SNC2D
SCIENTIFIC NOTATION,
SIGNIFICANT DIGITS,
& METRIC CONVERSIONS
SCIENTIFIC NOTATION
 Scientists often have to work with very large
or very small numbers.
 It’s a system that uses a simpler form of
these numbers.
 In scientific notation, all numbers are
written in the form:
a x 10n
 In this form, a can be greater than or equal
to 1 but less than 10 and n can be any value.
SCIENTIFIC NOTATION
 For large numbers, move the decimal place to the left.
 The number of times you move the decimal point to
the left will be equal to the exponent on the base 10.
 Example:
1500
(the exponent will be +3)
1.5 x 103
 For small numbers, move the decimal place to the
right.
 Note, the exponent on the base is negative.
 Example:
0.0505
(the exponent will be -2)
5.05 x 10-2
SCIENTIFIC NOTATION
 On a scientific calculator, enter using the following
sequence:
5
.
0
5
EXP
or
EE
+/-
 Practice converting the numbers below from
standard form into scientific notation
8.2 x 106
8,200,000 = ______________________
5.088 x 1013
50,880,000,000,000 = ______________
-4
1.2
x
10
0.00012 = ________________________
4.58 x 10-9
0.00000000458 = __________________
2
QUESTION
 What is the length of the screw?
QUESTION
 NOW ... what is the length of the screw?
A ruler marked in millimeters can generally
make a much more precise measurement
than a ruler marked in centimeters.
SIGNIFICANT DIGITS
 Every experiment involves some uncertainty in
measurement.
 Significant digits are CERTAIN digits (considered
accurate) plus one UNCERTAIN (estimated) digit
used in the measurement.
 For example, the length of the screw:
5.N Vs 5.1N
The precision of a measurement can be shown by
the number of significant digits in the value.
SIGNIFICANT DIGITS RULES & EXAMPLES
 Any non-zero digit is significant.
 Ex. 227.4 has four significant digits.
 Zeros used to space a number to the right of a decimal
point are not significant.
 Leading zeros are not significant (to the left of non-zero
digits)
 Ex. 0.000147 has only three significant digits.
 Trailing zeros, to the right of any non-zero digits, are not
significant (when there is no decimal).
 Ex. 74,000 has only two significant digits.
 All other zeros are significant.
 Ex. 60.59 has 4 significant digits.
CALCULATING WITH SIGNIFICANT DIGITS
ROUNDING RULE:
 Rounding after the last significant digit
 < 5 ... Leave it
 > 5 ... Round up
 = 5 ... Round to the even number
 Example: round numbers to 4 significant figures
 12.364
 12.36
 12.366
 12.37
 12.365
 12.36
 12.3649  12.36
 12.36501  12.37
CALCULATING WITH SIGNIFICANT DIGITS
RULE:
 In any calculation, the number of significant digits
in the answer cannot be greater than the number
of significant digits of any measured value.
 For example, suppose you do the following calculation:
5.73 x 2.1 = 12.033
 In this situation, the second measurement has the
fewest significant digits. Therefore, the answer must
also have just two significant digits and should be
reported as 12.
CERTAINTY RULE FOR
MULTIPLICATION & DIVISION
RULE:
 The answer has the same number of digits as the
least significant figure (regardless of placement).
 Ex. 77.3 x 0.56 = 43.288 = 43
 Ex. 2.541 x 4.01 = 10.18941 = 10.2
 Ex. 539.7 / 40. = 13.4925 = 13
PRECISION RULE FOR
ADDITION & SUBTRACTION
RULE:
 The answer has the same number of decimal
places as the least number in the question.
 Ex. 187.6 + 54.321 = 241.921 = 241.9
METRIC CONVERSIONS
Metric system:
 The system of units used by most scientists.
 Also known as System International (SI) units.
 In the metric system, different units for the same
quantity are related to one another by prefixes.
 Each prefix represents a multiple of 10.
METRIC CONVERSIONS
 All the conversions are multiples of 10.
 Converting from one unit to another, such as from
meters to centimeters, simply involves shifting the
decimal point to the left or right.
Example:
12.56 meters = 1,256 centimeters = 0.01256 kilometers.
 Follow the diagram in the handout.
METRIC CONVERSIONS
Tips for solving unit conversion problems:
 Always be aware of the unit you start with and the
unit you have been asked for.
 When converting any type of measures:
 To convert from a larger to smaller metric unit you
always multiply
 To convert from a smaller to larger unit you always
divide
METRIC CONVERSIONS
 This is the metric conversion stair chart. You
basically take a place value chart turn it sideways
and expand it so it looks like stairs.
 The Latin prefixes literally mean the number
indicated. Meter, liter or gram can be used
interchangeably.