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Chapter 3: Scientific Measurement

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by

Krystiana Ceselka

on 24 January 2014

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Transcript of Chapter 3: Scientific Measurement

Chapter 3: Scientific Measurement
Scientific Notation
In
Scientific Notation
, a given number is written as the product of two numbers:
A coefficient and 10 raised to a power
Ex: the number 702,000,000,000,000,000,000,000 can be wrtten as 7.02 x 10^23
The coefficient is 7.02
The power of 10 or exponent is 23

Scientific Notation
How do you write numbers in scientific notation?
The coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer.
A
positive exponent
indicates how many times the coefficient must be multiplied by 10
A
negative exponent
indicates how many times coefficient must be divided by 10.
Scientific Notation
Multiplication and Division
To multiply numbers written in scientific notation multiply the coefficients and add the exponents
To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator
Measurement
Measurement
is a quantity that has both a number and a unit
Measurements are fundamental to the experimental sciences
In Chemistry you often encounter
very large
numbers
Ex:
a single gram of hydrogen contains 602,000,000,000,000,000,000,000 hydrogen atoms
Or
very small

numbers
Ex:
the mass of an atom of gold is 0.000 000 000 000 000 000 000 327 gram
By:
Krystiana Ceselka and Jasmine Varma

Positive
Negative
Scientific Notation
When adding and subtracting numbers in scientific notation without a calculator
Exponents
must
be the same
Decimal points
must
be aligned before you add and subtract

Accuracy and Precision
Accuracy
is the measure of how close a measurement comes to the actual or true value of whatever is measured
Precision
is a measure of how close a series measurements are to one another, irrespective of the actual value
How do you evaluate accuracy and precision?
Accuracy
: the measured value must be compared to the correct value
Precision
: must compare the values of two or more repeated measurements
Percent Error
Accepted value
is the correct value for the measurement based on reliable references
Experimental Value
the value measured in a lab
Error
is the difference between the
experimental value
and the
accepted value
Percent Error
is the absolute value of the
error
divided by the
accepted

value
multiplied by 100%
Significant Figures
Significant figures
in a measurement include all of the digits that are known, plus a last digit that is estimated
Why must measurements be reported to the correct number of significant figures?
Because calculated answers often depend on the number of significant figures in the values used in the calculations
Significant Figure Rules
All digits 1-9 are significant
Embedded zeros embedded between significant digits
are always
significant
Trailing zeros in a number are significant
only
if the number contains a decimal point
The leading zeros at the beginning of a number are
never
significant
Zeros following a decimal significant figure
are always
significant
Exceptions to the rule are number with an
unlimited
number of sig figs
Significant Figures
Rounding
First determine the number of sig figs, then count from the left, and round
< 5: stays the same
> 5: increases by 1
Multiplying and Dividing
Limit and round the the
least number
of
significant figures
in any of the factors
least number
of
decimal places
Units of Measurement
The standards of measurement used in science are those of the metric system
All metric units are based on multiples of 10
They can be converted between units easily
The
International System of Units
(SI) is a revised version of the metric system
Temperature Scales
Scientists commonly use two equivalent units of temperature: the degree Celsius and the kelvin
The
Celsius scale
uses the freezing point of water (0°C) and the boiling point of water (100°C) as reference values
On the
Kelvin scale
the freezing point of water is 273.15 kelvins (K) and the boiling point is 373.15 K
Density
Density
is the ratio of the mass of an object to its volume
It is an intensive property that depends only on the composition of a substance, not on the size of the sample
Conversion Factor
A
conversion factor
is a ratio of equivalent measurements
The measurement in the numerator is equivalent to the denominator
Examples: the ratios
100 cm/1 m
and
1 m/ 100 cm
What happens when a measurement is multiplied by a conversion factor?
The numerical value changes
The actual size of the quantity measured remains the same
Dimensional Analysis
Dimensional analysis
is a way to analyze and solve problems using the units, or dimensions, of the measurements
Many problems in chemistry are conveniently solved using dimensional analysis
What kind of problems can you solve using dimensional analysis?
Conversion problems in which a measurement with one unit is changed to an equivalent measurement with another unit
1.
When multiplying with scientific notation
A) divide the coefficients, subtract exponents
C) subtract exponents, divide exponents
2.The standards of measurements in science are those of the metric system. All metric units are based on multiples of:
A) 5
B)100
C)10
D)1000
3. Conversion factor is:
A) a ratio of equivalent measures
B) the ratio of the mass of an object to its volume
C) a quantity that has a number and a unit
D) a given number written as a product of two numbers
4. What is the formula for converting Celsius to Kelvin?
A) K= C-273
B) K= C*273
C) K= C/273
D) K= C+273
5. If the temperature is 478K, what is the temperature in Celsius?
A) 204C
B) 207C
C) 205C
D) 206C
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