Measurement

Measurement

CHM 1010 PGCC Barbara A. Gage

Measurement

• Determined magnitude of a property• Based on a standard• Must have a unit (which is based on

the standard)• Number of digits in a measurement

depends on the device used• Values must be expressed in

scientific notation if they are 1000 or more or in the thousandths (0.00X)


Significant Figures• When making a measurement you

must record all digits you are sure of and one that is a reasonable estimate (regardless of where the decimal place falls)

• The object below is 4.86 cm. You can be certain of the 4 and 8. The 6 is an estimate and can vary +/- 1 between measurements.


Significant figures

• The graduated cylinder at the right contains 38.34 mL of liquid.

It is assumed that you can visuallydivide the space between lines into ten parts.


Significant Figures

• When you encounter a measurement assume that all non-zero digits or zeros between other digits are significant.

23.789 dm 5 sig figs2.04 gal 3 sig figs52 kg 2 sig figs


Significant Figures

• Zeros may serve as actual measured values or place holders in estimated measurements. Place holder zeros are NOT significant because they are really not measured values.

• Place holder zeros can be removed by expressing the number in scientific notation.


Significant Figures

120,000 2 significant figuresThis is an estimate that can be written as1.2 x 105.

0.0040500 5 significant figuresThe zeros before and immediately after the

decimal point can be eliminated using scientific notation. The last zeros remain because they are actual measurements.

4.0500 x 10-3


Significant Figures –Addition and Subtraction


•When you are adding and subtracting numbers you only count the columns where you are sure of all the values in that column.

Significant Figures –Multiplication and Division

• When multiplying or dividing two or more values, the answer should contain the number of digits in the value with the least number of significant figures.

0.003570 4 sig figsX 23.4 3 sig figs0.083538 5 sig figs (calculator answer)

You can only trust the answer to 3 sig figs so the correct answer is 8.35 x 10-2.


Measurement Systems

• Everyday measurements in the USA are generally made using the English system.

• The scientific community and most other countries use the metric system.


UnitsEnglish System Metric System

Length inch, foot, yard, mile meter (or metre) (m)

Volume teaspoon, cup, gallon liter (or litre) (L)

Mass ounce, pound, ton gram (g)


•The units in the English system do not have a common conversion factor. 12 in = 1 ft 3 ft = 1 yd 1760 yd = 1 mi

•The units in the metric system have a common factor which is 10. The metric system uses a common base unit and prefixes to change the size of the unit.

Metric Prefixes


The boxed prefixes must be memorized.

Converting Measurements

• Often it is necessary to convert a measurement made in one unit to another unit.

Ex. 2.45 cm = ? mIn the metric system you can just shift

the decimal point or set up a conversion factor. 2.45 cm = 0.0245 m



• Using a conversion factor: 100 cm = 1 m• 100 cm or 1m both ratios =

1 1 m 100 cm


1 m2.45 cm x = 0.0245 m

100 cm


• If Baltimore is 35 miles away, how far is it in km?

• Using a conversion factor: 1.61 km = 1 mi


1.61 km35 mi x = 56 km

1 mi


• How many mL are in 0.875 gal? 1.06 qt = 1 L 4 qt = 1 gal


34 qt 1 L 1000 mL.875 gal x x x = 3.30 x 10 mL

1 gal 1.06 qt 1 L

Problem…

• A gas particle has a velocity of 752 m/s. What is its velocity in mi/hr?

1.61 km = 1 mi


3m 1 km 1 mi 60 s 60 min mi752 x x x x = 1.68 x 10

s 1000 m 1.61 km 1 min 1 hr hr

Problem…• A synthesis process requires 6.2 fl. oz. of

activator for every 2.5 tons of starting material. What is the concentration of activator in the final product in mL/kg?

1 fl oz = 29.6 mL 2000 lb = 1 ton 2.20 lb = 1 kg


6.2 fl oz 1 ton 2.20 lb 29.6 mL mL x x x = 0.081

2.5 ton 2000 lb 1 kg 1 fl oz kg

Density

• Property derived from two measurements, mass and volume

• Density = Mass/Volume• Will have a unit that contains both

mass and volume such as g/cm3, lb/gal, kg/L

• Does not depend on the size of the sample


Density

• What is the density of a sample of metal that has a mass of 34.58 g and when placed in 15.0 mL of water causes the level to rise to 22.4 mL?


34.58 gMD = = = 4.7 g/ mL

V 7.4 mL

22.4 mL - 15.0 mL = 7.4 mL


Accuracy and Precision

• Accuracy = how close a result comes to the true value

• Precision = reproducibility of a measurement


Precision and Accuracy


“a” is precise butnot accurate

“b” is accurate and precise

“c” is not preciseor accurate

Consider 3 persons shooting darts at a target…

Accuracy and Precision• Measurements of the same object made by

three students; actual value = 15.71 cmStudent 1 Student 2 Student 314.72 cm 15.80 cm 15.72 cm14.71 14.71 15.7114.72 13.25 15.8214.82 14.96 15.7314.71 12.81 15.71Precise not accurate Not accurate or precise Accurate and precise


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Measurement