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

Jul 8, 2018

$- 3.671 \times {10}^{13}$

#### Explanation:

Given: $2.9 \times {10}^{11} - 3.7 \times {10}^{13}$

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

$2.9 \times {10}^{11} = 0.029 \times {10}^{13}$

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:

$.029 \times {10}^{13} - 3.7 \times {10}^{13} = - 3.671 \times {10}^{13}$

Jul 8, 2018

$- 3.671 \times {10}^{13}$

#### Explanation:

Factor out ${10}^{11}$ giving:

${10}^{11} \left(2.9 - 3.7 \times {10}^{2}\right)$

${10}^{11} \left(2.9 - 370\right)$

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:

$2 - 4 \textcolor{w h i t e}{\text{dd")=color(white)("dd")1xx(2-4)color(white)("dd") =color(white)("dd}} - 1 \times \left(- 2 + 4\right)$

Applying the above approach we have:

${10}^{11} \left(2.9 - 370\right) \textcolor{w h i t e}{\text{d")=color(white)("d}} - {10}^{11} \left(- 2.9 + 370\right)$

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

$370.0$
$\underline{\textcolor{w h i t e}{37} 2.9 \leftarrow \text{ Subtract}}$

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

Still will not work so write:

$3 {\cancel{7}}^{6} {\cancel{0}}^{9} . {\cancel{0}}^{10}$
ul(color(white)(37dd)2color(white)("d").color(white)(".")9 larr" Subtract")
$3 \textcolor{w h i t e}{\text{.")6color(white)("d")7color(white)("d").color(white)("d}} 1$

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

$- {10}^{11} \left(- 2.9 + 370\right) \textcolor{w h i t e}{\text{d")=color(white)("d}} - {10}^{11} \left(367.1\right) = - 367.1 \times {10}^{11}$

$\textcolor{w h i t e}{\text{dddddddddddddddddddddddddddddd.d}} = - 3.671 \times {10}^{13}$