# Scientific Notation Worksheet With Answer Key

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 × 10
14
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