Measurements and conversions
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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

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Measurements and Conversions

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Measurements and conversions

Measurements and Conversions


Why measure

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


Measurements and conversions

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)


Metric prefixes

Metric Prefixes


Measurements and conversions

  • 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.


Measurements and conversions

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


Measurements and conversions

  • 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.


Converting to scientific notation

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

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

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 up1

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

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 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

    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 to use Sig Fig

    • When something is MEASURED

    • Not when something is COUNTED


    Coast to coast sig figs

    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

    Coast to Coast practice

    • 47.08020

    • 10

    • 5400600

    • 1.158

    • 0.007013

    • 100.


    Rounding numbers in calculations

    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 to round off significant figures

    • When the rules for rounding change

      • i.e. going from addition  division or

        multiplication  addition

    • At the end of the problem, and you are giving the final answer


    Conversions that you are responsible for knowing

    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

    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

    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

    Unit Analysis Practice

    • 5.75 min  months

    • 135 km  cm

    • 17.5 oz  gal

    • 1.5 mile  inch

    • 145 mg  hg

    • 135 mL  L


    Measurements and conversions

    • 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


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