Transcript Significant Figures

The Mathematics of Chemistry
Significant Figures
Uncertainty of Measurement
• The last digit on any physical
measurement is always an approximation.
• Significant figures are the number of digits
that can be accurately measured and the
first uncertain digit.
Rules for Finding Significant
Figures
All nonzero digits are
significant.
00340.003210
Rules for Finding Significant
Figures
All sandwiched zeros are
significant.
00340.003210
Rules for Finding Significant
Figures
All zeros to the right of all non-zero
digits are only significant if a
decimal point is shown.
00340.003210
Rules for Finding Significant
Figures
All leading zeros before the first
nonzero digit are NOT
significant.
00340.003210
Total Significant Figures?
00340.003210
9
How many significant figures?
800.1
4
How many significant figures?
0800.10
5
How many significant figures?
800
1
How many significant figures?
800.*
3
*Trailing zeros to the right of a non-zero digit are not
significant unless they are followed by a decimal
point.
How many significant figures?
0.008
1
How many significant figures?
0.180
3
Using significant figures when
adding and subtracting.
• When adding or subtracting amounts of
substance, the final amount can only be as
precise as the least precise number in the
calculation.
• If you add 0.03 g of NaCl to 155 g of water,
the total mass should be expressed as 155 g
because the mass of water has the least
precise measurement.
Using significant figures when
adding and subtracting.
• Find the number of significant figures in
the decimal portion of each of the
numbers in the problem.
• Add or subtract the numbers.
• Round the answer to match the least
number of places in the decimal portion
of any number in the problem.
Using significant figures when
adding and subtracting.
892.542
20.629
0.18
+ 4.20
3
3
2
2
917.551
The least amount of significant figures to the right of the decimal in the
numbers is 2. Therefore the answer should only have 2 significant
figures to the right of the decimal.
917.55
Using significant figures when
multiplying and dividing.
• When multiplying or dividing numbers the
answer should have the same number of
significant figures as the least precise
number.
Using significant figures when
multiplying and dividing.
• Find the number of significant figures in
each of the numbers involved in the
calculation.
• Complete the calculation.
• Write the answer in the number of
significant figures as the beginning
number with the least significant figures.
Using significant figures when
multiplying and dividing.
28.3 X 5.0 = 141.5
28.3 has 3 significant figures and 5.0 has
2 significant figures, therefore the answer
should be written 140 so that it only has 2
significant figures.
140