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Measurements and Conversions

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Measurements and Conversions

- 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

- Standard for many scientific measurements

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 ___ kg2.75 mL ___ L

150 mm ___cm0.0150 m ___cm

0.195 cg ___ mg0.750 L ___mL

2.46 mg ___ kg5.79 HL ___ L

7.53 km ___cm0.0432 g ___mg

4150 cL ___ L739 dm ___ m

81.8 cg ___kg418.2 m ___ km

- Scientific Notation – a way of showing very large or small numbers.
- 4.7 x 1034.7 E 34.7 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.

- 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

- 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

- 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

- 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

- Exact numbers - counting numbers
- Not measurements

- A stated value that is certain

- Example: 100 years = 1 century, 1 foot = 12 inches

- Accuracy
- How close the measured value is to the accepted value

- Precision
- How close a series of measurements are to each other

- 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 something is MEASURED
- Not when something is COUNTED

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

- 47.08020
- 10
- 5400600
- 1.158
- 0.007013
- 100.

- 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 the rules for rounding change
- i.e. going from addition division or
multiplication addition

- i.e. going from addition division or
- At the end of the problem, and you are giving the final answer

- 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

- 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.

- 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

- 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 hr365.25 day 1 yr
- 135 km cm
- 135 km1000 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 mile5280 ft12 in = 95,000 in
- 1 mile1 ft