N9: calculate with and interpret standard form A × 10^n , where 1 ≤ A < 10 and n is an integer

What is standard form?

A system of writing numbers which is particularly useful when dealing with very large or small numbers

How to write in standard form

An example of standard form is 4.5×10²

A has to be between 1 and 10 (like 4.5)

N has to be an integer (like 2)

Is 45×10² standard form?

45×10² is not standard form, and would be converted to 4.5×10³

How do I tell if the indice should be positive or negative?

When making a number larger in its standard form, use a negative indice

When making a number smaller in its standard form, use a positive indice

Convert 0.008856 into standard form

0.008856 must be multiplied by 1000 to become 8.856

The multiplication of 1000 is translated to 10^-3 because it got bigger by a factor of 1000 as 10×10×10

In standard form: 8.856×10^-3 (the number of decimal places doesn’t matter)

Adding and subtracting with standard form

Convert the numbers into true form

Add/subtract as needed

Convert back into standard form

5×10² x 3×10^6

5×3=15

2+6=8

15×10^8=1.5×10^9

5.26×10^-2 - 4.772×10^-3

4.772×10^-3=0.004772

5.26×10^-2=0.0526

0.0526-0.004772=0.047828

0.047828=4.7828×10^-2