Quantitative Analysis

English-Metric Conversions&

Scientific Notation

• Quantity – something that has magnitude, size, or amount (length, mass, volume)

• Unit – a quantity adopted as a standard of measurement (meter, kilogram, liter)

• Conversion Factor – ratio equating two different units; used to convert from one unit to the other

Density• Mass divided by volume

for any substance• Often used to identify a

substance• More dense objects sink

to the bottom• Common conversion

factor

International System of Units (or SI units) –measurement system used by the scientific community worldwide

Base Units are: meters, kilograms, seconds,and kelvins

Length Conversions

Metric to Metric

1000 millimeters (mm) = 1 meter (m)

100 centimeters (cm) = 1 meter (m)

1000 meters (m) = 1kilometer(km)

English to English

1 mile (mi) = 5280 feet (ft)

1 yard (yd) = 3 feet (ft)

1 foot (ft) = 12 inches (in)

Metric to English

2.54 cm = 1 in

Practice

Convert 12350 millimeters to miles

Mass – the amount of matter in a

substance

– doesn’t change

Weight – a force due to gravity

-- can change depending on

location

Mass & Weight Conversions

Metric to Metric

1000 milligrams (mg) = 1 gram (g)

100 centigrams (cg) = 1 gram (g)

1000 grams (g) = 1 kilogram (kg)

English to English

16 ounces (oz) = 1 pound (lb)

2000 pounds (lb) = 1 ton

Metric to English

453.59 g = 1 lb

Practice

Convert 13.5 kilograms to ounces

Volume Conversions

Metric to Metric

1000 milliliters (mL) = 1 liter (L)

1000 liters (L) = 1 kiloliter (kL)

1 cubic centimeter (cm3) = 1 milliliter (mL)

English to English

1 gallon (gal) = 4 quarts (qt)

1 cubic foot (ft3) = 7.475 gallons (gal)

Metric to English

1 L = 1.06 qt

PracticeConvert 6.75 cubic feet to cubic

centimeters

Time Conversions Universal Units

60 seconds (sec) = 1 minute (min)

60 minutes (min) = 1 hour (hr)

24 hours (hr) = 1 day

365 days = 1 year (yr)

7 days = 1 week (wk)

PracticeConvert 35.6 days to seconds

Significant Figures

How many digits does my answer have to have?!

It depends on how accurate your measurements are.

Nonzero digits are always significant

46.3 m has ___ sig. figs.

6.295 g has ___ sig. figs.

Zeros between nonzero digits are significant

40.7 L has ___ sig. figs.

87009 km has ___ sig. figs.

Zeros in front of nonzero digits are not significant

0.009587 m has ___ sig. figs.

0.0009 kg has ___ sig. figs.

Zeros at the end of a number AND to the right of a decimal point are

significant

85.00 g has ___ sig. figs.

9.070000000 cm has ___ sig. figs.

123000.00 mL has ___ sig. figs.

Zeros at the end of a number that does not have a decimal point are not

significant

8500 g has ___ sig. figs.

9070000000 cm has ___ sig. figs.

Rules for using Sig. Figs.

Where do I round off?

1. Multiplication and division: answer has same number of sig figs as the number in problem with fewest sig. figs.

12.4 x 7.943 =

246.83 / 26 =

2. Addition and subtraction: answer can only be as accurate as the least accurate number in problem (line up your numbers)

3.95 54.638

2.879 -31.22

+213.6

3. Problems with both addition (or subtraction) and multiplication (or division): round off after each operation

Converting 2 Unit Numbers

1. The number always goes with the unit on top

2. Convert top unit first, then bottom unit

Convert 970 kilometers per hour to feet per second

(970 km/hr ? ft/sec )

2 Unit Numbers as Conversion Factors

1. Start with the number that contains only one unit

2. Use the number that contains 2 units as a conversion factor in the middle of the problem

Example

On an average day the Delaware River flows past the Delaware Memorial Bridge at a rate of 7000 gal/sec .

How many minutes would it take for 6800 kL of water to pass the Delaware Memorial Bridge?

Scientific Notation Convenient way to express long numbers

Rule #1 – only one non-zero digit to left of decimal

Rule #2 – Large numbers have positive exponent, small numbers have negative exponent

Rule #3 – move decimal right, subtract from exponent

Rule #4 – move decimal left, add to exponent

PracticeConvert to Scientific Notation:

7538000 =

0.0000000000000896 =

Convert to regular numbers:

6.97 x 10-7 =

3.21 x 1023 =

Correct the following Scientific Notation:

0.0235 x 10-13 =

5635 x 10-9 =

32569 x 105 =

0.000054 x 1035 =

Multiplying

Multiply numbers, add exponents, correct Sci. Not.

(3.1 x 103) (5.01 x 104)

Multiplying

Multiply numbers, add exponents, correct Sci. Not.

(3.1 x 103) (5.01 x 104)

(3.1 x 5.01) x 103+4

Multiplying

Multiply numbers, add exponents, correct Sci. Not.

(3.1 x 103) (5.01 x 104)

(3.1 x 5.01) x 103+4

15.531 x 107

Multiplying

Multiply numbers, add exponents, correct Sci. Not.

(3.1 x 103) (5.01 x 104)

(3.1 x 5.01) x 103+4

15.531 x 107

1.5531 x 108

Multiplying

Try These:

(5.13 x 10-3) (9.87 x 1017)

(6.58 x10-8) (1.32 x10-14)

DividingDivide numbers, subtract exponents,

correct Sci. Not.

7.63 x 103 =

8.62 x 104

DividingDivide numbers, subtract exponents,

correct Sci. Not.7.63 x 103

= 7.63 x 103-4

8.62 x 104 8.62

DividingDivide numbers, subtract exponents,

correct Sci. Not.7.63 x 103

= 7.63 x 103-4

= 0.885 x 10-1

8.62 x 104 8.62

DividingDivide numbers, subtract exponents,

correct Sci. Not.7.63 x 103

= 7.63 x 103-4

= 0.885 x 10-1

8.62 x 104 8.62

0.885 x 10-1 = 8.85 x 10-2

DividingTry These, but…

…watch out for double negatives when subtracting!

5.32 x 10-13 1.49 x 10-5 3.21 x 107

1.25 x 10-47 7.25 x 109 6.11 x 10-11

Conversions with Sci. Not.

Convert 3.24 x 108 kilometers per hour to feet per second

(3.24 x 108 km/hr ? ft/sec )