Question

How do you write the answer in scientific notation given `((3.3times10^9)(2.8times10^-7))/(4.62times10^5)`?

Answer 1

`2.0xx10^(-3)`

Explanation:

We do this in 3 parts:

The numbers

The powers of 10

The final adjustment so that there is only 1 digit to the left of the decimal point and that that digit is greater than 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 1")`

`(3.3xx2.8)/4.62 = 2.0`

Note that step 3 not needed as there is only 1 digit non zero to right of decimal point.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Step 2")`

Note that `10^(-7) -> 1/10^7`

`10^9xx1/10^7xx1/10^5 =10^9/10^12 = 10^(9-12)=10^(-3)`
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`color(blue)("Putting it all together")`

`2.0xx10^(-3)`

Answer 2

Igot: `2xx10^-3`

Explanation:

We can deal first with the powers of ten using the rule of exponents to get:
`10^9*10^-7/10^5=10^(9-7)/10^5=10^(2-5)=10^-3`
next we deal with the numbers:
`3.3xx2.8=9.24`
and
`9.24/4.62=2`

so that we get:
`2xx10^-3`