# What is 0.9978+0.325?

Aug 28, 2016

$1.3228$

#### Explanation:

When adding decimals it is very important to line up the decimal point and place numbers of the same value..

$\textcolor{w h i t e}{\times \times \times} 0.9978$
$\textcolor{w h i t e}{\times \times} + \underline{0.325}$
$\textcolor{w h i t e}{\times \times} = 1.3228$

If there is no digit shown - treat it as 0.

When you add,you now add the digits with the same place value together.

so 9/10 must be above 3/10 and
9/100 must be above 2/100 and
7/1000 must be above 5/1000
8/10000 is alone.

Aug 29, 2016

$1.3228$

#### Explanation:

write as:

$\textcolor{b r o w n}{\text{counting column from the right}}$

$0.9978$
$\underline{0.3250} \leftarrow \text{ notice the place holder of 0 at the end of 0.325}$
$\underline{\textcolor{w h i t e}{0.3250}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Adding column 1}}$

$0.9 \textcolor{w h i t e}{.} 9 \textcolor{w h i t e}{.} 7 \textcolor{w h i t e}{.} \textcolor{red}{8}$
$\underline{0.3 \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{.} 5 \textcolor{w h i t e}{.} \textcolor{red}{0}}$
$\underline{\textcolor{w h i t e}{0.3 .2 .5 .0} \textcolor{g r e e n}{8}} \leftarrow \text{ 8 + 0 = 8 nothing to carry}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Adding column 2}}$

$0.9 \textcolor{w h i t e}{.} 9 \textcolor{w h i t e}{. .} \textcolor{red}{7} \textcolor{w h i t e}{.} 8$
$\underline{0.3 \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{. .} \textcolor{red}{5} \textcolor{w h i t e}{.} 0}$
$\textcolor{w h i t e}{.} \underline{\textcolor{w h i t e}{0.3 .2 .} \textcolor{g r e e n}{2} \textcolor{w h i t e}{.} 8} \leftarrow \text{ 7+5=12 giving " color(green)(2 )" and "color(magenta)(1)" to carry}$
$\textcolor{w h i t e}{\ldots \ldots} \textcolor{m a \ge n t a}{1}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Adding column 3}}$

$0.9 \textcolor{w h i t e}{.} \textcolor{red}{9} \textcolor{w h i t e}{.} 7 \textcolor{w h i t e}{.} 8$
$\underline{0.3 \textcolor{w h i t e}{.} \textcolor{red}{2} \textcolor{w h i t e}{.} 5 \textcolor{w h i t e}{.} 0}$
$\underline{\textcolor{w h i t e}{0.3} \textcolor{w h i t e}{.} \textcolor{g r e e n}{2} \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{.} 8} \leftarrow \text{ 9+2+1 =12 giving " color(green)(2 )" and "color(magenta)(1)" to carry}$
$\textcolor{w h i t e}{. .} \textcolor{m a \ge n t a}{1} \textcolor{w h i t e}{.} 1$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Adding column 4}}$

$\text{0.} \textcolor{w h i t e}{.} \textcolor{red}{9} \textcolor{w h i t e}{.} 9 \textcolor{w h i t e}{.} 7 \textcolor{w h i t e}{.} 8$
$\underline{\text{0.} \textcolor{w h i t e}{.} \textcolor{red}{3} \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{.} 5 \textcolor{w h i t e}{.} 0}$
ul("0."color(white)(.)color(green)(3)color(white)(.)2color(white)(.)2color(white)(.)8) larr" 9+3+1 =13 giving " color(green)(3 )" and "color(magenta)(1)" to carry"
$\textcolor{w h i t e}{} \textcolor{m a \ge n t a}{1} \textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{.} 1$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Adding column 5}}$

$\textcolor{red}{\text{0.}} \textcolor{w h i t e}{.} 9 \textcolor{w h i t e}{.} 9 \textcolor{w h i t e}{.} 7 \textcolor{w h i t e}{.} 8$
$\underline{\textcolor{red}{\text{0.}} \textcolor{w h i t e}{.} 3 \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{.} 5 \textcolor{w h i t e}{.} 0}$
ul(color(green)("1.")color(white)(.)3color(white)(.)2color(white)(.)2color(white)(.)8) larr" 0+0+1 =1 giving " color(green)(1 )" and "color(magenta)(0)" to carry"
$\textcolor{w h i t e}{} 1 \textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{.} 1$