going from a smaller number of significant figures to a larger.

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IMPORTANT REMINDER:Your calculator does not know how to do significantfigures. YOU must report numbers using the correct

number of significant figures.

If you trust the number your calculator gives you, youmight get the answer wrong!!!! TI or Casio don’t care

what grade you get on the test.

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ACCURACY AND PRECISION

1. Accuracy is the closeness of the measurements to the true or accepted value.

2. The accuracy of an instrument can only be determined if the true or or accepted value for the measured item is known.

3. Precision refers to the agreement among the numerical values of a set of numbers.

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Picture 1 is accurate and precise

Picture 2 is precise but not accurate.

Picture 3 is neither accurate or precise.

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4. Scientific instruments should be accurate. If instruments are accurate, they are also precise.

5. If an instrument is precise, it may not be accurate.

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Dimensional Analysis(Factor Label)

1. Dimensional Analysis (factor label) is a problem solving technique.

2. This method of problem solving uses conversion factors.

3. A conversion factor is a ratio that is equal to one.

Example:

4 quarters = $124 hours = 1 day 185 days = 1 student school year

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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion

1 foot1 foot

12 inches12 inches

12 inches12 inches

1 foot1 foot

“Conversion factors”“Conversion factors”

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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion

1 foot1 foot

12 inches12 inches

12 inches12 inches

1 foot1 foot

“Conversion factors”“Conversion factors”

3 feet3 feet12 inches12 inches

1 foot1 foot= 36 inches= 36 inches(( ))(( ))

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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion

1 foot = 12 inches1 foot = 12 inches

1 foot1 foot

12 inches12 inches= 1= 1

12 inches12 inches

1 foot1 foot= 1= 1

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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion

1 foot = 12 inches1 foot = 12 inches

1 foot1 foot

12 inches12 inches= 1= 1

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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion

1 foot = 12 inches1 foot = 12 inches

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