Scientific Notation
Scientific Notation Intro
Scientific Notation
 Consists of two parts
 1. mantissa
 The full size number that comes before x 10
 2. characteristic
 The exponent that comes after x 10 and is
superscript
Scientific Notation
 Example:
15
3.00 x 10
Mantissa
Characteristic
Scientific Notation
 To convert a normal number to scientific
notation, move the decimal either to the
left or right until you have a mantissa which
is greater than -10 or less than +10
Scientific Notation
 If the absolute value of the number is
smaller than 1, the characteristic will be
negative
 If the absolute value of the number is larger
than 1, the characteristic will be positive
Scientific Notation
 Example:
542
The absolute value of the number is greater than
one so the characteristic is positive
542
Moved to the left two spaces
5.42 x 102
Scientific Notation
 Example:
-45000000
The absolute value of the number is greater than
one so the characteristic is positive
-45000000
Moved to the left seven spaces
-4.5 x 107
 Example:
0.0040
The absolute value of the number is less than one so
the characteristic is negative
0.0040
Moved to the right three spaces
4.0
-3
x 10
 Example:
-0.209
The absolute value of the number is less than one so
the characteristic is negative
-0.209
Moved to the right one space
-2.09 x
-1
10
 Example:
9.245
The absolute value of the number is between -10 and
+10.
9.245
The decimal is not moved. In this case, the
characteristic is zero.
9.245 x100
Expanding Scientific Notation to
Regular notation
 If the characteristic is positive,
move the decimal to the right.
 If the characteristic is negative,
move the decimal to the left.
Expanding Scientific Notation to
Regular notation
Example
6.50 x 102
The characteristic tells us to move two
places to the right.
650.
Expanding Scientific Notation to
Regular notation
Example
6.50 x 10-2
The characteristic tells us to move two
places to the left.
0.0650
Fixing Incorrect Scientific Notation
 Fix the mantissa by moving the decimal
 Add the “fixed” characteristic to the
original characteristic
Example
20.4 x 106 (incorrect)
Moved over one space to the left (+) to
correct the mantissa
2.04 x
(6+1)
10
2.04 x 107 (correct)
Example
200.4 x 10-6 (incorrect)
Moved over two spaces to the left (+) to
correct the mantissa
2.004
(-6+2)
x 10
2.004 x 10-4 (correct)
Example
0.00340 x 108 (incorrect)
Moved over three spaces to the right (-) to
correct the mantissa
3.40
(8
+
-3)
x 10
3.40 x 105 (correct)
Example
0.00340 x 10-8 (incorrect)
Moved over three spaces to the right (-) to
correct the mantissa
3.40
(-8
+
-3)
x 10
3.40 x 10-11 (correct)
Adding and Subtracting Scientific
Notation
 The mantissa MUST have the
same characteristic.
 Then add or subtract the mantissa.
 Finally correct the scientific
notation if needed
Multiplying Numbers in Scientific
Notation
 Multiply the mantissas
 ADD the characteristics together
 Correct the number if the
mantissas are +10 or greater/-10 or
less.
Dividing Numbers in Scientific
Notation
 Divide the mantissas
 Subtract the characteristic of the
denominator from the
characteristic of the numerator
 Correct the number if the
mantissas are +10 or greater/-10 or
less.