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Measurements and Calculations. Units of Measurements. Measurement. Quantitative information Need a number and a unit Represents a quantity For example: 2 meters 2 is number Meters is unit Length is quantity

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Presentation Transcript
slide1

Measurements and Calculations

Units of Measurements

slide2

Measurement

  • Quantitative information
  • Need a number and a unit
  • Represents a quantity
  • For example: 2 meters
    • 2 is number
    • Meters is unit
    • Length is quantity
  • Units compare what is being measured to a defined measurement standard

UNITS MATTER!!

slide3

Measurement

  • Le Systeme International d’Unites : SI
  • System of measurement agreed on all over the world in 1960
  • Contains 7 base units
  • Units are defined in terms of standards of measurement that are objects or natural occurrence that are of constant value or are easily reproducible
  • We still use some non-SI units
si units
SI Units

Quantity

Symbol

Base Unit

Abbrev.

Length

l

meter

m

Mass

m

kilogram

kg

Time

t

second

s

Temp

T

kelvin

K

Amount

n

mole

mol

si units1

mega-

kilo-

k

M

106

103

deci-

BASE UNIT

d

---

10-1

100

centi-

c

10-2

milli-

m

10-3

micro-

10-6

nano-

n

10-9

pico-

p

10-12

SI Units

Prefix

Symbol

Factor

slide6

M

V

D =

Derived Units

  • Combination of base units.
  • Volume (m3 or cm3)
    • length  length  length

1 cm3 = 1 mL

1 dm3 = 1 L

  • Density (kg/m3or g/cm3)
    • mass per volume
slide7

Density

Mass (g)

Volume (cm3)

problem solving steps
Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

problem solving steps1
Problem-Solving Steps
  • List Givens and the Unknown
  • List Correct Formula
  • Math – Algebra
  • Compute – Conversions, etc.
  • 5. Answer Rounded with UNITS
si prefix conversions

To the left

or right?

SI Prefix Conversions

1. Find the difference between the exponents of the two prefixes.

2. Move the decimal that many places.

si prefix conversions1

NUMBER

=

UNIT

SI Prefix Conversions

0.532

532 m = _______ km

NUMBER

UNIT

si prefix conversions2

kilo-

mega-

M

k

106

103

deci-

BASE UNIT

d

---

100

10-1

centi-

c

10-2

milli-

m

10-3

micro-

10-6

nano-

n

10-9

pico-

p

10-12

SI Prefix Conversions

Prefix

Symbol

Factor

move left

move right

si prefix conversions3
1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

SI Prefix Conversions

0.2

32

45,000

0.0805

dimensional analysis
Dimensional Analysis
  • The “Factor-Label” Method
    • Units, or “labels” are canceled, or “factored” out
dimensional analysis1
Dimensional Analysis
  • Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

dimensional analysis2

qt

mL

Dimensional Analysis

How many milliliters are in 1.00 quart of milk?

1 L

1.057 qt

1000 mL

1 L

1.00 qt

= 946 mL

dimensional analysis3

lb

cm3

Dimensional Analysis

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

1 cm3

19.3 g

1 kg

2.2 lb

1000 g

1 kg

1.5 lb

= 35 cm3

dimensional analysis4

in3

L

Dimensional Analysis

How many liters of water would fill a container that measures 75.0 in3?

1 L

1000 cm3

(2.54 cm)3

(1 in)3

75.0 in3

= 1.23 L

dimensional analysis5

cm

in

Dimensional Analysis

Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm

1 in

2.54 cm

= 3.2 in

dimensional analysis6

cm

yd

Dimensional Analysis

Taft football needs 550 cm for a 1st down. How many yards is this?

1 ft

12 in

1 yd

3 ft

1 in

2.54 cm

550 cm

= 6.0 yd

dimensional analysis7

cm

pieces

Dimensional Analysis

A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1 piece

1.5 cm

100 cm

1 m

1.3 m

= 86 pieces