MEASUREMENTS IN CHEMISTRYScientific Notation, Significant Figures, Percent Error

UNITS OF MEASUREMENT

Put the following units in order from smallest to largest. Meter, centimeter, millimeter, kilometer Kilogram, centigram, milligram, gram Liter, microliter, picoliter, kiloliter

SI UNITS

UNITS OF MEASUREMENT

Put the following units in order from smallest to largest. millimeter, centimeter, meter, kilometer milligram, centigram, gram, kilogram picoliter, microliter, liter, kiloliter

What information do the prefixes centi, milli, kilo, etc. provide?

PREFIXES

SCIENTIFIC NOTATION

When studying chemistry it is common to encounter very large or very small numbers.

Need a system in which to shorten long number chains. Ex: The number of air molecules in a liter of air

at 20oC and normal barometric pressure is 25,000,000,000,000,000,000,000.

Ex: The distance between two hydrogen atoms in a diatomic hydrogen molecule is 0.000,000,000,074 meters.

In Scientific Notation, these long chains of numbers are written in the form of;

M x 10n

SCIENTIFIC NOTATION

M x 10n

Scientific notation is simply a number time 10 raised to an exponent.

M is a number greater than or equal to 1 and less than 10.

n is the exponent (the nth power or 10). It can be either positive or negative and represent the number of decimal places moved. Positive (+) n means a large number so the decimal

moves to the right by n places. Negative (-) n means a small number so the decimal

moves to the left by n places.

PRACTICE

Convert the following from scientific notation to their usual form. 6.39 x 10-4

3.275 x 10-2

8.019 x 10-6

PRACTICE

Convert the following from scientific notation to their usual form. 6.39 x 10-4 = 0.000639

3.275 x 102 = 327.5

8.019 x 10-6 = 0.000008019

PRACTICE

Express the following numbers in scientific notation. 843.4

0.00421

1.54

PRACTICE

Express the following numbers in scientific notation. 843.4 = 8.434 x 102

0.00421 = 4.21 x 10-3

1.54 = 1.54 or 1.54 x 100

SCIENTIFIC NOTATION CHEAT SHEET

When converting from standard notation to scientific notation… If the number is one or greater you will have a

positive exponent and move the decimal to the left.

If the number is less than one you will have a negative exponent and move the decimal to the right.

# of spaces moved by decimal = exponent

801236.98

8.0123698 x 105

0.0000508

5.08 x 10-5

SCIENTIFIC NOTATION CHEAT SHEET

When converting from scientific notation to standard notation… If the exponent is positive you will have a large

number (>1) and move the decimal to the right.

If the exponent is negative you will have a small number (<1) and move the decimal to the left.

Exponent = # of spaces to be moved by decimal

801236.98

8.0123698 x 105

0.0000508

5.08 x 10-5

SIGNIFICANT FIGURES

If you were measuring this granite block in inches, what would you determine its width to be?

SIGNIFICANT FIGURES

In measurements there is always some amount of uncertainty.

SIGNIFICANT FIGURES Repeating a particular measurement will usually not

obtain precisely the same result. The measured values vary slightly from one

another.

Precision – refers to the closeness of a set of values obtained from identical measurements of something.

Accuracy – refers to the closeness of a single measurement to its true value.

RULES FOR SIG FIGS

The number of digits reported for the value of a measured quantity.1. All nonzero numbers and zeros between are

significant.a. 909 cm, 1002 cm, 100,003 cm

2. Zeros at the beginning of a number are never significant.

a. 0.000912 cm, 0.01 cm, 0.000001001 cm

3. Zeros at the end of a number are significant only if a decimal is present, and to the right of the decimal.

a. 900 cm, 900.0 cm

SIGNIFICANT FIGURES IN CALCULATIONS

Multiplication and Division The answer is given with as many significant

figures in the measurement with the least amount of significant figures.

Addition and Subtraction The answer is given with as many significant

figures as the measurement with the least number of decimal places.

PERCENT ERROR

Sometimes it is important to calculate how far off a measured value has deviated from the true or accepted value.

For this we use Percent (%) Error.

A PROBLEM TO CONSIDER

A student measures the volume of a piece of zinc, by water displacement, to be 75.0 cm3 and the mass to be 562.5 g.

Now look up the accepted value for the density of zinc in Table S on your reference tables.

A PROBLEM TO CONSIDER

A student measures the volume of a piece of zinc, by water displacement, to be 75.0 cm3 and the mass to be 562.5 g.

Now look up the accepted value for the density of zinc in Table S on your reference tables.

A PROBLEM TO CONSIDER

Does your calculated value agree with the scientifically accepted value?

A PROBLEM TO CONSIDER

Does your calculated value agree with the scientifically accepted value?

A PROBLEM TO CONSIDER

How “ far off ” is your calculated value from the accepted value?

A PROBLEM TO CONSIDER

How “ far off ” is your calculated value from the accepted value?