Convert to scientific notation:

1
Convert to scientific notation

• 8960
• 0.00023
• 86,000
• 36,000,000
• 0.0000000253

2
Convert to scientific notation

• 8960 8.96 x 103
• 0.00023 2.3 x 10-4
• 86,000 8.6 x 104
• 36,000,000 3.6 x107
• 0.0000000253
• 2.53 x 10-8

3
Scientific Notation

• Coefficient is the first digit, then a decimal
  point, and then the rest of the number
• Exponent is x 10power

4
Enter the following on your calculator

• 5.3 x 108
• Make sure your calculator still shows exponent of
  8 after you press .

5
Calculate

• (6.02 x 1023)
• (1.7 x 10-19) ?

3.5 x 1042
6
Exponent Calculations

• Multiplication Multiply coefficients together.
  Add exponents
• Division Divide numerator coefficient by
  denominator. Subtract denominators coefficient

7
X and with Exponents

• (3.5 x 1010) x (2.6 x 107) (3.5 x 2.6) x 10107
  
• 9.1 x 1017
• (3.5 x 1010) (2.6 x 107) (3.5 2.6) x 1010-7
  
• 1.35 x 103

8
Exponent Calculations

• Addition or Subtraction Make any needed
  conversions so all numbers have the same
  exponent. Then add or subtract the coefficients.

9
and - with Exponents

• (3.5 x 1010) (2.6 x 107) (3500 x 107) (2.6
  x 107)
• 3502.6x107 3.5026x1010

10
and - with Exponents

• (3.5 x 1010) - (2.6 x 107) (3500 x 107) - (2.6
  x 107)
• 3497.4x107 3.497x1010

11
Converting to standard notation

• Ten to a positive exponent moves the decimal to
  the right that many times
• 3.9 x 10739,000,000
• Ten to a negative exponent moves the decimal to
  the left that many times
• 4.2 x 10-2 0.042 (4.2 100)

12
Write these out in standard notation

• 101
• 100
• 102
• 10-1
• 10-3

13
Write these out in standard notation

• 101 1. 10
• 100 1.
• 102 1. 100
• 10-1 1. 0.1
• 10-3 1. 0.001

14
Standard notation to scientific

• Reverse the direction
• 0.0058 ?
• 43,500,000,000 ?

15
Standard notation to scientific

• Reverse the direction
• 0.0058 5.83 x 10-3
• 43,500,000,000 4.35 x 1010

16
Scientific Notation sheet

• 1. 6.23 x105 2. 2.3 x 102
• 3. 3.4 x 10-3 4. 1.2 x 101
• 5. 8.90 x 105 6. 0.000045
• 7. 2980 8. 3.1
• 9. 0.000000633 10. 110
• 11. 3.245 x 10-3 12. 1.44 x 10-7
• 13. -3.155 x 10-3 14. 1.41 x 10-2
• 15. 2.25 x 104

17
Dimensional Analysis

• Draw a grid
• Write given with units
• Multiply by unit equalities to eliminate unwanted
  obtain wanted units
• Perform all operations to get final answer

18
Problem

• How many liters are in 22 gallons?

19
Problem

• How many liters are in 22 gallons?22 gal 3.785 L
  83 L 1 gal

20
Problem

• The density of air is 1 kg/m3. Convert this to
  g/cm3.

21
Problem

• The density of air is 1 kg/m3. Convert this to
  g/cm3. 1 kg 1000 g (1m)3 . m3 1 kg
  (100cm)3

22

• What is the volume of a piece of silicon (density
  2.33 g/cm3) with a mass of 83.8 g?

23

• What is the volume of a piece of silicon (density
  2.33 g/cm3) with a mass of 83.8 g? V 36.0
  cm3

24

• A nugget of gold (density 19.3 g/cm3) displaces
  0.950 cm3 of water. If a jeweler offers 8.00
  per gram for the nugget, how much money is it
  worth?

25

• A nugget of gold (density 19.3 g/cm3) displaces
  0.950 cm3 of water. If a jeweler offers 8.00
  per gram for the nugget, how much money is it
  worth? 146.00

26

• There are 7.0 x 106 red blood cells in 1.0 mm3 of
  blood. How many red blood cells are in 1.0 L of
  blood?

27

• There are 7.0 x 106 red blood cells in 1.0 mm3 of
  blood. How many red blood cells are in 1.0 L of
  blood?
• 7.0 x 1012 rbcs / L

28

• An automobile can travel 40.0 miles on one gallon
  of gasoline. How many kilometers per liter is
  this? (1.61 km 1 mile 1 L 0.264 gal.)

29

• An automobile can travel 40.0 miles on one gallon
  of gasoline. How many kilometers per liter is
  this? (1.61 km 1 mile 1 L 0.264 gal.)
  17.0 km/L

30

• Accuracy is how close you are to the standard or
  target.
• Precision is how close the measurements are to
  each other.

31
Significant Digits

• include all certain measured digits plus one
  estimated digit.

32
Significant Digits

• All nonzero digits
• Zeros that are between two nonzero digits.
• Zeros after a decimal point that follow sig.
  digit(s) 41.80 m

33
Insignificant Zeros serve as placeholders

• Zeros left of significant digits 0.0568 mLs
• Zeros at the end of a measurement having no
  decimal point 7000 km

34
Ocean Rule Pacific
Atlantic
35
Ocean rule of sig. dig.

• If a decimal point is present count digits from
  1st nonzero digit on Pacific side to the end.
• If a decimal point is absent count from the
  Atlantic (right) side.

36

• 95,600 meters
• 520 mLs
• 0.230 kg
• 0.0102 ms

• 10.002 ns
• 0.451 Pa
• 0.001 cm
• 25,600 L

37
Significant Digits

• are used only for measured quantities.

38
Review 1

• Dimensional Analysis is used for?

39
Review 1

• Dimensional Analysis is used for making
  conversions or with problems of mixed units.

40
Review 2

• Accuracy?
• Precision?

41
Review 2

• Accuracy how close the measurement is to the
  standard.
• Precision how close measurements are to each
  other.

42
Review 3

• How to take a correct measurement?

43
Review 3

• How to take a correct measurement? Use all
  marked digits plus one estimated digit

44
Review 4

• Error?

45
Review 4

• Error 100 measured - accepted
• accepted

46
Review 5

• of significant figures when adding or
  subtracting measurements?

47
Review 5

• of significant figures when adding or subtrct.
  measurements?Last digit in leftmost column is
  last column of answer

48
Review 6

• of significant figures when multiplying or
  dividing measurements?

49
Review 6

• of significant figures when multiplying or
  dividing measurements?The least digits in any
  of the measurements