Question

How do you write `13,560,000` in scientific notation?

Answer 1

`" "color(blue)(1.356xx10^7)`

Explanation:

`color(blue)("How it works")`

Scientific notation format is that you have a single, non zero digit to the left of a decimal point and everything else to the right of it.

The problem in doing this is that you changed the value. So you have to apply a correction that if it were to be implemented would return the number back to its original format.
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Example: Consider the value of 23

To convert this into the required format you would divide it by 10

so that `23 -: 10 = 2.3`

the problem is that `2.3!=23`

However: `2.3xx10` does
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`color(brown)("So what has happened?")`

We have done two thing.

`color(brown)("Step 1")`

We multiplied 23 by 1 but 1 was in the form of `10/10`

`" "color(brown)( 23xx10/10" " = " "23/10xx10)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Step 2")`

We applied the division but leave the other ten in place:

`" "color(brown)( 2.3 xx 10)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving your question")`

Given:`" " 13560000.0`

Keeping the decimal place still we have to slide the digits to the right for 7 digits to get: 1.356

So we have
`" "13560000.0xx10^7/10^7`

`" "13560000.0/10^7xx10^7`

`" "color(blue)(1.356xx10^7)`