Scientific Notation

1
Scientific Notation

• Used for very small or very large numbers
• Write out 1 million
• Write out 2.75 billion
• Write out 602 sexillion
• That is 24 digits total

2
Scientific Notation

• Consists as a product of 2 numbers.
• A coefficient and a power of 10
• 6.02 x 1023 602 sexillion
• 2.5 x 104
• 2.5 x 10 x 10 x 10 x 10
• Or 25000

3
Put the following into scientific notation

• A) 36,000
• B) 5,200,000
• C) .00521

4
Significant figures

• The digits known precisely 1 digit.
• A method of reporting measurements.
• Your odometer reads to the tenth. Its not
  appropriate to report a distance measured with an
  odometer as 14.745369328576 miles

5
Significant Figures

• Reporting measurements correctly is the easy part
• The line is between longer than 6.0 cm, shorter
  than 6.1 cm

• We know precisely 6.0, we can estimate the next
  digit
• 6.05cm
• This ruler measures to 3 SIGNIFICANT FIGURES

6
Significant figuresrules

• Leading Zeros are NOT significant
• 0.0065 PASCAL's
• 0.45 meters
• These are place holding zeros. Write these
  measurements in scientific notation to avoid
  place holding zeros

Reading other peoples measurements

• Every NON-zero is significant
• 24.7 m
• 74 ml
• 582 g
• Zeros between NON-zeros are significant
• 10035 ft
• 4007 g

7
Significant figuresrules
Reading other peoples measurements

• Ending zeros AFTER a decimal point ARE
  significant.
• 47.00m (4)
• 20.010 g (5)
• Ending zeros BEFORE a decimal point. Are NOT
  significant
• 7000m (1)
• These are once again place holders

• UNLIMITED
• Counting
• of kids in the class
• Exactly defined quantities
• 1hr60 minutes
• This is an exact definitionThe significant
  figures are unlimited.
• You could say 1 hr 60.000000000000 min

8
Significant Figures and calculations

• Have you ever asked a teacher How many numbers
  do I write down?
• The real answer depends on the number of
  significant figures in the calculation

35.448796415
9
Significant Figures and calculations

• ,-
• round to the same of places as the
  measurement with the least significant place
  value.
• Ex 45.716g
• 17.1 g
• 62.816g
• Report as 62.8 g

62.816
10
Significant Figures and calculations

• Multiplication and division.
• Round to the of significant figures in the
  least accurate term.
• Ex 17.8 x 357.8796
• Answer 6370.25688
• 17.8 has 3 significant figures
• Report the answer as 6370

6370.25688