Question

How to solve `2.9 xx 10^(11) - 3.7 xx 10^(13)` ?

Answer 1

`-3.671 xx 10^13`

Explanation:

Given: `2.9 xx 10^11 - 3.7 xx 10^13`

In order to subtract, you want the exponents to be the same. This allows the decimals to line up for subtracting.

`2.9 xx 10^11 = 0.029 xx 10^13`

Now subtract the two numbers before the exponents:

`.029 - 3.7 = -3.671`

Since both numbers have the same exponents, the solution will have the same exponent:

`.029 xx 10^13 - 3.7 xx 10^13 = -3.671 xx 10^13`

Answer 2

`-3.671xx10^13`

Explanation:

Factor out `10^(11)` giving:

`10^(11)(2.9-3.7xx10^2)`

`10^(11)(2.9-370)`

If the subtraction of a greater value is giving you a problem do this:

make the -370 look as though it is +370 when really it isn't

Note that by example:

`2-4color(white)("dd")=color(white)("dd")1xx(2-4)color(white)("dd") =color(white)("dd")-1xx(-2+4)`

Applying the above approach we have:

`10^(11)(2.9-370)color(white)("d")=color(white)("d") -10^(11)(-2.9+370)`

Consider just the `-2.9+370` bit first:

`370.0`
`ul(color(white)(37)2.9 larr" Subtract")`

`3cancel(7)^6 cancel(0)^(10).0`
`ul(color(white)(37dd)2color(white)("dd").9 larr" Subtract")`

Still will not work so write:

`3cancel(7)^6 cancel(0)^(9).cancel(0)^10`
`ul(color(white)(37dd)2color(white)("d").color(white)(".")9 larr" Subtract")`
`3color(white)(".")6color(white)("d")7color(white)("d").color(white)("d")1`

So the answer to this part is `367.1`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all back together

`-10^(11)(-2.9+370) color(white)("d")=color(white)("d")-10^(11)(367.1) =-367.1xx10^(11)`

`color(white)("dddddddddddddddddddddddddddddd.d")=-3.671xx10^13`