Measurement & Significant Figures

Report
Measurement &
Significant Figures
Rules for Measurement
Significant Figures
Scientific Notation
Rounding in Science
I. Significant Figures
A. All the digits in a measurement up to the estimated digit
are called significant figures
1.
2.
All numbers except zero are always significant
Zero is not considered significant when it is used as a place holder,
that is when it wasn’t measured
a.
Zeros is at the end of a non-decimal number are place holders and are
not significant
i.
b.
Ex. 3,400mL
Has 2 significant figures
Zeros at the beginning of a decimal number are also place holders and
are not significant
i.
c.
Ex. 0.000651L
Has 3 significant figures
Zeros between numbers are part of the measurement and are
significant
i.
d.
Ex. 3.006m
Has 4 significant figures
Zeros at the end of a decimal were are not simply place holders and
are part of the measurement; therefore, they are significant
i.
Ex. 0.0200
Has 3 significant figures
Comprehension Check
A. How many significant figures are in each number
below?
1. 3.250 g
a.
4 Significant Figures
2. 11.01cm
a.
4 Significant Figures
3. 0.006g
a.
1 Significant Figure
4. 350mL
a.
2 Significant Figures
5. 0.25cm
a.
2 Significant Figures
6. 100.662g
a.
6 Significant Figures
I. Scientific Notation
A. Scientific Notation is a shorthand method for
writing really large or small numbers
1. For example, the number below is an important
number in chemistry called Avogadro’s Number
602,213,700,000,000,000,000,000 atoms in scientific
notation the number is 6.022137x1023 atoms
2. Writing a number is scientific notation does not
change the value of the number, only its appearance
a.
Move the decimal place to the right of the first significant
figure
i.
ii.
If moving the decimal place makes the number smaller, the power
must increase to compensate
If moving the decimal place makes the number larger, the power
must decrease to compensate
Comprehension Check
A. Write the following numbers in scientific
notation
1. 1,002,000,000,000,000 g
a.
1.002x1015 g
2. 683,010,000,000,000,000,000 L
a.
6.8301x1020 g
3. 0.0000000203g
a.
2.03x10-8 g
4. 0.0000200m
a.
2.00x10-5 g
5. 64,000,000,000,000,000,000,000,000m
a.
6.4x1025 g
Rounding in Science
A. The number of significant figures reported tells
everyone how accurate the measurements were
1. We never want to over or under report the accuracy of
measurements
2. This means that we have to be careful when rounding
answers to math problems
B. Rules for rounding answer to calculations
1. For multiplication and division
a.
Round the final answer to same number of significant figures as
the number with the least number of significant figures
2. For addition and subtraction – we’ll learn this later
Comprehension Check
A. Calculate the following and round the answers
to the appropriate number of Sig Figs
1. 10.333g / 3.1mL
a.
3.333225806 g/mL  3.3 g/mL
2. 37.25m2 / 11.58m
a.
3.216753022 m  3.217 m
3. 894.005g (0.0758 mL/g)
a.
67.765579 mL
 67.8 mL
4. 1,250,000m (0.00002300 s/m)
a.
28.75 s 
28.75 s

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