Transcript Exponents and Scientific Notation
Slide 1
Scientific Notation
Students will be able to evaluate
variable expressions with negative
exponents and be able to write
numbers in scientific notation.
Slide 2
Scientific Notation
• Scientists often deal with very large or very
small numbers. To save time and space and be
able to write and compute with such numbers
more easily, a system of scientific notation was
developed.
• There are two factors to each number written in
scientific notation.
• The first factor is a number between 1 and 10.
The second factor is a power of 10.
• Example: 523,000,000 = 5.23 x 108
FHS
Pre-Algebra Review
2
Slide 3
Scientific Notation
• For a very small number, the power of 10 is usually
a negative number.
• Example: .00000345 = 3.45 x 10-6
• What is the method?
• Put a decimal point after the first non-zero
digit in the number.
• Then count the number of digits between the
original decimal point and the new decimal point.
(This is the power of 10.)
• If you move the decimal to left, the exponent is
positive; move decimal right, exponent is
negative.
FHS
Pre-Algebra Review
3
Slide 4
Scientific Notation Examples
Write the following numbers in scientific
notation:
1. 27,350,000,000
2. .000125
3. .000003786
4. 894,000,000
FHS
2.735 x 1010
1.25 x 10-4
3.786 x 10-6
8.94 x 108
Pre-Algebra Review
4
Slide 5
Scientific Notation with Calculator
• To change a number to scientific notation
using your calculator, you must change the
MODE to SCI. Hit MODE, then use arrow key
to go over to SCI and hit ENTER.
• Now you just type in the number [523,000],
hit ENTER and the answer will be written in
scientific notation like this 5.23E5 which
means 5.23 x 105. The E stands for
exponent.
FHS
Pre-Algebra Review
5
Slide 6
Expanded Form of Scientific Notation
If a number is written in scientific notation, we
need to be able to translate it into expanded
form.
Change these numbers into expanded form:
1. 3.47 x 107
34,700,000
2. 6.29 x 10-8
0.0000000629
3. 2.06 x 104
20,600
4. 5.8 x 10-3
0.0058
FHS
Pre-Algebra Review
6
Slide 7
Operations with scientific
notation numbers
• To multiply or divide two numbers written in
scientific notation, just type them into the
calculator and hit enter (just like any numbers you
multiply or divide).
• Make sure you type in the parentheses.
• Example: (2.35 x 10 5)*(6.83 x 10 8)
1.605 x 10 14
FHS
Pre-Algebra Review
7
Scientific Notation
Students will be able to evaluate
variable expressions with negative
exponents and be able to write
numbers in scientific notation.
Slide 2
Scientific Notation
• Scientists often deal with very large or very
small numbers. To save time and space and be
able to write and compute with such numbers
more easily, a system of scientific notation was
developed.
• There are two factors to each number written in
scientific notation.
• The first factor is a number between 1 and 10.
The second factor is a power of 10.
• Example: 523,000,000 = 5.23 x 108
FHS
Pre-Algebra Review
2
Slide 3
Scientific Notation
• For a very small number, the power of 10 is usually
a negative number.
• Example: .00000345 = 3.45 x 10-6
• What is the method?
• Put a decimal point after the first non-zero
digit in the number.
• Then count the number of digits between the
original decimal point and the new decimal point.
(This is the power of 10.)
• If you move the decimal to left, the exponent is
positive; move decimal right, exponent is
negative.
FHS
Pre-Algebra Review
3
Slide 4
Scientific Notation Examples
Write the following numbers in scientific
notation:
1. 27,350,000,000
2. .000125
3. .000003786
4. 894,000,000
FHS
2.735 x 1010
1.25 x 10-4
3.786 x 10-6
8.94 x 108
Pre-Algebra Review
4
Slide 5
Scientific Notation with Calculator
• To change a number to scientific notation
using your calculator, you must change the
MODE to SCI. Hit MODE, then use arrow key
to go over to SCI and hit ENTER.
• Now you just type in the number [523,000],
hit ENTER and the answer will be written in
scientific notation like this 5.23E5 which
means 5.23 x 105. The E stands for
exponent.
FHS
Pre-Algebra Review
5
Slide 6
Expanded Form of Scientific Notation
If a number is written in scientific notation, we
need to be able to translate it into expanded
form.
Change these numbers into expanded form:
1. 3.47 x 107
34,700,000
2. 6.29 x 10-8
0.0000000629
3. 2.06 x 104
20,600
4. 5.8 x 10-3
0.0058
FHS
Pre-Algebra Review
6
Slide 7
Operations with scientific
notation numbers
• To multiply or divide two numbers written in
scientific notation, just type them into the
calculator and hit enter (just like any numbers you
multiply or divide).
• Make sure you type in the parentheses.
• Example: (2.35 x 10 5)*(6.83 x 10 8)
1.605 x 10 14
FHS
Pre-Algebra Review
7