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3.1. Using and Expressing Measurements. Using and Expressing Measurements How do measurements relate to science?. 3.1. Using and Expressing Measurements. A measurement is a quantity that has both a number and a unit.

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Using and Expressing Measurements

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3.1

### Using and Expressing Measurements

• Using and Expressing Measurements

• How do measurements relate to science?

3.1

### Using and Expressing Measurements

• A measurement is a quantity that has both a number and a unit.

• it is important to be able to make measurements and to decide whether a measurement is correct.

### Scientific Notation

• Scientific Notation Pre-Test

### Scientific Notation

• 210, 000,000,000,000,000,000,000

• This number is written in decimal notation. When numbers get this large, it is easier to write it in scientific notation

• Where is the decimal in this number?

• 210, 000,000,000,000,000,000,000.

• Decimal needs moved to the left between the 2 and the 1 ( numbers that are between 1-10)

• When the original number is more than 1 the exponent will be positive.

• 2.1 x 1023

• Exponents show how many places decimal was moved

• Express 4.58 x 106 in decimal notation

• Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right

• 4,580, 000

• express the number 0.000000345 in scientific notation.

• Decimal moved between first 2 non-zero digits and will be moved 7 times

• 3.45 x 10 -7

• The exponent is negative because the original number is a very small number

• Express the following in scientific notation or standard notation

• 1. 74171.72. .07882

• 3. 5264. .0000573

• 5. 5.8 x 10 -76. 5.256 x 106

3.1

### Accuracy, Precision, and Error

• Accuracy, Precision, and Error

• What is the difference between accuracy and precision?

3.1

### Accuracy, Precision, and Error

• Accuracy and Precision

• Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.

• Precision is a measure of how close a series of measurements are to one another.

3.1

### Accuracy, Precision, and Error

• To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.

• To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

3.1

3.1

### Accuracy, Precision, and Error

• Determining Error

• The accepted (Known) value is the correct value based on reliable references.

• The experimental value is the value measured in the lab.

• The difference between the experimental value and the accepted value is called the error.

3.1

### Accuracy, Precision, and Error

• The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Experimental – known

3.1

### Accuracy, Precision, and Error

• Percent Error

• (Error)3.00-measurement X 100

• 3.00

3.1

### Accuracy, Precision, and Error

• Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

### REVIEW

• % ERROR

• The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error?

• What is 5.256X10-6 in standard format

• What is 118000 in scientific notation

3.1

### Significant Figures in Measurements

• All measurement contains some degree of uncertainty.

• The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

• Measurements must always be reported to the correct number of significant figures

• Using pages 66-72 – fill in your notes regarding the rules of significant figures

• ### Counting Significant Figures

Number of Significant Figures

• 38.15 cm4

• 5.6 ft2

• 65.6 lb___

• 122.55 m___

• Complete: All non-zero digits in a measured number are (significant or not significant).

Timberlake lecture plus

Number of Significant Figures

• 0.008 mm1

• 0.0156 oz3

• 0.0042 lb____

• 0.000262 mL ____

• Complete: Leading zeros in decimal numbers are (significant or not significant).

Timberlake lecture plus

### Sandwiched Zeros

Number of Significant Figures

• 50.8 mm3

• 2001 min4

• 0.702 lb____

• 0.00405 m ____

• Complete: Zeros between nonzero numbers are (significant or not significant).

Timberlake lecture plus

### Trailing Zeros

Number of Significant Figures25,000 in. 2

• 200 yr1

• 48,600 gal3

• 25,005,000 g ____

• Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.

Timberlake lecture plus

### Learning Check

• A. Which answers contain 3 significant figures?

• 0.4760 2) 0.00476 3) 4760

• B. All the zeros are significant in

• 1) 0.00307 2) 25.300 3) 2.050 x 103

• C. 534,675 rounded to 3 significant figures is

• 1) 535 2) 535,000 3) 5.35 x 105

Timberlake lecture plus

### Significant Figures in Calculations

• A calculated answer cannot be more precise than the measuring tool.

• A calculated answer must match the least precise measurement.

• Significant figures are needed for final answers from

1) adding or subtracting

2) multiplying or dividing

Timberlake lecture plus

### Adding & Subtracting

• The answer has the same number of decimal places as the measurement with the fewest decimal places.

• 25.2one decimal place

• + 1.34two decimal places

• 26.54

• answer 26.5 one decimal place

Timberlake lecture plus

### Learning Check

• In each calculation, round the answer to the correct number of significant figures.

• A. 235.05 + 19.6 + 2.1 =

• 1) 256.75 2) 256.83) 257

• B. 58.925 - 18.2 =

• 1) 40.725 2) 40.733) 40.7

Timberlake lecture plus

### Solution

• A. 235.05 + 19.6 + 2.1 =

• 2) 256.8

• B. 58.925 - 18.2=

• 3) 40.7

Timberlake lecture plus

### Multiplying and Dividing

• Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Timberlake lecture plus

• Multiplication + Division

• Answer should have the same number of significant figures as the measurement with the least.

• You may need to round your answer in order to achieve this

### Learning Check

• A. 2.19 X 4.2 =

• 1) 9 2) 9.2 3) 9.198

• B. 4.311 ÷ 0.07 =

• 1)61.582) 62 3) 60

• C. 2.54 X 0.0028 =

• 0.0105 X 0.060

• 1) 11.32) 11 3) 0.041

Timberlake lecture plus

### Solution

• A. 2.19 X 4.2 = 2) 9.2

• B. 4.311 ÷ 0.07 = 3) 60

• C.2.54 X 0.0028 = 2) 11 0.0105 X 0.060

• Continuous calculator operation =

• 2.54 x 0.0028  0.0105  0.060

Timberlake lecture plus

3.1

### Significant Figures in Calculations

• Rounding

• To round a number, you must first decide how many significant figures your answer should have.

• Your answer should be rounded to the number with the least amount of significant figures

### QUIZ

• How many significant figures are in the number

• 603.040b. 0.0828c. 690,000

2. Perform the following operations and report to the correct number of sig. figs

• 4.15 cm X 1.8 cm

• 36.47 + 2.721 + 15.1

• 5.6 x 107 x 3.60 x 10-3