Transcript Measurement and Calculations

MEASUREMENT AND
CALCULATIONS
Chapter 9.2
Significant Digits
► The
international agreement about the correct
way to record measurements:
► Record all those digits that are certain plus one
uncertain digit, and no more.
► These “certain-plus-one” digits are called
significant digits.
► The certainty of a measurement is determined by
how many certain digits (plus one) are obtained
by the measuring instrument.
SIGNIFICANT DIGITS
► All
digits included in a stated value ( except
leading zeros) are significant digits.
► The position of the decimal point is not important
when counting significant digits.
► Examples:
► 30.95 – 4 sig figs
► 4.03 – 3 sig figs
► 0.04 – 1 sig fig ( leading zeros don’t count)
► 0.5060 – 4 sig figs
► 120. – 3 sig figs
PRACTICE
Significant Digits
► 1)
► 2)
► 3)
► 4)
► 5)
1.02 Km = _______ significant Digits
0.32 cm = _______ significant Digits
3600 kg = _______ significant Digits
20.060 L = ______ significant Digits
0.0030 g = ______ significant Digits
Multiplying or Dividing
SIGNIFICANT DIGITS
► When
multiplying or dividing significant
digits, you round to the value with the least
total number of sig. figs.
► Example:
► 4.62
x 0.035 = 0.1617 = 0.16
► 107.45 ÷ 6.40 = 16.7890 = 16.8
ADDING OR SUBTRACTING
SIGNIFICANT DIGITS
► When
adding or subtracting, you round to
the value with the least number of digits
after the decimal.
► EXAMPLE:
► 1.2
+ 3.08 + 7.60 = 11.88 = 11.9
► 10.013 – 1.07 = 8.943 = 8.94
PRACTICE
► 1)
(2.4)(6.16) = ______ = _____
► 2) 16.1 – 2.4 = ______ = _____
► 3) 4.1 ÷ 8.6 = ______ = _____
► 4) 6.105 + 0.12 = ____ = _____
ORDER OF OPERATIONS
Significant Digits
► You
will come across problems involving
both x / ÷ and + / - . This is done step by
step using the above rules.
► EXAMPLE:
► 4.3
÷ 1.2 – 6.1 = 3.58333 – 6.1
► 3.6 – 6.1
► 2.5
PRACTICE
1) (6.2)(4.3) – 12
6.1
2) 42 – (2.2)(1.3)
ROUNDING NUMBERS
► If
the digit after the digit to be rounded is 5
or larger, round up. If not round down.
► Example:
9.147 cm rounded to three Sig. Figs. Digits
is 9.15 cm.
► 7.23 g rounded to two Sig. Figs. Digits is 7.2
g.
►
TRY THESE
ROUNDING QUESTIONS
► 0.0327
rounded to one Sig. Fig. Digit
► 15.430 rounded to three Sig. Fig. Digits
► We
now can apply these two concepts to
basic mathematical calculations.
REARRANGING FORMULAS
► You
must isolate the variable you are trying to
solve for.
► To accomplish this you need to use the opposite
operation that is indicated.
► EXAMPLE:
► d = vt ( rearrange for v )
► Divide by t because vt is multiplication.
►d = v
►t
is an easy way to rearrange three
part equations using the pie method.
► There
v=d/t
► EXAMPLE:
t=d/v
D
V
► This
d = vt
T
does not work for equations such as:
► a = vf – vi OR
c = 2πr
►
T
PRACTICE
► 1)
c = m / v ( rearrange for m )
► 2) a = ½ bh ( rearrange for h)
► ANSWER:
► 1)
m = cv
► 2) h = 2a/b
CONVERTING UNITS
► You
must understand the metric system to
effectively convert.
Examples:
► Nano
1 m = 100 cm
► Micro
Multiply
1 m = 1000 mm
► Milli
► Centi
► Basic
► Kilo
► Mega
► Giga
Symbols: m, g, L
Examples:
Divide
1 g = 0.001 kg
1 g = 0.00001 mega
grams
► However,
you may have to use the conversion
factor method that does not involve the metric
system or has more than one unit.
► Example:
► 1)How many hours is 20.5 minutes?
► 20.5 min x 1 hour = 0.34166 = 0.342 h
►
60 min
► 2)
How many m/s is 5km/h?
► 5 km x 1 h
x 1000 m = 5000 m=1.388 1m/s
►
h 3600s 1 km
3600 s
STEPS FOR SOLVING WORD
PROBLEMS
► 1)
List all the known and the unknown from the
problem.
► 2) Select the best formula which uses the known
and unknown.
► ( be careful of extraneous info.)
► 3) Substitute the information into the equation.
► 4) calculate
► 5) round with appropriate significant digits.
► 6) Write a sentence answer.
QUESTIONS
► Text
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