Measurements and Conversions

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# Measurements and Conversions - PowerPoint PPT Presentation

Measurements and Conversions. Why Measure?. Measurements give specific information Different types: - Base Units: System International Units (or Metric) Standard for many scientific measurements - Derived Units Combinations of base units Ex: density or volume. Metric Units

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### Measurements and Conversions

Why Measure?
• Measurements give specific information
• Different types:

- Base Units: System International Units (or Metric)

• Standard for many scientific measurements

- Derived Units

• Combinations of base units
• Ex: density or volume
Metric Units

Mass – the amount of matter in an object, grams (g)

Volume – the amount of space an object occupies, liter (L)

Length – distance between two points, meter (m)

Converting with metric units
• K H D __ d c m
• Place 1 under starting prefix
• Place 2 under ending prefix
• Draw an arrow from 1 to 2. This is the direction to move the decimal point.
• Count the number of places to go from 1 to 2. Be sure to count the __ space.
• Move decimal point and rewrite number.
Make the following metric conversions

13.5 g  ___ kg 2.75 mL  ___ L

150 mm  ___cm0.0150 m  ___cm

0.195 cg  ___ mg 0.750 L  ___mL

2.46 mg ___ kg 5.79 HL  ___ L

7.53 km  ___cm0.0432 g  ___mg

4150 cL ___ L 739 dm  ___ m

81.8 cg  ___kg418.2 m  ___ km

• 4.7 x 103 4.7 E 3 4.7 exp3
• 4.7 x 10 x 10 x 10 = 4,700
• Only significant numbers remain
• The “number out front” is only allowed to have one nonzero digit to the left of the decimal point.
Converting TO Scientific Notation
• Place the decimal after the first digit
• Count from the original decimal place to the new location.
• That number will become the exponent.
• If you counted:
• To the left (starting # > 1) then + exponent
• To the right (starting #< 1) then - exponent
• Write “new” number x 10exponent
• Do not write any placeholding zeros
• Non-significant numbers
Converting FROM Scientific Notation
• The exponent or power tells how many places the decimal point will be moved.
• If the exponent is positive, the decimal point moves to the right.

- The number will be > 1

• If the exponent is negative, the decimal point moves to the left.

- The number will be < 1

Warm-Up
• Convert the following:

1. 41,300 L to kL

2. 13,200 kg to g

3. 72 cm to mm

• 41.3 kL
• 13,200,000g
• 720mm
Warm-Up
• Express is Scientific Notation:
• 1600
• 0.0053
• 134.8

1. 1.6 x 103

2. 5.3 x 10-3

3. 1.348 x 102

Reliability of Measurements
• Exact numbers - counting numbers

- Not measurements

- A stated value that is certain

• Example: 100 years = 1 century, 1 foot = 12 inches
• Measured numbers- have uncertainty because of the equipment/device used and the observer
Accuracy and Precision
• Accuracy

- How close the measured value is to the accepted value

• Precision

- How close a series of measurements are to each other

Significant Figures
• Scientists use significant figures to show how precisely an experiment was performed
• Significant Figures (sig figs) – all known digits in a measurement plus one estimated digit.
• Scientists use rules to determine the number of significant figures in a particular value
When to use Sig Fig
• When something is MEASURED
• Not when something is COUNTED
Coast to Coast Sig Figs

Atlantic/Pacific Rule:

• If a decimal point is absent, count from the Atlantic (right) side starting with the first nonzero digit.
• If a decimal point is present, count from the Pacific (left) side starting with the first nonzero digit
Coast to Coast practice
• 47.08020
• 10
• 5400600
• 1.158
• 0.007013
• 100.
Rounding numbers in calculations
• Add/subtract: the answer will have the same number of places past the decimal point as the measurement with the fewest places past the decimal point.
• Multiply/divide: the answer will have the same number of sig figs as the measurement with the fewest number of sig figs.
• Rounding off numbers: 0-4 drop, 5-9 add 1
• Defined or exact numbers have an infinite number of significant figures.
WHEN to round off significant figures
• When the rules for rounding change
• i.e. going from addition  division or

• At the end of the problem, and you are giving the final answer
Conversions that you are responsible for knowing…
• 12 in = 1 ft
• 3 ft = 1 yd
• 5280 ft = 1 mile
• 60 sec = 1 min
• 60 min = 1 hr
• 24 hr = 1 day
• 7 day = 1 wk
• 365.25 days = 1 yr
• 16 oz = 1 lb
• 2000 lb = 1 ton
• 8 oz = 1 cup
• 2 cups = 1 pint
• 2 pints = 1 quart
• 4 quarts = 1 gallon
Unit Analysis/Dimensional Analysis
• A method of converting from 1 set of units to another set of units using a series of conversion factors.
• A conversion factor is a fraction made from the two parts of the equivalency.
• 12 in. = 1 ft
• Each equivalency can produce two conversion factors.
Convert 22 inches to feet
• List possible conversion factors:
• Set up grid with starting number and units in the upper left side
• Plug in conversions so that the same units are on the diagonal
Unit Analysis Practice
• 5.75 min  months
• 135 km  cm
• 17.5 oz  gal
• 1.5 mile  inch
• 145 mg  hg
• 135 mL  L
5.75 min  month
• 5.75 min_ 1 hr 1 day 1 yr 12 mos= 1.31 x 104 months
• 60 min 24 hr 365.25 day 1 yr
• 135 km  cm
• 135 km 1000 m 1 cm = 13,500,000 cm
• 1 km 0.01 m
• 17.5 oz  gal
• 17.5 oz 1 qt 1 gal = 0.138 gal
• 32 oz4 qt
• 1.5 mile  inch
• 1.5 mile 5280 ft 12 in = 95,000 in
• 1 mile 1 ft