Transcript Scientific Notation

Scientific Notation
Mrs Vass
BJH
Scientific Notation
 Definition: Scientific notation is a symbol that
expresses any number as a power of ten multiplied by
a number between 1 and 10 (including 1).
 Scientific notation allows you to work with very large
numbers and very small numbers.
 A number like 5 000 000 000 would be
5.0 x 10 9
 5 > 1 and < 10 and there are 9 places past where the
new decimal place would be.
 Write the scientific notation for 67 000 000 000
 which is
6.7 x 1010
Scientific Notation
 Which of the following
numbers are in scientific
notation? If it is not,
explain why.
 a. 3 x 106
 Answers
 b. 4.6 x 10-4
 B) is correct for the same reasons as A
 c.
 A) is correct scientific notation as the
decimal number is less than 10 and equal
to or greater than 1. It is also written in a
power of 10
 C) is not
0.2 x 108
 d. 2.8 x 100
correct as the decimal number
is less than 1
 D) is not correct
as the decimal is
correct but it is not written in a power of 10
. If it was changed to 102 it would be
correct
Scientific Notation
 How do we represent very small numbers in
scientific notation?
 Recall that 0.005 = 5 x 1
or 5 x 1

1000
103

Therefore, armed with the above knowledge, our
previous knowledge of negative exponents, and the
definition for scientific notation, 0.005 is represented in
scientific notation
as
5. 0 x 10 -3
.
Scientific Notation
 The calculator only holds 7 digits.
 So if you have a number like 760 000 000 it
would show it as 7.62 x 10 8 .
 If you have a positive exponent for 10, then the
decimal place will move to the right and make
the number bigger such as
3.45 x 105 = 345 000
 If you have a negative exponent , the decimal
point will move to the left and make the number
smaller such as 3.45 x 10 –5 = . 0000345
Scientific Notation Trivia







106 million
109 billion
1012 trillion
1015 quadrillion
1018 quintillion
1021 sextillion
10100 googol
Scientific Notation Trivia
 The word googol was created in 1938
by the 11 year old nephew of the
American mathematician Edward
Kasner.
Operations with Scientific
Notation
 Numbers can be written in standard form ( as a
number) and scientific notation.
 You can do operations such as add, subtract ,
multiply and divide with scientific notation.
 Scientific notation allows you to solve more easily
with very large or very small numbers.
 Remember that scientific notation is written in
POWERS OF 10
Adding numbers with
scientific notation:
 1.4 x 10-3 + 2.3 x 10-3
 If the power of 10 is the same then you
can take out the power of 10 and then
ADD the other two factors.
 For example:
 (1.4 + 2.3 ) x 10-3
 3.7 x 10-3 written in standard form it
would be 0.0037
Addition with Scientific
Notation
 If the numbers are not in the same power of
10, then you might be able to rewrite the
numbers so that they are in the same power of
10.
 5.3 x 104 + 6.2 x 10 5 could be rewritten as
 0.53 x 10 5 + 6.2 x 10 5
 ( Now you can solve it as shown in previous slide)
 (0.53 + 6.2) x 10 5
 6.73 x 10 5 written in standard form is 674000
Subtraction with
Scientific Notation
 Subtraction is done the same way as
addition. Take out the power of 10 and
then subtract the other factors.
 7.3 x 103 - 6.2 x 10 3
 ( 7.3 – 6.2) x 10 3
 1.1 x 10 3
 written in standard form it is 1100
Multiplying in Scientific
Notation
 When you multiply or divide with scientific notation ,
you will use your exponent laws. Remember , when we
multiply powers with the same base , we add the
exponents:
 (2.2 x 104 ) x ( 1.2 x 10 7)
 Remember that the Commutative Property
allows us to rearrange the FACTORS without
affecting the answer.
 SO : 2.2 x 1.2 x 104 x 10 7

2.64 x 10 (4 + 7)

2.64 x 10 11
or
264 000 000 000
Dividing with Scientific
Notation
 12.4 x 10 10 ÷ 3.2 x 10 6

12.4
3. 2
and
1010
10 6
 3.875 x 10 (10 – 6)
 = 3.875 x 104
OR
38750
 You need to divide the first factors and then
apply the exponent laws to the powers of 10.