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Writing scientific notation

Scientific notation is sort of a “shorthand” method for writing very large or very small numbers.  Basically it makes it easier to write out numbers with many digits.  For example, scientific notation can take a number like

\(1,234,000,000,000,000,000,000,000,000,000\)

and rewrite it as

\(1.234 \times {10^{30}}\)

Now which would you rather write??

To write scientific notation, we follow a few simple steps.

  • Place a decimal point after the first nonzero number.
  • Write all numbers up to the last nonzero number (unless told to round)
  • Write the power of 10
  • If you moved the decimal place to the right, the power of 10 decreases by 1
  • If you moved the decimal place to the left, the power of 10 increases by 1

Let’s look at an example.

Example:  Write \(0.262 \times {10^5}\) in scientific notation.

Solution:  It appears that this number is already written in scientific notation, but if you look closely, you will see that the first principal of scientific notation is violated.  That is, the decimal must be placed after the first nonzero number:  Then

\(0.262\)

becomes

\(2.62\)

and we had to move the decimal one place to the right to make this happen.  So, according to the third principal from above, the power of 10 now decreases by 1.  Then

\(0.262 \times {10^5} = 2.62 \times {10^4}\)

We have successfully written a number in scientific notation.  Let’s try another example.

 

Example:  Write \(0.0054\) in scientific notation.

Solution:  Following the principals from above,

\(0.0054\)

becomes

\(5.4\)

we moved the decimal three places to the right to accomplish this.  So the power on 10 will decrease by 3.  Then

\(0.0054 = 5.4 \times {10^{ - 3}}\)

 

Below you can download some free math worksheets and practice.


Downloads:
1715 x

Write each number in standard notation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Exponents-Writing-scientific-notation-easy


Watch bellow how to solve this example:

 

Downloads:
1762 x

Write each number in scientific notation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Exponents-Writing-scientific-notation-medium

Watch bellow how to solve this example:

 

Downloads:
1802 x

Write each number in scientific notation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Exponents-Writing-scientific-notation-hard

Watch bellow how to solve this example:

 
 
 

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