Video

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Video Measurement Every Measurement You Take

• Play while students are coming into the class.

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(No Transcript)
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Do you know how to take a measurement?
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Do you know how to work with the measurements you
take?
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Chapter 2

• Significant Digits

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Taking Measurements

• All measurements involve one estimation.
• If the measuring device is digital it will take
  the estimation for you.

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Electronic Measuring Devices

• Digital readout measuring diameter of 1.0420
  inches.
• The last zero is the estimated digit.

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Taking Measurements

• All measurements involve one estimation.
• If the measuring device is scaled you must take
  the estimation yourself.

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Scaled Measuring Devices
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Scaled Measuring Devices

• Bottom ruler gives a measurement of 8.? cm.

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Scaled Measuring Devices

• Measure the length of the metal using the top
  ruler.

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How to read a meniscus.
.
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How to read a meniscus.
ml
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Read the Volume in mL
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Significant Digits
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(No Transcript)
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Rules for Significant Digits

• All non-zero digits are significant.
• Trailing zeros after the decimal point ARE
  significant.
• Zeros between significant digits are significant.
• All other zeros are NOT significant unless
  indicated to be so by having a bar placed over
  them.

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How to Determine Significant Digits

• Underline the leftmost nonzero digit.
• Use the rules for significant digits to determine
  the rightmost significant digit.
• Every digit in between the leftmost and rightmost
  significant digits are significant as well.

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Counting or Exact Numbers
Counting numbers If there are 10 people in a room there are not 9.5 or 10.76 people in the room. Counting numbers are exact.
Ones in Conversion Factors 1 kilometer 1000 meters.  Exactly 1 km is equal to exactly 1000m. The 1 is considered to be an exact number and so is the 1000. Since Counting numbers and metric conversions are exact they have an infinite number of significant digits.
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Determine the Significant Digits(Examples in
Notebook)

• 70.12 L
• 0.000800 mg
• 82.003 µm
• 27.0 km
• 50 people
• 1.002 cm
• 200 kg

• -270.8 ºC
• 1000 mL
• 42,729.00 cm
• 225 beans
• 99.294 dm
• 0.06900 m
• 3,200,000 µL

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Determine the Significant Digits (Examples in
Notebook)

• 70.12 L 4
• 0.000800 mg 3
• 82.003 µm 5
• 27.0 km 3
• 50 people infinite
• 1.002 cm 4
• 200 kg 2

• -270.8 ºC 4
• 1000 mL 1
• 42,729.00 cm 7
• 225 beans infinite
• 99.294 dm 5
• 0.06900 m 4
• 3,200,000 µL 5

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Are Significant Figures Important?

• A student was given an assignment and a budget of
  50 to complete it. Get a cube of metal which
  has a mass of 83 grams. He knew the density of
  the metal was 8.67 g/mL, and used this to
  calculate the cube's volume.

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Are Significant Figures Important?

• Believing significant figures were invented just
  to make life difficult for chemistry students and
  had no practical use in the real world, he
  calculated the volume of the cube to be about
  9.573 mL.

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Are Significant Figures Important?

• He then calculated that the edge of the cube had
  to be 2.097 cm. He took his plans to the machine
  shop where his friend had the same type of work
  done the previous year. The shop foreman said,
  "Yes, we can make the cube according to your
  specifications."

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Are Significant Figures Important?

• "That's OK," replied the student. "It's
  important."
• He knew his friend has paid 35, and he had been
  given 50 out of the school's research budget to
  get the job done.

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Are Significant Figures Important?

• He returned the next day, expecting the job to be
  done. "Sorry," said the foreman. "We're still
  working on it. Try next week."
• Finally the day came, and our friend got his
  cube. It looked very, very smooth and shiny and
  beautiful in its velvet case.

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Are Significant Figures Important?

• Seeing it, our hero had a premonition of disaster
  and became a bit nervous. But he summoned up
  enough courage to ask for the bill.

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Are Significant Figures Important?

• "500, and cheap at the price. We had a terrific
  job getting it right -- had to make three before
  we got one right."

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Are Significant Figures Important?

• "But--but--my friend paid only 35 for the same
  thing!"
• "No. He wanted a cube 2.1 cm on an edge, and your
  specifications called for 2.097cm.

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Are Significant Figures Important?

• We had yours roughed out to 2.1 that very
  afternoon, but it was the precision grinding and
  lapping to get it down to 2.097 which took so
  long and cost the big money.

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Are Significant Figures Important?

• The first one we made was 2.089 on one edge when
  we got finshed, so we had to scrap it. The second
  was closer, but still not what you specified.
  That's why the three tries."
• "Oh! I see. I should have paid attention to sig
  figs in science class. Guess I am going to pay
  now instead."

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Math Operations with Significant Digits

• When multiplying and/or dividing your answer must
  reflect the smallest number of significant
  digits.

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Math Operations with Significant Digits

• When multiplying and/or dividing your answer must
  reflect the smallest number of significant
  digits.
• (17.3 cm)(28 cm) 484.4 cm2

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Math Operations with Significant Digits

• When multiplying and/or dividing your answer must
  reflect the smallest number of significant
  digits.
• (17.3 cm)(28 cm) 484.4 cm2 480 cm2

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Math Operations with Significant Digits

• When multiplying and/or dividing your answer must
  reflect the smallest number of significant
  digits.
• (17.3 cm)(28 cm) 484.4 cm2 480 cm2
• 708g 4.700ml 150.63829 g/ml

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Math Operations with Significant Digits

• When multiplying and/or dividing your answer must
  reflect the smallest number of significant
  digits.
• (17.3 cm)(28 cm) 484.4 cm2 480 cm2
• 708g 4.700ml 150.63829 g/ml 151g/ml

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Addition and/or Subtraction reflects the fewest
decimal placesdecimal places.

• 24.6 cm - 17.01 cm 7.59 cm

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Addition and/or Subtraction reflects the fewest
decimal placesdecimal places.

• 24.6 cm - 17.01 cm 7.59 cm 7.6 cm

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Addition and/or Subtraction reflects the fewest
decimal placesdecimal places.

• 24.6 cm - 17.01 cm 7.59 cm 7.6 cm
• 8.5g 1.32g 0.18g

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Addition and/or Subtraction reflects the fewest
decimal placesdecimal places.

• 24.6 cm - 17.01 cm 7.59 cm 7.6 cm
• 8.5g 1.32g 0.18g 10g

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Addition and/or Subtraction reflects the fewest
decimal placesdecimal places.

• 24.6 cm - 17.01 cm 7.59 cm 7.6 cm
• 8.5g 1.32g 0.18g 10g 10.0g

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Homework

• Worksheet Significant Digits Rounding.