MEASURING IN SCIENCEMetric System, units, significant figures, rounding, and scientific notation

ENGLISH VS METRIC SYSTEM

• Dime width is a millimeter• Brick mass is a kilogram• Jumbo paperclip’s mass is a gram

• 2.54cm = 1 inch• 1.0 liter – 1.06 quart• 1.0 pound = 2.2 kilograms

COMMON METRIC UNITSFrom section 2.1, pages 32-39LENGTH, m distance between point A and B

ruler, meter stick

VOLUME, L amount of space an object takes upgraduated cylinder, ruler  

MASS, g amount of matter in an objecttriple beam balance, electronic balance 

DENSITY, g/mL amount of mass in a given volumemeasure mass & volume, D = M / V

TEMPERATURE, °C an indirect measure of heatthermometer

BASE VS. DERIVED UNITS• What is the difference between a base unit and a derived

unit?

• BASE UNIT is a defined unit based on an object or event in the physical world. It is independent of other units. Examples: meter, liter, newton, coulomb

• DERIVED UNIT is defined by a combination of base units. Examples: volume = cm x cm x cm, speed = distance/ time, density = mass/volume

METRIC CONVERSIONS

DIVIDE BY 10

MULTIPLY BY 10

PRACTICE• 25m = ___________mm

• 2.6cL = ___________L

• 1500Kg = ______________ g

• 23.2dam = _____________ dm

PREFIXES

PERCENT ERROR• Calculation of percent error is one way to make a

distinction between an observed value and a true or literature value. Percent error can be used to describe the accuracy of results of laboratory investigations if a generally accepted (true or literature value) is known. Percent error is always positive. Take the absolute value.

% error = [observed value-true/literature value] x 100true/literature value

PRACTICEIn each of the following, show a setup for your calculation. Do any necessary arithmetic below and write your answers in the spaces at the right. 1. The density of mercury is known to be 13.8 g/cm3. Results of an experiment give that density to be 14.2 g/cm3. Calculate the percent error.  

 

PRACTICE2. The volume of a rectangular solid is known to be 556 cm3. A student takes the following measurements for the dimensions of the rectangular solid: 8.34 cm x 6.19 cm x 10.42 cma. What volume is calculated for the rectangular solid from these measurements?

b. What is the percent error of these results?

ACCURACY AND PRECISIONWhen taking measurements during a lab, you may need to know if your data is reliable. There are two ways to check reliability.Precision: One way is to repeat the measurement several times. A reliable result will give the same measurement time after time. This is how close a set of measurements for a quantity are to each other, but still can be regardless of correctness.

Accuracy: This is how close a measurement is to the correct (standard, literature) value for the quantity.•  

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PRACTICETwo students massed the same sample on two different laboratory balances. The results were as follows:

Balance A 12.11 g 12.09 gBalance B 12.1324 g 12.1322 g

Which balance is more precise?  If the mass of the sample is actually 12.1 g, which is more accurate?

SCIENTIFIC NOTATION• Scientific notation is a way of writing numbers that makes

it easy to handle very large or very small numbers. • Imagine having to write all the zeros associated with

Avogadro’s Number – 6.02 x 1023!602,214,130,000,000,000,000,000

SCIENTIFIC NOTATIONTo put a number in Scientific Notation• If the number is less than one, move the decimal to the

right. The exponent is negative and equals the number of places you moved the decimal point.

0.00004567 4.567 x 10-5

 • If the number is greater than one, move the decimal to the

left. The exponent is positive.1234 1.234 x 103

SCIENTIFIC NOTATIONTo take a number out of Scientific NotationIf the exponent is negative, move the decimal point to the left. The number is less than one.

4.567 x 10-5 .00004567 If the exponent is positive, move the decimal point to the right. The number is greater than one.

1.234 x 103 1234

DO NOW• Go get the 400mL beaker from your lab drawer.• Pour out 10mL of green Hendrixium from the back desk.• Record the volume as accurately as you can on the paper

provided.• Now, pour your Hendrixium into the 250mL beaker in your

drawer. Record the volume as accurately as you can.• Then, pour your volume of Hendrixium into the 50mL beaker

on your desk. Record the volume as accurately as you can.• Finally, pour your volume of Hendrixium into the 10mL

graduated cylinder. Record the volume.• Pour out the Hendrixium, clean and the dry the beaker and

return it to the counter top. Return to your seat.

MEASURING SIGNIFICANTLY• 400mL beaker• 250mL beaker• 50mL beaker• 10mL graduated cylinder

• Michael Phelps• Justin Gatlin

SIGNIFICANT FIGURES Helps to determine the exactness of measurements. The

last place in a number is the inexact number – all others have been measured with certainty.

The lines below are the same length, but have different measurements.

  Look at the examples. Which one can have more

significant figures? 

SIGNIFICANT FIGURESATLANTIC-PACIFIC RULE• This rule divides measurements

into two kinds – those with a decimal point and those without.

• If a decimal point is present in the number, count significant digits from the Pacific side. (If decimal point is present, count from the Pacific side.)

• If a decimal point is absent, count from the Atlantic side.

• You should start counting with the first nonzero digit you find. Thereafter, all digits, including zero, are significant.

SIGNIFICANT FIGURES1. Digits other than zero are always significant.2. One or more final zeros used after the decimal point are

always significant.3. Zeros between two other significant digits are always

significant.4. Zeros used solely for spacing the decimal point are not

significant. The zeros are place holders only.

SIGNIFICANT FIGURES• Counting numbers and defined constants or conversions

have an infinite amount of significant figures.• Use scientific notation to represent accurate

measurements such as 7000 g. This has 1 significant digit, but was accurately measured to 4 significant digits. Should be rewritten as 7.000 x103. This indicates 4 significant digits.

PRACTICECalculate the number of significant figures in the following measurements.

1. 45.601 g _______2. 0.00701 m _______3. 75,000 km _______4. 0.2460 mg _______5. 78,621.0 mL _______6. 4.567 m _______

ROUNDING NUMBERSSometimes you will be asked to round a number to a particular number of significant digits. Rules for Rounding:• If the digit to the immediate right of the last significant

figure is less than five, do not change the last significant digit. 2.532 2.53

• If the digit to the immediate right of the last significant figure is five or greater, round up the last significant figure.

2.536 2.54

SIGNIFICANT FIGURES IN CALCULATIONSMeasurements that include inherent uncertainty are often used in calculations. In order to keep the appropriate level of uncertainty, simple rules for significant figures have been developed. ADDITION and SUBTRACTION• The number of significant figures to the right of the decimal point in

the final sum or difference is determined by the lowest number of significant figures to the right of the decimal point in any of the original numbers.

MULTIPLICATION and DIVISION• The number of significant figures in the final product or quotient is

determined by the original number that has the smallest number of significant figures.

SIGNIFICANT FIGURES IN CALCULATIONS7. 43.71 cm3 14.92 cm3

8. 2.80 m x 1.127 m

9. 14.702 g- 8.9 g

   

10. 18.007 cm+114.915 cm