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Using and Expressing Measurements

- Using and Expressing Measurements
- How do measurements relate to science?

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

- http://www.youtube.com/watch?v=H578qUeoBC0
- 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. 74171.7 2. .07882
- 3. 526 4. .0000573
- 5. 5.8 x 10 -7 6. 5.256 x 106

Accuracy, Precision, and Error

- Accuracy, Precision, and Error
- What is the difference between accuracy and precision?

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.

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.

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.

Accuracy, Precision, and Error

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

Experimental – known

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.

- 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

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 cm 4
- 5.6 ft 2
- 65.6 lb ___
- 122.55 m ___
- Complete: All non-zero digits in a measured number are (significant or not significant).

Timberlake lecture plus

Leading Zeros

Number of Significant Figures

- 0.008 mm 1
- 0.0156 oz 3
- 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 mm 3
- 2001 min 4
- 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 yr 1
- 48,600 gal 3
- 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) 256.8 3) 257
- B. 58.925 - 18.2 =
- 1) 40.725 2) 40.73 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

- 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) 11.3 2) 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

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
- 603.040 b. 0.0828 c. 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

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