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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.

Tutorial

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 10^{8}

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.**

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

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 10^{6}) + (2.6 x 10^{5})

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 10^{5}) + (2.6 x 10^{5})

Our answer will be 36.6 x 10^{5} 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 10^{6}.

Our final answer is **3.66 x 10 ^{6}**

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