Transcript Unit 7 Measurements scientific notation and

Measurements in Chemistry
Scientific notation and Significant Figures
SCIENTIFIC NOTATION
 We commonly measure objects that are many times
larger or smaller than our standard of comparison
 Writing large numbers of zeros is tricky and confusing
the sun’s
diameter is
1,392,000,000 m
an atom’s
average diameter is
0.000 000 000 3 m
 Scientific notation expresses a number as the
product of two factors: M x 10n
 1 ≤ M 10 and n is an integer
 Numbers > one have a positive exponent
 Numbers < one have a negative exponent.
 Ex.
120000 = 1.2 X 105
0.000054 = 54 x 10-4 (incorrect)
0.000054 = 5.4 x10-5 (CORRECT)
Writing a Number In Scientific Notation
0.00012340
1 Locate the Decimal Point
0.00012340
2 Move the decimal point to the right of the first
non-zero digit from the left
1.2340
3 Multiply the new number by 10n
 where n is the number of places you moved the
decimal pt.
1.2340 x 104
4 if the number is 1, n is +; if the number is < 1, n is
1.2340 x 10-4
Writing a Number In Scientific Notation
154000
1 Locate the Decimal Point
154000.
2 Move the decimal point to the right of the first nonzero digit from the left
1 . 54000
Multiply the new number by 10n
 where n is the number of places you moved the
decimal pt.
1 . 54 X 105
if the number is 1, n is +; if the number is < 1, n is -
Writing a Number in Standard Form
1.234 x 10-6
 since exponent is -6, make the number smaller by
moving the decimal point to the left 6 places
 if you run out of digits, add zeros
000 001.234
0.000 001 234
Learning Check
Change to scientific notation.
12,340 =
0.369 =
0.008 =
2,050,000,000 =
Learning Check
Change to scientific notation.
12,340 = 1.234 x 104
–1
3.69
x
10
0.369 =
0.008 =
8 x 10–3
2,050,000,000 = 2.05 x 109
Using the Exponent Key
on a Calculator
EE
EXP
EE or EXP means “times 10 to the…”
23:
How
How to type out 6.02 x 1023
6
0
.
2
EE
2
3
Don’t do it like this…
6
WRONG!
0
.
yx
2
2
3
WRONG!
…or like this…
6
.
0
2
x
1
…or like this:
6
.
0
EE
2
3
TOO MUCH WORK.
0
2
x
1
0
yx
2
3
1.2 x 105
Example:

2.8 x 1013
Type this calculation in like this:
1
.
2
EE
5
2
.
8
EE
1
Calculator gives…
or…
This is NOT written…
But instead is written…

3
4.2857143 –09
4.2857143 E–09
4.3–9
4.3 x 10–9
=
Learning Check (we will learn how to round later)
-6
 - 8.7 x 10
6
 1.23 x 10
-16
 9.86 x 10
-4
11
 3.3 x 10
11
7.5 x 10
4.35 x 10
5.76 x 10
8.8 x 10
6.022 x 10
23
-4
-3
 - 5.1 x 10
-8
Learning Check (we will learn how to round later)
 - 8.7 x 10
6
 1.23 x 10
-16
 9.86 x 10
-4
= 5.84178499 x 10-13
11
 3.3 x 10
11
= 2.904 x 1023
4.35 x 10
5.76 x 10
8.8 x 10
= -6.525 x 10-9
-6
7.5 x 10
6.022 x 10
23
-4
-3
 - 5.1 x 10
-8
= 5.3505 x 103 or 5350.5
= -3.07122 x 1016
 Classwork: p 948 #1-3
What is a Measurement?
 quantitative observation
 They have a number and a
unit (indicates what your
are measuring Ex. m, s, C)
Accuracy and Precision
Figure 2.29a
-Accuracy refers to how close the measured result is to
the true value
-Precision refers to closeness to another series of
measurement made on the same object- repeatability
SIGNIFICANT FIGURES (DIGITS)
 Our measurements should reflect the
precision of the instrument we used.
2.5 cm
2.51 cm
INCORRECT: 2.50154 cm Why? I can’t read all
this numbers with my instrument.
 The significant figures (sig figs) of a
measurement are those digits known with
certainty (read directly from the instrument)
plus the last digit which is estimated.
2.34 cm
 Counting Significant Figures in Measurements
1. All nonzero digits are significant
Ex. 725 cm
5.8 C
has 3 sig. fig.
has 2 sig. fig.
2. Zeros between nonzero digits are significant.
Ex. 5.04s
7008 L
has 3 sig. fig.
has 4 sig. fig.
3. Zeros at the end of a number AND to the
right of the decimal point are significant.
Ex. 74.50 g
has 4 sig figs
208.250 km
has 6 sig figs
74, 000 hours
has 2 sig figs
200 m
has 1 sig fig
4. Zeros at the beginning of numbers are not
significant.
Ex. 0.0052mm has 2 sig fig
0.00000007800 g has 4 sig. fig.
5. Counted values (18 students) and numbers in
defined relationships (1m=100cm) have
unlimited number of significant figures and
never affect the number of significant figures
in the results of a calculation.
Zeros at the end of a number without a
written decimal point are ambiguous and
should be avoided by using scientific
notation
Ex. if 150m has 2 sig. figs. then 1.5 x 102 m
A decimal point is written intentionally to
indicate the zero is significant.
Ex. 150.m has 3 sig. figs.
Learning Check: Determining the Number
of Significant Figures in a Number
 How many sig figs are in each of the measurements?
0.0035 m
1.080 km
2371 C
2.97 × 105 kg
1 dozen = 12
100,000 days
100,000. days
Learning Check: Determining the Number
of Significant Figures in a Number
 How many sig figs are in each of the measurements?
0.0035 m
1.080 km
2371 C
2.97 × 105 kg
1 dozen = 12
100,000 days
100,000. days
2 sig figs
4 sig figs
4 sig figs
3 sig. figs. – only decimal parts count
unlimited
1 sig figs.
6 sig figs.
Rounding using Significant
Figures
Multiplication and Division with
Significant Figures
 when multiplying or dividing measurements with
significant figures, the result has the same number of
significant figures as the measurement with the fewest
number of significant figures
5.02m × 89.665m × 0.10m= 45.0118m3 = 45m3
3 sig. figs. 5 sig. figs. 2 sig. figs.
2 sig. figs.
5.892 m ÷
6.10s
= 0.96590 m/s = 0.966 m/s
4 sig. figs. 3 sig. figs.
3 sig. figs.
Rounding

when rounding to the correct number of
significant figures, if the number after the
place of the last significant figure is
1. 0 to 4, round down
2. 5 to 9, round up
Rounding
 Ex: round to 2 significant figures
 0.0234 rounds to 0.023 or 2.3 × 10-2
 because the 3 is where the last sig. fig.
will be and the number after it is 4 or less
 0.0237 rounds to 0.024 or 2.4 × 10-2
 because the 3 is where the last sig. fig.
will be and the number after it is 5 or
greater
 0.0299865 rounds to 0.030 or 3.0 × 10-2
 because the 9 is where the last sig. fig.
will be and the number after it is greater
than 5
Learning Check: Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1. 1.01 × 0.12 × 53.51 ÷ 96 =
2. 56.55 × 0.920 ÷ 34.2585 =
Learning Check: Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1. 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556
2. 56.55 × 0.920 ÷ 34.2585 = 1.51863
Determine the Correct Number of Sig. Figs. for
each Calculation and Round the Result
1. 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556 = 0.068
3 sf
2 sf
4 sf
2 sf
result should
have 2 sf
7 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up
2. 56.55 × 0.920 ÷ 34.2585 = 1.51863 = 1.52
4 sf
3 sf
6 sf
result should
have 3 sf
1 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up
Addition and Subtraction with
Significant Figures
 when adding or subtracting measurements with
significant figures, the result has the same number
of decimal places as the measurement with the
fewest number of decimal places
5.74 + 0.823 +
2.651 = 9.214 = 9.21
2 dec. pl.
3 dec. pl. 3 dec. pl.
2 dec. pl.
4.8 1 dec. pl
3.965
=
3 dec. pl.
0.835 =
0.8
1 dec. pl.
Determine the Correct Number of Sig. Figs. for
each Calculation and Round Result
1. 0.987 + 125.1 – 1.22 = 124.867
2. 0.764 – 3.449 – 5.98 = -8.664
Determine the Correct Number of
Sig. Figs. And Round the Result
1. 0.987 + 125.1 – 1.22 = 124.867 = 124.9
3 dp
1 dp
2 dp
result should
have 1 dp
2. 0.764 – 3.449 – 5.98 = -8.664
3 dp
3 dp
2 dp
8 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up
result should
have 2 dp
=
-8.66
6 is in place
of last sig. fig.,
number after
is 4 or less,
so round down
Both Multiplication/Division and
Addition/Subtraction with Sig. Figs.
 when doing different kinds of operations with
measurements with significant figures, do whatever
is in parentheses first, find the number of significant
figures in the intermediate answer, then do the
remaining steps
3.489 × (5.67 – 2.3) =
2 dp
1 dp
3.489 ×
3.37
=
3.489 ×
3.4
= 12
4 sf
2 sf
2 sf
 Classwork: p951 #4 p953 #5-6