This document provides an overview of scientific notation, accuracy, precision, significant figures, and proper reporting of calculations involving measurements. Key points include: - Scientific notation is used to represent very large or small numbers between 1-10 with an exponent. - Accuracy refers to how close a measurement is to the true value, while precision refers to the agreement between repeated measurements. - When measuring, all certain digits and one uncertain digit are recorded as significant figures. - Calculations should be reported with the same number of significant figures or decimal places as the least precise input measurement.

1. Lecture 3.1-
Measurements

2. SCIENTIFIC NOTATION
is used to represent very large
or very small numbers

3. SCIENTIFIC NOTATION
6.02 x 1023

4. SCIENTIFIC NOTATION
6.02 x 1023
must be
between
1-10

5. SCIENTIFIC NOTATION
6.02 x 1023
must be The power of ten
between determines the size of
1-10 the number

6. SCIENTIFIC NOTATION
6.02 x 1023
must be The power of ten
between determines the size of
1-10 the number
Positive power = big number(greater than 10)
Negative power = small number(less than one)

7. SCIENTIFIC NOTATION
6.02 x 1023
must be The power of ten
between determines the size of
1-10 the number
Positive power = big number(greater than 10)
Negative power = small number(less than one)
EX. 0.00567g = 5.67 x 10-3g a small number
437,850g = 4.3785 x 105g a large number

8. To convert from standard notation to
scientific notation move the decimal point
to make a number between 1 and 10 then
count how many spaces you moved it.
positive
because it
is a big
number
negative
because it is a
small number

9. Accuracy and Precision
• Accuracy measures how close a
measurement comes to the actual
value.
• Precision measures how close a
series of measurements are to each
another.

10. 3.1

11. Just because a measuring device
works, you cannot assume it is
accurate.
The scale has not been properly zeroed,
so the reading obtained for the person’s
weight is inaccurate.

12. Significant digits
When measuring we record all
certain digits plus one uncertain
digit

13. Significant digits
When measuring we record all
certain digits plus one uncertain
digit, so there is always some
degree of uncertainty
in measurement.

14. Significant digits
When measuring we record all
certain digits plus one uncertain
digit, so there is always some
degree of uncertainty
in measurement.
In science we account
for this by using
significant digits or
significant figures

15. The more significant digits in a
measurement the more accurate the
measuring device was.

16. The more significant digits in a
measurement the more accurate the
measuring device was.

17. The more significant digits in a
measurement the more accurate the
measuring device was.

21. The number of significant
digits tells us how accurate
the measuring device was.

22. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
3 rules

23. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
3 rules
1. Non-zero integers are always significant
101,300
0.0003020

24. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
101,300
0.0003020

25. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
101,300
0.0003020
2. Zeros-
captive zeros (in between non-zero integers)
are ALWAYS significant

26. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
101,300
0.0003020
2. Zeros-
captive zeros (in between non-zero integers)
are ALWAYS significant
leading zeros (in front) are NEVER
significant

27. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
101,300
0.0003020
2. Zeros-
captive zeros (in between non-zero integers)
are ALWAYS significant
leading zeros (in front) are NEVER
significant
trailing zeros (at the end) are ONLY
significant IF there is a decimal point.

28. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
3. Exact numbers are considered to have
infinite significant figures

29. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
3. Exact numbers are considered to have
infinite significant figures
Exact numbers come from counting or from
definitions

30. COUNTING THE NUMBER OF
SIGNIFICANT DIGITS
3. Exact numbers are considered to have
infinite significant figures
Exact numbers come from counting or from
definitions
Counting  there are 15 students in the library
Definition  1m = 1000mm
15, 1, and 1000 are exact numbers in these situations

31. Reporting calculations with the
correct number of significant digits

32. Reporting calculations with the
correct number of significant digits
Our calculations are only as
precise as our least precise
measurement.

33. Our calculations are only as precise as
our least precise measurement

34. Our calculations are only as precise as
our least precise measurement
If 30 beans have a mass of
17.3g what is the average mass?

35. Our calculations are only as precise as
our least precise measurement
If 30 beans have a mass of
17.3g what is the average mass?
17.3g/30 =

36. Our calculations are only as precise as
our least precise measurement
If 30 beans have a mass of
17.3g what is the average mass?
17.3g/30 = 0.576666666666666666g

37. Our calculations are only as precise as
our least precise measurement
If 30 beans have a mass of
17.3g what is the average mass?
17.3g/30 = 0.576666666666666666g
Does it really make sense to claim
such precision when we only
measured out to one tenth of a gram?

38. 17.3g/30 = 0.576666666666666666g
This
number
has three
significant
digits

39. 17.3g/30 = 0.576666666666666666g
This This number
number has infinite
has three significant
significant digits
digits

40. 17.3g/30 = 0.576666666666666666g
This This number
number has infinite
has three significant
significant digits
digits The least precise number has
3 significant digits so the answer
should have only 3 significant
digits.

41. 17.3g/30 = 0.576666666666666666g
This This number
number has infinite
has three significant
significant digits
digits The least precise number has
3 significant digits so the answer
should have only 3 significant
digits. 0.577g

42. For multiplication and division report
the number of significant digits in the
least precise measurement.

43. For multiplication and division report
the number of significant digits in the
least precise measurement.
4.56 x 1.4 = 6.4 two sig figs in result

44. For multiplication and division report
the number of significant digits in the
least precise measurement.
4.56 x 1.4 = 6.4 two sig figs in result
4 x 7.65321 = 3 x 101 one sig fig in result

45. For multiplication and division report
the number of significant digits in the
least precise measurement.
4.56 x 1.4 = 6.4 two sig figs in result
4 x 7.65321 = 3 x 101 one sig fig in result
For addition and subtraction report the
same number of DECIMAL PLACES as
the least precise measurement.

46. For multiplication and division report
the number of significant digits in the
least precise measurement.
4.56 x 1.4 = 6.4 two sig figs in result
4 x 7.65321 = 3 x 101 one sig fig in result
For addition and subtraction report the
same number of DECIMAL PLACES as
the least precise measurement.
18 + 32.657 = 51 result is a whole number

47. For multiplication and division report
the number of significant digits in the
least precise measurement.
4.56 x 1.4 = 6.4 two sig figs in result
4 x 7.65321 = 3 x 101 one sig fig in result
For addition and subtraction report the
same number of DECIMAL PLACES as
the least precise measurement.
18 + 32.657 = 51 result is a whole number
18.1 + 32.657 = 50.8 report to tenths place

48. ROUNDING OFF RESULTS
When performing a chain of calculations
round off your answers only at the end.
13.44 round down 13.4
13.45 round up 13.5