Question

How do you write 345,000,000,000 in scientific notation?

Answer 1

`3.45 xx 10^11`

Explanation:

1. Imagine you have 345,000,000,000.
2. Keep moving the dot till you have 3.45
3. Then count how many spaces you've moved

To get to 3.45, it took you 11 moves so you would have

`3.45 xx 10^11` as your answer

Answer 2

`color(brown)(3.45 xx 10^(11))`

`color(blue)("A different way of looking at it!")`

Explanation:

`color(purple)("Some thoughts and a demonstration")`

There are different ways this can be explained. I tend to use this one!

`color(blue)("Objective: ")`
To end up with the most significant number to the left of the decimal point and all the rest to the right of it. This is don by doing the equivalent of keeping the decimal point where it is and then 'sliding' the numbers left or right to achieve this state.

`color(blue)("Corrective measure")`
In doing the above we have effectively changed its value. This has to be corrected by making a mathematical adjustment.

`color(blue)("Demonstration")`

`color(brown)("Example 1")`
Suppose we were given the value of 10.5
Keep the decimal place still and slide the number to the right one space.

So we have `10.5 " become " 1.05`

To change this back to the original value multiply by 10 giving:

`10.5 -> 1.05`
`10.5 = 1.05 xx 10`

`color(brown)("Example 2")`

Given: 0.00564

`0.00546 -> 5.46`

Which is not the same value until we divide it by 1000

`0.00546 = 5.46 xx 1/1000`

`0.00546 = 5.46 xx 1/10^3`

`0.00546 = 5.46 xx 10^(-3)`

`color(green)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")`
`color(green)("Solution to your question")`

`color(brown)("Given: 345,000,000,000")`

Slide this to the right 11 times giving:

`345,000,000,000 -> 3.45`

Applying the correction:

`345,000,000,000 = 3.45 xx 10^11`

`color(blue)("Write as "3.45 xx 10^(11))`