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SIGNIFICANT
FIGURES
What are they?
 It
is important to be honest when reporting
a measurement, so that it does not appear
to be more accurate than the equipment
used to make the measurement allows.
 Using significant figures communicates
your accuracy in the measurement or
calculation.
Which numbers are significant?
 All

nonzero digits are significant
Examples:
1457 has 4 sig figs
54.1 has 3 sig figs
Which numbers are significant?

All nonzero digits are significant
 Examples:
1457 has 4 sig figs
54.1 has 3 sig figs
 Leading

zeroes are NOT significant
Examples:
0125 has 3 sig figs
0.003 has 1 sig fig
Which numbers are significant?


All nonzero digits are significant
 Examples:
1457 has 4 sig figs
54.1 has 3 sig figs
Leading zeroes are NOT significant
 Examples:
0125 has 3 sig figs
0.003 has 1 sig fig
 Captive

zeroes are significant
Examples:
1002 has 4 sig figs
0.203 has 3 sig figs
Which numbers are significant?

All nonzero digits are significant

Examples:
1457 has 4 sig figs
54.1 has 3 sig figs
 Leading zeroes are NOT significant

Examples:
0125 has 3 sig figs
0.003 has 1 sig fig
 Captive zeroes are significant

Examples:
1002 has 4 sig figs
0.203 has 3 sig figs
 Trailing
zeroes are significant IF AND
ONLY IF they are to the right of the
decimal point

Examples
1.00 has 3 sig figs
150 has 2 sig figs
Which numbers are significant?





All nonzero digits are significant

Examples:
1457 has 4 sig figs
54.1 has 3 sig figs
Leading zeroes are NOT significant

Examples:
0125 has 3 sig figs
0.003 has 1 sig fig
Captive zeroes are significant

Examples:
1002 has 4 sig figs
0.203 has 3 sig figs
Trailing zeroes are significant IF AND ONLY IF they are to the right of the decimal
point

Examples
1.00 has 3 sig figs
150 has 2 sig figs
Exact numbers have infinite significant figures.

Examples
25 students has infinite sig figs
Reporting Calculations with correct
Sig Figs
 For
addition and subtraction, the limiting
term is the one with the smallest number of
decimal places.

Example:
12.11  two decimal places
18.0
 one decimal place
+ 1.013  three decimal places
31.123
31.1 answer reported w/ correct sig figs
Reporting Calculations with correct
Sig Figs
 For
multiplication and division, the
limiting term is the one with the smallest
number of sig figs.

Example:
1.2
x
4.56
=
5.472

5.5
final answer is only allowed two sig figs
284.2 ÷ 2.2
=
129.18

130
final answer is only allowed two sig figs
ROUNDING REVISITED
 When
the answer to a calculation contains
too many significant figures, it must be
rounded off.
 If the digit to be removed

is less than 5, the preceding digit stays the
same.
• Example 1.33 rounds to be 1.3

is equal or greater to 5, the preceding digit is
increased by 1.
• Example
5.56 rounds to be 5.6
SCIENTIFIC NOTATION
~REVIEWED
 A shorthand
way of representing very
large or very small numbers
 Allows us to remove zeroes that are only
serving as place holders
SCIENTIFIC NOTATION
~REVIEWED
 The
number is written with one nonzero
digit to the left of a decimal point multiplied
by ten raised to a power
1.3 x 1025
(Remember the exponent can be positive or
negative)
SCIENTIFIC NOTATION
~REVIEWED
 If
you move the decimal point to the left,
the exponent increases.

Example:
256,000,000  2.56 x 108
 If
you move the decimal point to the right,
the exponent decreases.

Example:
0.000000000028  2.8 x 10-11
Calculations w/ Scientific Notation
 Adding/subtracting
exponents must be
made the same* then add or subtract
Example:
1.4 x 103
+ 2.5 x 104

0.14 x 104
+ 2.5 x 104
2.64 x 104
2.6 x 104
Convert all others to the largest exponent.
Calculations w/ Scientific Notation
 multiply numbers and add
exponents then make sure you have
proper scientific notation
 Multiplying

Example:
(2.5 x 1012)(1.1 x 103) = (2.5)(1.1) x 10(12+3)
= 2.75 x 10152 sig figs2.8 x 1015
 Dividing
divide number and subtract
exponents then make sure you have
proper scientific notation

Example:
(2.5 x 105)/(3.6 x 107) = (2.5/3.6) x 10(5-7)
= 0.694 x 10-2 6.9 x 10-3