Measurement

Measurement A quantity that has both a number and a unit Which is a measurement? 12 cm 134.54 0.0034

The Metric System Standard units of measurement (SI) Temperature conversion: Quantity Unit Symbol Length meter m Mass kilogram kg Temperature Kelvin K Time second s Amount of substance mole mol Converting temp; think about the alphabet --C to K goes up in the alphabet, so add --K to C goes down in the alphabet so subtract °C + 273 = Kelvin

Metric Prefixes Prefix Meaning Factor Kilo (k) 103 Centi (c) 10−2 1000 times larger than the unit 103 Centi (c) 100 times smaller than the unit 10−2 Milli (m) 1000 times smaller than the unit 10−3 Micro (μ) 1 million times smaller than the unit 10−6 Nano (n) 1 billion times smaller than the unit 10−9

Scientific Notation Used to write really big and small numbers 6.02 ×1023 The coefficient is equal to or greater than 1 and less than 10 The exponent is a positive or negative integer Circle and label coefficient

Writing Scientific Notation For large numbers— move the decimal to the left until one digit remains in front Count the number of times the decimal moves The exponent is positive Example: 3,000  3 x103 405,000  4.05 x105 Underline large numbers, left, positive

For small numbers— move the decimal to the right until one digit is in front Count the number of times the decimal moves The exponent is negative Example: 0.00034  3.4 x10−4 0.0000005070  5.070 x10−7 Underline small numbers, right, negative

Accuracy How close a measurement comes to the actual value of whatever is measured The more # of significant digits, the more accurate the value

Precision How close a series of measurements are to one another or “repeatability” You must compare two or more measurements to each other

Accuracy vs Precision

Example: Jack has a height of 70 inches. Which sets of measurements are Accurate and precise Precise but not accurate Neither precise nor accurate 69.5 in., 70.5 in., 70.1 in. 45.3 in., 62.1 in., 84.3 in 78.3 in., 78.0 in., 78.1 in

Percent Error To find out how close you are to an accepted or actual value Percent error =  exp val – act val  x 100% act val error Point out the absolute value sign, we don’t care if we measured high or low

Example: Your data reads 99. 1g but the accepted value is 101 Example: Your data reads 99.1g but the accepted value is 101.0g, what is your percent error? Percent error = 99.1g − 101.0g × 100 101.0g %error = 1.88% Point out the absolute value sign, we don’t care if we measured high or low

Measuring with Accuracy Includes all the digits that are known, plus one that is estimated

Measuring with a Ruler 1. Measuring error = 1/10 of smallest division ii. Reading error is equal to 1/10 of the smallest division on the ruler iii.

What is the following measurement? Practice What is the following measurement?

**Measure from the bottom of the meniscus Measuring a Liquid **Measure from the bottom of the meniscus

Practice ii. i.

iv. iii.

Still More measurements not on the note takers

Sig Figs Show the Uncertainty in Measured Data Review - Significant Figures Sig Figs Show the Uncertainty in Measured Data Measured data is written to convey 2 things! the magnitude of the measurement the extent of its reliability Worker #1 reports a mass of 12 g Worker #2 reports a mass of 12.0142 g 12 g means 12 ± 1 g 12.0142 g means 12.0142 ±0.0001 g 12 g has 2 sig figs 12.0142 g has 6 sig fig 12.0142 g is the more precise (certain, reliable) number The more significant figures a measurement has, the more precise (certain) it is.

Making Measurements in the Lab: Correct Sig Figs in Recording Thermometer Data A. The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit. 23°C 23°C 22°C 22°C 21°C 21°C you record 21.6°C you record 21.68°C

Making Measurements in the Lab: Correct Sig Figs-Glassware with Graduations 0 mL 1 mL 2 mL Example Y A. If the glassware is marked every 10 mLs, the volume you record should be in mLs. (Example X) B. If the glassware is marked every 1 mL, the volume you record should be in tenths of mLs. C. If the glassware is marked every 0.1 mL, the volume you record should be in hundredths of mLs. (Example Y) 30 mL 10 mL Example X 30-mL beaker: the volume you record should be 13 mL Buret marked in 0.1 mL you record volume as 0.67 mL

Making Measurements in the Lab: Recording Masses with Sig Figs A. Record EVERY number (especially zeros) that appears on the display of the electronic balance. B. Trailing zeros MUST be recorded.