Dimensional Analysis

Conversions&

Scientific Notation

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

• Unit – a standard of measurement (meter, kilogram, liter) “how something is measured”

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

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)

Metric to English

2.54 cm = 1 in

PracticeConvert 70 inches to centimeters

Convert 1235 centimeters to feet

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)

Metric to English

453.59 g = 1 lb

PracticeConvert 4 pounds to grams

Convert 13.5 kilograms to pounds

Volume Conversions

Metric to Metric

1000 milliliters (mL) = 1 liter (L)

1000 liters (L) = 1 kiloliter (kL)

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

Metric to English

1 L = 1.06 qt

PracticeConvert 15 liters to quarts

Convert 6.75 quarts to milliliters

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)

PracticeConvert 35.6 days to hours

Convert 15000 seconds to days

Density• Mass divided by volume

for any substance• Often used to identify a

substance• More dense objects sink

to the bottom• Common conversion

factor

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 108 =

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 103) (9.87 x 1017)

(6.58 x108) (1.32 x1014)

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

5.32 x 1047 1.49 x 109 3.21 x 107

1.25 x 1013 7.25 x 105 6.11 x 1011

Conversions with Sci. Not.

Convert 3.24 x 108 kilometers per hour to feet per second

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