Computations with Scientific Notation

Computations with Scientific Notation

Adding and/or Subtracting in SciNote

Stacking uneven blocks makes bad things happen.

Just like stacking building blocks that are the same size... When adding or subtracting in scientific notation, the exponents must be the same. Fortunately you can adjust a number to make the exponents the same.

 $\left(8\ \degree\ 10^5\right)\ +\ \left(7\ \degree\ 10^8\right)\ =?$  

The operation!  Addition.  
So the exponents must be the same.  
Since '5' is the smallest exponent we will change it, by adding 3 to it.  This will make it like the other exponent.  But...

Because we add 3 to the exponent we must move the decimal three times.  Remember the "see-saw effect" ?

SEESAW effect...

When one side gets 'bigger', the other must get 'smaller'.

Adjust then ADD

Remembering "Seesaw"...

when you add 3 to the exponent (bigger)

then you must move the decimal 3 times to the left (smaller).

Add the lead numbers (7 + .008),

keep the base and exponent (10⁸)

That's it! Subtraction is the same except you Subtract the lead numbers.

Steps to Computing in SciNote

• FIRST -Determine what is the operation.   $\ \ \times\ \div\ +\ -$  
  

• NEXT - if ADDITION OR SUBTRACTION  change the smaller exponent and move the decimal. 

• NEXT- perform the operation with the (new) lead numbers.

• NEXT- if MULTIPLICATION OR DIVISION, also perform the operation with the base and exponent (remember the exponent rules_

• NEXT- check the answer to make sure it is in "Proper" Scientific Notation

• Celebrate!!!

Multiple Choice

 $\left(2.0\times10^5\right)\ +\ \left(2.0\times10^4\right)\ =?$  

•  $4.0\ \times\ 10^2$   

•  $2.0\ \times10^1$  

•  $2.2\times10^4$  

•  $2.2\times10^5$  

Multiple Choice

(8 x 10⁴) - (2 x 10⁴)

• 16 x 10¹⁶

• 16 x 10⁸

• 6 x 10⁸

• 6 x 10⁴

Multiple Choice

 $\frac{8\times10^4}{4\times10^4}$   

•  $12\times10^4$  

•  $2\times20^4$  
  

•  $2\times10^0$  
  

•  $2\times10^8$  
  

Multiple Choice

(2 x 10⁹)(4 x 10⁴)

• 8 x 10¹³

• 8 x 10³⁵

• 8 x 10⁵

• 6 x 10¹³

Multiple Select

You need three things for a number to be in proper scientific notation. Must name all three, but do not answer more than three.

Which three are they???

• must be in base 10

• the number left of the decimal must be between 1 and 9 (including 1&9)

• must have a ninja one

• must have an exponent

• the number left of the decimal must be negative