Online College Courses for Credit

Scientific Notation - 8.1 - Lesson 9

Scientific Notation - 8.1 - Lesson 9

Author: Todd Parks

Student Outcomes

Students write, add and subtract numbers in scientific notation and understand what is meant by the term leading digit.

  • Knowing how to write numbers in scientific notation allows us to determine the order of magnitude of a finite decimal. 
  • We now know how to compute with numbers expressed in scientific notation.
See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

29 Sophia partners guarantee credit transfer.

312 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


Scientific Notation

The key to scientific notation is realizing why it was created:  So that we didn't have to write a LOT of zeros when trying to display a REALLY BIG number like 7,000,000,000,000 or a really small number like 0.0000000000352.

*Our key rule is to make sure we have only one number before the decimal point that is between 1 and 9.

Therefore:  567,000,000 = 5.67x 108

Remember:  Every time you multiply by 10, you change the number by ONE place value.


In order for a number to be in scientific notated form, the number portion must be a number or decimal number 1 or more and less than 10.


Scientific Notation - 8.1 - Lesson 9

A brief overview of the first page of the common core's lesson 9.

Adding Scientific Notated Numbers

We have a rule that we need to follow when we want to add numbers that are in scientific notated form.

RULE: Be sure that exponents are the same.

We need exponents to be the same to add our base numbers together, and sometimes we need to increase or decrease place values of scientific notated numbers so that they are the same as the number we are adding.

Here is an example:  (3.4 x 106)  +  (2.6 x 105)

We can not add these until the exponents are the same.

Sooooo...Let's change the larger exponent of 6 to a 5.  This means that the number 3.4 increases it's size by one place value and becomes 34.

Now we have:  (34 x 105)  +  (2.6 x 105

Our answer will be 36.6 x 105 but WAIT...this isn't in scientific notated form!!

So we decrease the number 36.6 by one place value to become 3.66 and the exponent grows by one place value to become  x 106.

Our final answer is 3.66 x 106

Scientific Notation - 8.1 - Lesson 9

A brief overview of the first page of the common core's Lesson 9