Suppose we want to compute the sum of two numbers with different numbers of decimal places, such as
19+5.6.
Here, there are no decimal places in
19,
\color{blue}1
5.6.
In order to add the two numbers, we need the two numbers to have the same number of decimal places. We can achieve this by attaching an extra zero behind the decimal place in the first number, so that it has
\color{blue}1
19\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\underbrace{0}_{\large\text{[math]\color{blue}1[/math] zero}}\!\!
Remember that whenever we attach an extra zero behind the decimal place, the number remains unchanged. So the number
19.0
19.
Now the addition problem reads
19.0 + 5.6,
and we can add the decimal numbers using the usual method. First, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!&
\end{array}
Then, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
Therefore,
19 + 5.6 = 24.6.
What is the value of
6 + 16.4?
There are no decimal places in
6
\color{blue}1
16.4.
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has
\color{blue}1
6\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{[math]\color{blue}1[/math] zero}}\!\!\!
Next, we line up the decimal points:
\begin{array}{cccccccc}
& && \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!&
\end{array}
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\
& && \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!
\end{array}
Therefore,
6 + 16.4 = 22.4.
There are no decimal places in $12$ and there is $\color{blue}1$ decimal place in $5.2.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}1$ decimal zero:
\[
12\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{$\color{blue}1$ zero}}\!\!\!
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\! & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\! &
\end{array}
\]
Therefore, $12 + 5.2 =\bbox[3pt,Gainsboro]{\color{blue} 17.2}.$
There is $\color{blue}1$ decimal place in $58.4$ and there are no decimal places in $3.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the second number so that it has $\color{blue}1$ decimal zero:
\[
3\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{$\color{blue}1$ zero}}\!\!\!
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! &
\end{array}
\]
Therefore, $58.4 + 3=\bbox[3pt,Gainsboro]{\color{blue} 61.4}.$
There is
\color{blue}1
15.4
\color{blue}2
20.79.
In order to add the two numbers, we need them to have the same number of decimal places. So, we rewrite the first number so that it has
\color{blue}2
15.4=15.4{\color{red}0}
Next, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& &
\end{array}
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\!
\end{array}
Therefore,
15.4 + 20.79 = 36.19.
There are $\color{blue}2$ decimal places in $1.45$ and $\color{blue}1$ decimal place in $9.2.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the second number so that it has $\color{blue}2$ decimal places:
\[
9.2=9.2{\color{red}0}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\! & & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& \!\!\!\! 1 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! &
\end{array}
\]
Therefore, $1.45 + 9.2 =\bbox[3pt,Gainsboro]{\color{blue} 10.65}.$
On a particular weekend, Sam rode his bicycle for $5.3\,\textrm{mi}.$ After that, he rode for a further $2.45\,\textrm{mi}.$ Find the total distance that Sam traveled.
a
$7.75\,\textrm{mi}$
b
$7.7\,\textrm{mi}$
c
$6.98\,\textrm{mi}$
d
$75.7\,\textrm{mi}$
e
$7.48\,\textrm{mi}$
To find the total distance that Sam traveled, we need to calculate the sum $5.3 + 2.45.$
There is $\color{blue}1$ decimal place in $5.3$ and there are $\color{blue}2$ decimal places in $2.45.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}2$ decimal places:
\[
5.5 = 5.3{\color{red}0}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 5 \!\!\!\!
\end{array}
\]
So, $5.3 + 2.45 = 7.75.$
Therefore, the total distance that Sam traveled is $7.75\,\textrm{mi}.$
What is the value of
32.54 + 16.854?
There are
\color{blue}2
32.54
\color{blue}3
16.854.
To add the two numbers, we need them to have the same number of decimal places. So, we rewrite the second number so that it has
\color{blue}3
32.54=32.54{\color{red}0}
Next, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & &
\end{array}
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & & \\
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\!
\end{array}
Therefore,
32.54 + 16.854 = 49.394.
There are $\color{blue}2$ decimal places in $25.14$ and there are $\color{blue}3$ decimal places in $6.723.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}3$ decimal places:
\[
25.14=25.14{\color{red}0}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\! & \!\!\!\! \color{blue}\substack{ \\ } \!\!\!\! & & \!\!\!\! \color{blue}\substack{ \\ } \!\!\!\! & \\
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& \!\!\!\! \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
\]
Therefore, $25.14+ 6.723=\bbox[3pt,Gainsboro]{\color{blue}31.863}.$
There are $\color{blue}3$ decimal places in $4.362$ and there are $\color{blue}2$ decimal places in $5.24.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the second number so that it has $\color{blue}3$ decimal places:
\[
5.24 = 5.24{\color{red}0}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& & & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & & & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& \\
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& \!\!\!\! \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 2 \!\!\!\! &
\end{array}
\]
Therefore, $4.362 + 5.24 =\bbox[3pt,Gainsboro]{\color{blue} 9.602}.$
Sometimes, we will need to place more than one zero to the right of a decimal point.
For instance, to find the value of
78.9 + 45.962,
\color{blue}1
78.9
\color{blue}3
45.962.
To add the two numbers, we need them to have the same number of decimal places. So, we rewrite the first number so that it has
\color{blue}3
78.9=78.9{\color{red}00}
Next, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & &
\end{array}
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & & \\
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
Therefore,
78.9 + 45.962 = 124.862.
What is the value of
56 + 10.3691?
There are no decimal places in
56,
\color{blue}4
10.3691.
To add the two numbers, we need them to have the same number of decimal places. So, we rewrite the first number so that it has
\color{blue}4
56\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\underbrace{0000}_{\large\text{[math]\color{blue}4[/math] zeros}}\!
Next, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & & &
\end{array}
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
Therefore,
56 + 10.3691 = 66.3691.
There are no decimal places in $8$ and there are $\color{blue}4$ decimal places in $23.4532.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}4$ decimal places:
\[
8\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\underbrace{0000}_{\large\text{$\color{blue}4$ zeros}}\!
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & & & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\
& & \!\!\!\! \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! &
\end{array}
\]
Therefore, $8 + 23.4532 = \bbox[3pt,Gainsboro]{\color{blue}31.4532}.$
There is $\color{blue}1$ decimal place in $24.6$ and there are $\color{blue}3$ decimal places in $7.437.$
To add the numbers, they both need the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}3$ decimal places:
\[
24.6=24.6{\color{red}00}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & &
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & & \\
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Therefore, $24.6 + 7.437 = \bbox[3pt,Gainsboro]{\color{blue}32.037}.$
Diana bought $2$ pounds of strawberry jelly beans and $1.5$ pounds of orange jelly beans for her birthday party. How many pounds of jelly beans did Diana buy in total?
a
$3$ pounds
b
$3.5$ pounds
c
$4$ pounds
d
$2.5$ pounds
e
$4.5$ pounds
To find the total number of pounds of jelly beans that Diana bought, we need to calculate the sum $2 + 1.5.$
There are $\color{blue}0$ decimal places in $2$ and $\color{blue}1$ decimal place in $1.5.$
To add the numbers, they both need to have the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}1$ decimal place:
\[
2 = 2.{\color{red}0}
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!&
\end{array}
\]
Finally, we proceed by adding the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!
\end{array}
\]
Therefore, Diana bought a total of $3.5\,\textrm{lbs}$ of jelly beans.
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