# Simplify #(8.33xx10^3)+(4.1xx10^5)# giving your solution in scientific notation?

##### 2 Answers

#### Explanation:

In Algebra:

These terms cannot be added because the indices are not the same so they are not like terms

In scientific notation you do exactly the same:

But sometimes adding creates a small problem:

But unlike algebra, in scientific notation, you can change the value of the index by moving the decimal point.

If it moves to the left, the index increases.

If it moves to the right, the index decreases

=

=

=

What you want to avoid is writing the numbers in numeral form (with lots of zero's) adding them and then changing them back to standard form. While that might work for small indices, it is simply not practical with bigger indices!

#### Explanation:

Given:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write equation(1) as:

However, 1 is the same as

Swap round the numbers (condition of being 'commutative' )

But

Factor out the