Download I. Using Measurements - Ms. Robbins` PNHS Science Classes

MEASUREMENT
I.
Using Measurements
A.Accuracy and Precision
B.Percent Error
I
II
III
C.Significant Figures
D.Scientific Notation
E.Proportions
C. Johannesson
A. Accuracy vs. Precision
 Accuracy - how close a measurement
is to the accepted value
 Precision - how close a series of
measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
C. Johannesson
B. Percent Error
 Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
C. Johannesson
 100
B. Percent Error
 A student determines the density of a
substance to be 1.40 g/mL. Find the % error if
the accepted value of the density is 1.36 g/mL.
% error 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.9 %
C. Johannesson
 100
Are Significant Figures Important? A Fable






A student once needed a cube of metal which had to have a mass of 83 grams. He knew the
density of this metal was 8.67 g/mL, which told him the cube's volume. Believing significant
figures were invented just to make life difficult for chemistry students and had no practical
use in the real world, he calculated the volume of the cube as 9.573 mL. He thus determined
that the edge of the cube had to be 2.097 cm. He took his plans to the machine shop where
his friend had the same type of work done the previous year. The shop foreman said, "Yes,
we can make this according to your specifications - but it will be expensive."
"That's OK," replied the student. "It's important." He knew his friend has paid $35, and he had
been given $50 out of the school's research budget to get the job done.
He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still
working on it. Try next week." Finally the day came, and our friend got his cube. It looked
very, very smooth and shiny and beautiful in its velvet case. Seeing it, our hero had a
premonition of disaster and became a bit nervous. But he summoned up enough courage to
ask for the bill. "$500, and cheap at the price. We had a terrific job getting it right -- had to
make three before we got one right."
"But--but--my friend paid only $35 for the same thing!"
"No. He wanted a cube 2.1 cm on an edge, and your specifications called for 2.097. We had
yours roughed out to 2.1 that very afternoon, but it was the precision grinding and lapping to
get it down to 2.097 which took so long and cost the big money. The first one we made was
2.089 on one edge when we got finshed, so we had to scrap it. The second was closer, but
still not what you specified. That's why the three tries."
"Oh!"
C. Significant Figures
 Indicate precision of a measurement.
 Recording Sig Figs
 Sig figs in a measurement include the
known digits plus a final estimated
digit
2.35 cm
C. Johannesson
C. Significant Figures
 Counting Sig Figs (See page 47)
 Count all numbers EXCEPT:
 Leading
zeros -- 0.0025
 Trailing
zeros without
a decimal point -- 2,500
C. Johannesson
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
C. Johannesson
C. Significant Figures
Numbers in Scientific Notation
5,280 m = 5.28 x 103 m  3 sig figs
2. 0.080 km = 8.0 x 10-2 km  2 sig figs
3. 194,000 mL = 1.94 x 105mL  3 sig figs
1.
Now turn to ws 2-2 C and
work on practice problems
C. Significant Figures
 Calculating with Sig Figs
 Multiply/Divide - The # with the fewest
sig figs determines the # of sig figs in
the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
C. Johannesson
C. Significant Figures
 Calculating with Sig Figs (con’t)
 Add/Subtract - The # with the lowest
decimal value determines the place of
the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
C. Johannesson
224 g
+ 130 g
354 g  350 g
C. Significant Figures
 Calculating with Sig Figs (con’t)
 Exact Numbers do not limit the # of
sig figs in the answer.
 Counting
 Exact
 “1”
numbers: 12 students
conversions: 1 m = 100 cm
in any conversion: 1 in = 2.54 cm
C. Johannesson
C. Significant Figures
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
6. 18.9 g
- 0.84 g
18.06 g  18.1 g
C. Johannesson
D. Scientific Notation
65,000 kg  6.5 × 104 kg
 Converting into Sci. Notation:
 Move decimal until there’s 1 digit to
its left. Places moved = exponent.
 Large # (>1)  positive exponent
Small # (<1)  negative exponent
C. Johannesson
 Only include sig
figs.
D. Scientific Notation
Practice Problems
7. 2,400,000 g
2.4 
8. 0.00256 kg
2.56 
9. 7  10-5 km
0.00007 km
10. 6.2  104 mm
62,000 mm
C. Johannesson
6
10
g
-3
10
kg
D. Scientific Notation
 Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
C. Johannesson
E. Proportions
 Direct Proportion
y
y x
x
 Inverse Proportion
1
y
x
y
C. Johannesson
x