UNIT 1 SECTION 2Metric Measurement, Scientific Notation, & Sig Figs

THE INTERNATIONAL SYSTEM OF UNITS

If everyone is to understand what your measurements mean, you must agree on the units that will be used.By international agreement, a set of units called "The International System of Units" has been defined for scientific work. This system was adopted in 1960 by the General Conference on Weights and Measures.

These units are also called metric units or SI units.

SI HAS SEVEN BASE UNITS

Quantity Unit NameUnit

Abbreviation

Length meter m

Mass kilogram kg

Time second s or sec

Temperature Kelvin K

Amount of Substance mole mol

Electric Current ampere A

Luminous Intensity candela cd

ADVANTAGES OF USING SISI Units make measuring and calculating easier.

Measurements are always expressed as decimals rather than fractions.

It is very easy to change from one unit to another since they

are based on 10.

It is universally understood.

SI PrefixesPrefixes can be placed in front of the base units.

These prefixes are used to represent quantities that are larger or smaller than the base units. These

prefixes must be memorized.

Prefix Unit Abbreviation Meaning

Giga- G 1,000,000,000 (billion)

Mega- M 1,000,000 (million)

Kilo- k 1,000 (thousand)

Hecto- h 100 (hundred)

Deca- da 10 (ten)

(Base) UNITS with NO PREFIX 1

Deci- d .1 (tenth)

Centi- c .01 (hundredth)

Milli- m .001 (thousandth)

Micro- .000001 (millionth)

Nano- n .000000001 (billionth)

To convert from one metric unit to another, count how many “steps” it takes to get to the desired level. If

you go UP, move the decimal to the RIGHT. If you go DOWN, move

the decimal to the LEFT.

CONVERSION OF METRIC UNITS

Metric Conversion Examples:

1) 86 g = _______________ mg86,000

2) 9824 cL = __________________ L

98.24

3) 872 µs = _______________ ms

.872

4) .678 g = _______________ kg.000678

5) 1 km = _______________ mm

1,000,000

Metric Unit of LengthThe meter (m) is the SI base unit of

length.Prefixes are used to indicate

distances longer and shorter than a meter.

Length: straight line distance between 2 points. What name and symbol is given to each of the

following units of length?a).000001 m

b).001 mc).01 md).1 me)10 mf) 1000 m

Micrometer mMillimeter mmCentimeter cmDecimeter dm

Decameter damKilometer km

Metric Unit of VolumeVolume:

How much space something takes up.

The cubic meter (m3) is the SI derived unit for measuring volume.

When chemists measure the volumes of liquids and gases, they often use a non-SI unit called the liter.

The two units, _________________, are interchangeable.

mL and cm3

Metric Unit of MassMass:

The amount of matter in an object.

Weight: Force with which gravity pulls on matter.

Mass and weight are

often confused. Mass is not affected by

gravitational pull.

Your weight on the moon

would be less, but your mass on the moon would be the same.

The ____________is the SI base unit for measuring mass.kilogram (kg)

STATE THE QUANTITY THAT IS MEASURED BY EACH OF THE FOLLOWING UNITS:

1. centigram 2. millimeter3. Kelvin  4. millisecond 

1.Mass2.Length3.Temperatu

re4.Time

Why? So scientists can easily express numbers that are very large and/or very small.

Examples:The mass of one gold atom is .000 000 000 000 000 000 000 327 grams.

One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms. Scientists can work with very large

and very small numbers more easily if the numbers are written in scientific notation.

Scientific Notation

WHAT IS SCIENTIFIC NOTATION?

• In scientific notation, a number is written as the product of two numbers…..

….. A simple number (coefficient) multiplied by a power of 10

1. Move the decimal to the right of the first non-zero

number.2. Count how many places the

decimal had to be moved.3. If the decimal had to be

moved to the right, the exponent is negative.

4. If the decimal had to be moved to the left, the exponent is positive.

HOW to write a number in scientific notation:

** Scientific Notation can be reversed to write the number in standard form again.

FOR EXAMPLE:The number 4,500 is written in scientific notation as ______________.4.5 x 103

The coefficient is _________.The coefficient must be a number greater than or equal to 1 and smaller than 10.

4.5

The power of 10 or exponent in this example is ______.3

The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

Practice ProblemsPut these numbers in scientific notation.

1) .000122) 10003) 0.014) 125) .9876) 5967) .000 000 7

PROBLEMS

1)1.2 x 10-4

2) 1 x 103

3) 1 x 10-2

4) 1.2 x 101

5) 9.87 x 10-1

6) 5.96 x 102

7) 7.0 x 10-7

ANSWERS

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS

PROBLEMS ANSWERS

1) 4.9 X 102

2) 3.75 X 10-2

3) 5.95 X 10-4

4) 9.46 X 103

5) 3.87 X 101

6) 7.10 X 100

7) 8.2 X 10-5

1) 490

2) .0375

3) .000595

4) 9460

5) 38.7

6) 7.10

7) .000082

WHAT ARE SIGNIFICANT FIGURES (AKA SIG FIGS)?

The significant digits in a measurement are all of the digits known with certainty plus one final digit, which is uncertain or is estimated.

For example: Study the diagram below.

Using the ruler at the top of the diagram, what is the length of the darker rectangle found in between the two rulers?

Answer: The length is between 4 and 5 cm. The “4” is certain, but the distance past 4 cm will have to be estimated. A possible estimate might be 4.3. Both of these digits are significant. The first digit is certain and th second digit is uncertain because it is an estimate.

Using the ruler at the bottom of the diagram, what is the length of the darker rectangle found in between the

two rulers?

Answer: The edge of the rectangle is between 4.2 cm and 4.3 cm. We are certain about the 4.2, but the next digit will have to be estimated. As possible estimation might be 4.27. All three digits would be significant. The first two digits are certain and the last digit is uncertain.

The last digit in a measurement is

always the uncertain digit.

It is significant even if it is not certain.

The more significant digits a value has, the more accurate

the measurement will be.

Please remember…

THERE ARE A FEW RULES

THAT DETERMINE HOW

MANY SIGNIFICANT DIGITS

A MEASUREMENT HAS.

YOU WILL NEED TO LEARN

THESE RULES!

Rule #1: Non-zero digits are ALWAYS significant.

Rule #2: Any zeros between sig figs ARE significant.

Rule #3: A final zero or trailing zero in the decimal portion ONLY are significant.

PRACTICE PROBLEMS

How many significant digits are in each of the following examples?

 

1) 47.12) 97003) 0.0059650004) 5605) 0.05096) 701.9057) 50.008) 50.0129) 0.00000910) 0.0000104

Answers:1)32)23)74)25)36)67)48)59)110)3

When you +, -, ×, or ÷, your answer should only be as precise as the least precise measurement in the calculation.

Sig Figs in Calculations

DETERMINING SIGNIFICANT DIGITS WHEN ROUNDING

1) 689.683 grams (4 significant digits)

 2) 0.007219 (2 significant digits)

 3) 4009 (1 significant digit) 4) 3.921 x 10-1 (1 significant

digit) 5) 8792 (2 significant digits) 6) 309.00275 (5 significant

digits) 7) .1046888 (3 significant digits) 

1)689.7

2)0.0072

3)4000

4)4 x 10-1

5)8800

6)309.00

7) .105