Scientific Notation
Scientific notation is used to express very large numbers.
Scientific Notation
A positive number is written in scientific notation if it is written in the form:
a × 10 r
where a is a number between 1 and 10 and r is a power of 10.
In other words, a number in scientific notation is written as the product of a number and a power
of 10. The number has one digit to the left of the decimal point. The power of ten indicates how
many places the decimal point was moved.
The decimal number 650,000 written in scientific notation would be 6.5 × 10 5 because the
decimal point was moved 5 places to the left to form the number 6.5. It is equivalent to
6.5(10)(10)(10)(10)(10).
Example: Write the decimal number 235,000 in scientific notation.
Solution: Place a decimal point in 235 (the non-zero part of 235,000) so that it is a number
between 1 and 10.
2.35
Count the number of decimal places required to move the decimal point back to its
original position.
2.35000

5 places
Write in scientific notation with 5 as the power of 10.
2.35 × 10 5
Practice: Write the numbers in scientific notation.
a) 256,000,000,000,000
b) 600,000
Solution: a) 256,000,000,000,000 = 2.56 × 1014
b) 600,000 = 6 × 10 5
To convert a number from scientific notation to decimal form we reverse the previous steps.
Example: Write 4.27 × 10 7 in decimal form.
Solution: 4 2700000


 = 42,700,000
7 places
Practice: Write the numbers in decimal form.
a) 2.3 × 10 5
b) 4.5 × 10 9
Solution: a) 230,000
b) 4,500,000,000
Entering numbers in a calculator using scientific notation.
Scientific calculators have the capacity to accept and perform calculations using scientific
notation. To enter a number in scientific notation, use the "EE" or "EXP" key. When using
scientific notation on a calculator, do not type in "x10", or “^”, the "EE" or "EXP" key replaces
that part of the number.
Example: Enter 2.35 × 10 5 on a scientific calculator.
Solution: enter 2.35 "EE" 5 or 2.35 "EXP" 5. The calculator displays the number in one of many
possible formats. For example: 2.35E5, 2.35EE5, or 2.35 E 5 , etc., just to name a few. Practice
entering some numbers in scientific notation to familiarize yourself with your calculator’s
notation.
Perform the calculations using a scientific notation.
(
)(
Example: Multiply 2.35 × 10 5 5.8 × 10 6
)
Solution: enter 2.35 "EE" 5 or 2.35 "EXP" 5
press the multiply “X” key
enter 5.8 ”EE” 6 or 5.8 ”EXP” 6
press “=” or “ENTER”
1.363 × 1012
Practice: Use a calculator to perform the calculations. Round decimals to three places.
3.6 × 10 29
a) 4.62 × 1015 2.4 × 10 5
b) 4.62 × 1015 ÷ 2.4 × 10 5
c)
2.3 × 10 3 7.1 × 10 7
(
)(
)
Solution:
a) 1.1088 × 10 21
(
) (
b) 1.925 × 1010
)
(
)(
)
c) 2.205 × 1018
Homework:
1. Write each number in scientific notation: a) 245,000,000,000 b) 15,000
2. Write each number in decimal notation: a) 6.98 × 10 4 b) 3.0 × 10 9
c) 7,895,000
c) 4.7 × 1014
Perform each of the calculations using a scientific calculator. Leave your answer in scientific
notation. Round decimals to three places.
3.5 × 10 3 4.8 × 10 2
3. 4.53 × 10 5 3.98 × 10 4
4.
5. 8.5 × 1013 ÷ 2.25 × 10 2
(
)(
)
( 7.91 × 10 )( 6.52 × 10 )
6.
11
5
8.1 × 10 8
Answers:
1. a) 2.45 × 1011
(
)(
1.95 × 1017
7.
4.25 × 10 3 2.3 × 10 4
b) 1.5 × 10 4
2. a) 69,800
b) 3,000,000,000
4. 1.68 × 10 6
5. 3.778 × 1011
(
)(
)
(
) (
( 4.2 × 10 )( 3.44 × 10 )
8.
( 2.1 × 10 )( 5.2 × 10 )
9
)
3
8
4
c) 7.895 × 10 6
c) 470,000,000,000,000
6. 6.367 × 10 8
3. 1.803 × 1010
7. 1.995 × 10 9
8. 1.323 × 1010
)