Suppose we want to subtract two numbers with different numbers of decimal places, such as
4.7-3.16 \, .
Here, there is only
\color{blue}1
decimal place in
4.7,
while there are
\color{blue}2
decimal places in
3.16.
In order to subtract 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 last digit in the first number, so that it has
\color{blue}2
decimal places:
4.7=4.7{\color{red}0}
Now, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 6 } \!\!\!\! & \!\!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{\!7\!} \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\!
\end{array}
Therefore,
4.7-3.16 = 1.54\,.
What is the value of
5.98-0.432?
There are
\color{blue}2
decimal places in
5.98
and there are
\color{blue}3
decimal places in
0.432.
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has
\color{blue}3
decimal places:
5.98=5.98{\color{red}0}
Now, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& & &
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 7 } \!\!\!\! & \!\!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! \cancel{\!8\!} \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Therefore,
5.98-0.432= 5.548\,.
a
$4.16$
b
$3.31$
c
$3.61$
d
$2.51$
e
$2.61$
There is $\color{blue}1$ decimal place in $6.1$ and there are $\color{blue}2$ decimal places in $2.49.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has $\color{blue}2$ decimal places:
\[
6.1=6.1{\color{red}0}
\]
Now, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 5 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel 1 \!\!\!\!& \!\!\!\! \cancel 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore,
\[
6.1-2.49 = 3.61
\]
a
$1.993$
b
$2.137$
c
$2.027$
d
$1.881$
e
$2.453$
There are $\color{blue}3$ decimal places in $4.521$ and there are $\color{blue}2$ decimal places in $2.64.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the second number so that it has $\color{blue}3$ decimal places:
\[
2.64{\color{red}0}
\]
Now, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& & &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 3 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 14 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\12 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ } \!\!\!\! \\
& & \!\!\!\! \cancel 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel 5 \!\!\!\!& \!\!\!\! \cancel 2 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\hline
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore,
\[
4.521-2.64=1.881
\]
Find the value of
9.4-0.254.
There are is
\color{blue}1
decimal place in
9.4
and there are
\color{blue}3
decimal places in
0.254.
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has
\color{blue}3
decimal places:
9.4 = 9.4{\color{red}00}
Now, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!& & &
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & & & \!\!\!\!\! \color{blue}\substack{\\ 3 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\!\! & \!\!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\! & \!\!\!\! \cancel{\!4\!} \!\!\!\! & \!\!\!\! \cancel{\!0\!} \!\!\!\! & \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 6 \!\!\!\!
\end{array}
Therefore,
9.4-0.254=9.146\,.
a
$3.232$
b
$2.339$
c
$3.432$
d
$3.262$
e
$2.233$
There is $\color{blue}1$ decimal place in $8.7$ and there are $\color{blue}3$ decimal places in $5.468.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has $\color{blue}3$ decimal places:
\[
8.7=8.7{\color{red}00}
\]
Now, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& & &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 6 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel7 \!\!\!\!& \!\!\!\! \cancel 0 \!\!\!\!& \!\!\!\! \cancel 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Therefore,
\[
8.7-5.468 = 3.232
\]
a
$31.348$
b
$30.828$
c
$31.748$
d
$31.052$
e
$30.957$
There is $\color{blue}1$ decimal place in $64.2$ and there are $\color{blue}3$ decimal places in $33.148.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has $\color{blue}3$ decimal places:
\[
64.2=64.2{\color{red}00}
\]
Now, we line up the decimal points:
\[
\begin{array}{cccccccc}
& \!\!\!\! 6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 3 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& & &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& \!\!\!\!\! \color{blue}\substack{\\ } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{\\ } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& \!\!\!\! 6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel2 \!\!\!\!& \!\!\!\!\cancel 0 \!\!\!\!& \!\!\!\! \cancel 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 3 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& \!\!\!\! 3 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Therefore,
\[
64.2-33.148=31.052
\]
To subtract a decimal from a whole number, we convert the whole number to an equivalent decimal so that both numbers have the same number of decimal places.
For example, to calculate
4-0.4,
first notice that
4
has no decimal places and there is
\color{blue}1
decimal place in
0.4.
To subtract 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}1
decimal place:
4\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{[math]\color{blue}1[/math] zero}}\!\!\!
Now, we subtract as normal, lining up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!&
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 3 } \!\!\!\!\!\! & & \!\!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel{\!4\!} \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
Therefore,
4-0.4 = 3.6\,.
There are no decimal places in
1
and there are
\color{blue}2
decimal places in
0.56.
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has
\color{blue}2
decimal places.
1\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{00}_{\large\text{[math]\color{blue}2[/math] zeros}}\!\!\!
Now, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 0 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\! & \!\!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel{\!1\!} \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! 0 \!\!\!\! & \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 4 \!\!\!\!
\end{array}
Therefore,
1-0.56 = 0.44\,.
a
$1.0$
b
$6.3$
c
$10$
d
$5.3$
e
$5.7$
There are no decimal places in $7$ and there is $\color{blue}1$ decimal place in $1.7.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has $\color{blue}1$ decimal place:
\[
7\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{$\color{blue}1$ zero}}\!\!\!
\]
Next, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!&
\end{array}
\]
Then, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 6 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
\]
Therefore:
\[
7-1.7 = 5.3
\]
a
$5.84$
b
$3.16$
c
$4.16$
d
$4.26$
e
$2.62$
There are no decimal places in $5$ and there are $\color{blue}2$ decimal places in $0.84.$
To subtract the numbers, they both need the same number of decimals. Therefore, we rewrite the first number so that it has $\color{blue}2$ decimal places:
\[
5\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{00}_{\large\text{$\color{blue}2$ zeros}}\!\!\!
\]
Now, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 4 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel5 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel0 \!\!\!\!& \!\!\!\! \cancel0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
\]
Therefore,
\[
5-0.84 = 4.16
\]
Carol bought
3
yards of polyester fabric to make two shirts. She cut the fabric into two pieces and found that one piece was
1.4
yards long. How long was the other piece of fabric?
To find the length of the second piece of fabric, we need to calculate the difference
3 - 1.4.
There are
\color{blue}0
decimal places in
3
and there is
\color{blue}1
decimal place in
1.4.
To subtract the numbers, both need to have the same number of decimals. Hence, we rewrite the first number so that it has
\color{blue}1
decimal place:
3\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{0}_{\large\text{[math]\color{blue}1[/math] zero}}\!\!\!
First, we line up the decimal points:
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!&
\end{array}
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 2 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel{\!3\!} \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{\!0\!} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
Therefore,
3 - 1.4 = 1.6,
and we conclude that the second piece was
1.6
yards long.
There were $12$ liters of drinking water in a container from which Mike took $0.9$ liters to fill his water bottle. How much water was left in the container?
a
$12.1$ liters
b
$12.9$ liters
c
$11.1$ liters
d
$10.1$ liters
e
$10.9$ liters
To find how much water was left in the container, we need to calculate the difference $ 12- 0.9.$
There are $\color{blue}0$ decimal places in $12$ and there is $\color{blue}1$ decimal place in $0.9.$
To subtract the numbers, both must have the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}1$ decimal place:
\[
12 = 12.{\color{red}0}
\]
First, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & & \!\!\!\! . \!\!\!\!&
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! \cancel{2} \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{0} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore, $11.1$ liters of water was left in the container.
Adam had a $9$-foot rope which he cut into two pieces. If one piece was $4.38$ feet long, how long was the other piece?
a
$4.72$ feet
b
$4.62$ feet
c
$4.52$ feet
d
$5.62$ feet
e
$5.52$ feet
To find the length of the other piece, we need to calculate the difference $9- 4.38.$
There are $\color{blue}0$ decimal places in $9$ and there are $\color{blue}2$ decimal places in $4.38.$
To subtract the numbers, both must have the same number of decimals. Hence, we rewrite the first number so that it has $\color{blue}2$ decimal places:
\[
9 = 9.{\color{red}00}
\]
First, we line up the decimal points:
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & & \!\!\!\! . \!\!\!\!& &
\end{array}
\]
Next, we proceed by subtracting the two numbers just as we would with whole numbers:
\[
\begin{array}{cccccccc}
& & \!\!\!\!\! \color{blue}\substack{ \\ 8 } \!\!\!\! & & \!\!\!\!\! \color{blue}\substack{ \\ 9 } \!\!\!\! & \!\!\!\!\! \color{blue}\substack{ \\ 10 } \!\!\!\! \\
& & \!\!\!\! \cancel{9} \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! \cancel{0} \!\!\!\!& \!\!\!\! \cancel{0} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Hence,
\[9- 4.38= 4.62.\]
So, the other piece was
$4.62$ feet long.
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