Download SIGNIFICANT DIGITS and SCIENTIFIC NOTATION

SIGNIFICANT DIGITS and SCIENTIFIC NOTATION
The physical sciences such as physics and chemistry, require you to have a good working
knowledge of the METRIC system and be able to mathmatically manipulate accurate
measurements. The topics of Scientific Notation and Significant Digits (figures) are two key
concepts that must be learned to work with measurements.
Merrill Chemistry - Read pages 34-42, Questions 10-18, 33-34
SIGNIFICANT DIGITS in a number are the number of digits that give reasonable, reliable
information. To detemine the number of significant digits in a measurement we use the
following rules:
1. The digits 1 through 9 are always significant.
2. If zeros appear BETWEEN significant digits, they are considered significant.
eg. 1004 contains 4 S.D.
3. If zeros appear to the right of the decimal in a number ENDING IN ZEROS, they are
significant. (an actual value of zero has been measured)
eg. 154.00 contains 5 S.D.
4. If a zero appears in a number only to fix the position of the decimal place in a number less
than one, it is NOT significant.
eg. 0.154 contains 3 S.D.
5. Terminal zeros (those at the end of a number with NO decimal point shown) in a number are
usually NOT significant.
eg. 1540 contains 3 S.D.
NOTE: to avoid confusion with zeros, rewrite all numbers in SCIENTIFIC NOTATION to
determine the number of significant digits. Numbers that have been COUNTED as
opposed to being measured are assumed to have an INFINITE # of significant digits.
(eg. 20 cars)
EXPONENTS & SCIENTIFIC NOTATION
A large or small number may be converted to scientific notation (also known as standard
notation) using a decimal number between 1 and 10 and a power with base ten. Large numbers
have positive exponents while numbers less than one have negative exponents.
eg. 75000 = 7.5 x 104
0.75 = 7.5 x 10-1
When adding or subtracting with scientific notation, each number must be the SAME POWER
OF TEN. When multiplying or dividing the BASES must be the same.
eg. 1.70 x 103 + 3.10 x 103 = 4.80 x 103
1.60 x 102 x 2.40 x 104 = 3.84 x 106
Mathematical Operation Involving Significant Digits
In chemistry you will need a good scientific calculator that can do the following: add, subtract,
multiply, divide, exponents, square roots, scientific notation, and log10x. Make sure that you
carefully read the operating instructions for your calculator.
1. When adding or subtracting, the answer must be given the same number of places after the
decimal point as the measurement that has the LEAST number of places after the decimal
point.
eg. 25.1 + 22.11 = 47.21 Answer is 47.2
2. When multiplying or dividing, the answer must have the same number of significant digits as
the measurement with the FEWEST significant digits.
eg. 17.21 x 11.1 = 191.031
Answer is 191
3. When ROUNDING to the appropriate number of significant digits the following rules
should be used:
a) if less than five, round down
b) if more than five, round up
c) if exactly five, round to make an EVEN number
eg. Round to 3 S.D.
47.21 = 47.2
47.26 = 47.3
47.250 = 47.2
PRACTICE PROBLEMS
1. Determine the number of significant digits in the following:
a) 747 ______
d) 0.056 _____
g) 7065 _____
b) 1011 ______
e) 350 ______
h) 0.604 _____
c) 3.50 ______
f) 6.02 ______
i) 10.04 ______
j) 7.0200 ______
2. Round the following to THREE significant digits:
a) 462.2 = _____
c) 474.50 = _____
e) 687.50 = _____
h) 0.027650 = _____
b) 453.6 = _____
d) 687.54 = _____
f) 688.50 = _____
I) 0.027654 = _____
g) 12.750 = ______ j) 0.027750 = _____
3. Express the following in scientific notation to THREE significant digits:
a) 6 780 000 _______________________
b) 2 170 _________________________
c) 0.075 6
d) 10.7
_______________________
_________________________
4. Perfom the following operations an express your answer to the appropriate number of
significant digits:
a) 17.8 + 14.73 + 16
b) 0.647 + 0.03 + 0.31
c) 0.02 x 47
d) 14.72 - 6.8
e) 181.8 ÷75
f) 24.78 - 0.065
g) 13.65 ÷2.26
h) 13 x 752
i) 9.74 x 0.12 ÷ 1.28
5. Carry out the operations indicated:
a) 4.73 x 102 + 6.6 x 101
b) (7.72 x 106 ) ÷ (2.82 x 102)
c) 6.54 x 105 - 2 x 103
d) (6.73 x 10-5) ÷ (2.32 x 10-2)