Exercises: addition and subtraction of decimal numbers

With these exercises, you can practice adding and subtracting decimal numbers. Can you solve them all?

1
Add up the following decimal numbers.
$0.44 + 0.234$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$0.44 + 0.234$
Write both numbers underneath each other, and fill up the "shorter number" ( $0.44$ ) with zeros.
$\begin{array}{l} 0.440 \\ + 0.234 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 0.440 \\ + 0.234 \\ 0.674 \end{array}$

$2.983 + 0.230$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$2.983 + 0.23$
Write both numbers underneath each other, and fill up the "shorter number" ( $0.23$ ) with zeros.
$\begin{array}{l} 2 .9 8 3 \\ + 0 .2 3 0 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 2 .9 8 3 \\ + 0_{1} {.2}_{1} 3 0 \\ 3 .2 1 3 \end{array}$

$9.33 + 4$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$9.33 + 4$
Write both numbers underneath each other, and fill up the "shorter number" ( $0.23$ ) with zeros.
$\begin{array}{rcl} 9.33 \\ + 4.00 \end{array}$
Now, perform an addition in columns.
$\begin{array}{rcl} 9.33 \\ + 4.00 \\ 13.33 \end{array}$

$0.00034 + 0.032$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$0.00034 + 0.032$
Write both numbers underneath each other, and fill up the "shorter number" ( $0.032$ ) with zeros.
$\begin{array}{l} 0.00034 \\ + 0.032 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 0.00034 \\ + 0.032 \\ 0.03234 \end{array}$

$0.983 + 2.78 + 11.673$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$0.983 + 2.78 + 11.673$
Write both numbers underneath each other, and fill up the $2.78$ with zeros.
$\begin{array}{l} 0 .9 8 3 \\ 2 .7 8 0 \\ + 11 .6 7 3 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 0 .9 8 3 \\ 2 .7 8 0 \\ + 11_{2} {.6}_{2} 7 3 \\ 15 .4 3 6 \end{array}$

$2.3 + 3.2$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$2.3 + 3.2$
Write both numbers underneath each other.
$\begin{array}{l} 2.3 \\ + 3.2 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 2.3 \\ + 3.2 \\ 5.5 \end{array}$

$22 + 7.535 + 0.093$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$22 + 7.535 + 0.093$
Write both numbers underneath each other, and fill up the $22$ with zeros after the decimal point.
$\begin{array}{l} 22.0 0 0 \\ 7.5 3 5 \\ + 0.0 9 3 \end{array}$
Now, perform an addition in columns.
$\begin{array}{l} 22.0 0 0 \\ 7.5 3 5 \\ + {0.0}_{1} 9 3 \\ 29.6 2 8 \end{array}$
2
Subtract the following decimal numbers:
$0.45 - 0.29$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$0.45 - 0.29$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other.
$\begin{array}{l} 0.4 5 \\ - 0.2 9 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 0. \overset{3}{4} \overset{15}{5} \\ - 0.2 9 \\ 0.1 6 \end{array}$

$0.965 - 0.83$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$0.965 - 0.83$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other. Fill up the "shorter number" ( $0.83$ ) with zeros.
$\begin{array}{l} 0.965 \\ - 0.830 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 0.965 \\ - 0.830 \\ 0.135 \end{array}$

$1.782 - 0.234$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$1.782 - 0.234$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other.
$\begin{array}{l} 1.7 8 2 \\ - 0.2 3 4 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 1.7 \overset{7}{8} \overset{12}{2} \\ - 0.2 3 4 \\ 1.5 4 8 \end{array}$

$34.98 - 1.061$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$34.98 - 1.061$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other. Fill up the "shorter number" ( $34.98$ ) with zeros.
$\begin{array}{l} 3 4.9 8 0 \\ - 1.0 6 1 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 3 4.9 \overset{7}{8} \overset{10}{0} \\ - 1.0 6 1 \\ 3 3.9 1 9 \end{array}$

$4.913 - 2.911$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$4.913 - 2.911$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other.
$\begin{array}{l} 4.913 \\ - 2.911 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 4.913 \\ - 2.911 \\ 2.002 \end{array}$

$2.043 - 1.921$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$2.043 - 1.921$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other.
$\begin{array}{l} 2. 043 \\ - 1. 921 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} \overset{1}{2} . \overset{10}{0} 43 \\ - 1. 921 \\ 0. 122 \end{array}$

$11.693 - 7.777$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$11.693 - 7.777$
Write the figures one below the other. Make sure that the decimal marks are directly underneath each other.
$\begin{array}{l} 11.693 \\ - 7.777 \end{array}$
Now, perform a subtraction in columns.
$\begin{array}{l} 1 \overset{\overset{10}{0}}{1} . \overset{16}{6} \overset{8}{9} \overset{13}{3} \\ - 7. 7 7 7 \\ 3. 9 1 6 \end{array}$

Subtract the following fractions and decimal numbers

$1.04 - \frac{1}{2}$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$\begin{array}{l} 1.04 - \frac{1}{2} \end{array}$
First, convert $\frac{1}{2}$ into a decimal number.
$\begin{array}{l} 1.04 - 0.5 \end{array}$
Subtract the two decimal numbers in columns.
$\begin{array}{l} \begin{array}{l} 1 .04 \\ - 0.50 \\ 0.54 \end{array} \end{array}$
Alternative solution
$1.04 - \frac{1}{2}$ $=$
↓
Convert into a fraction.
$=$ $\frac{104}{100} - \frac{1}{2}$
↓
Calculate the common denominator (100).
$=$ $\frac{104}{100} - \frac{50}{100}$
$=$ $\frac{54}{100}$
$=$ $\frac{27}{50}$
$=$ $0.54$
$\frac{6}{3} - 0.23$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$\begin{array}{l} \frac{6}{3} - 0.23 \end{array}$
You may first shorten $\frac{6}{3} = 2$ and then subtract the two decimal numbers. For this, write $2$ as $2.00$ .
$\begin{array}{l} 2.00 \\ - 0.23 \\ 1.77 \end{array}$
Alternative solution
$\frac{6}{3} - 0.23$ $=$
$=$ $\frac{6}{3} - \frac{23}{100}$
$=$ $\frac{600}{300} - \frac{69}{300}$
$=$ $\frac{531}{300}$
$=$ $\frac{177}{100}$
$=$ $1.77$
$1.8 - \frac{1}{8} - 0.08$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$1.8 - \frac{1}{8} - 0.08$
Since there are already two decimal numbers, you may also convert $\frac{1}{8}$ into a decimal number.
$= 1.8 - 0.125 - 0.08$
$= 1.595$

$0.94 - \frac{4}{11}$

$2.98 - \frac{4}{11}$

For this task you need the following basic knowledge: Addition and subtraction of decimal numbers
$2.98 - \frac{4}{11}$ $=$
↓
As $\frac{4}{11}$ is a periodic fraction, you should convert the decimal number into a fraction.
$=$ $\frac{298}{100} - \frac{4}{11}$
↓
Calculate the common denominator (1100).
$=$ $\frac{3278}{1100} - \frac{400}{1100}$
$=$ $\frac{2878}{1100}$
$=$ $\frac{1439}{550}$

4
We consider the following sum: $1 + 0.1 + 0.01 + 0.001 + \dots$
(Perhaps you already know that $0. 2 = \frac{2}{9}, 0. 3 = \frac{3}{9} = \frac{1}{3}, 0. 7 = \frac{7}{9}$ and so on.)
What are the three next terms in the sum after $0.001$ ? How are two successive summands related to each other?

For this task you need the following basic knowledge: Decimal Numbers
The next three terms are:
$0.0001$
$0.00001$
$0.000001$
Each summand is a tenth of its predecessor.

Calculate the value of the above sum both as a repeating decimal and as a fraction.

For this task you need the following basic knowledge: Decimal Numbers
$\to$ Since each additional summand is a tenth of its predecessor, the result must be $1. 1$ .
$1. \underset{tenth}{\overset{+ 0.1}{1}} \underset{hundredths}{\overset{+ 0.01}{1}} \underset{thousandths}{\overset{+ 0.001}{1}} and so on.$
$\frac{10}{9}$ is the fraction corresponding to $1. 1$ .

Calculate the value of the difference $3 - 0.2 - 0.02 - 0.002 - \dots$ both as a repeating decimal and as a fraction.

For this task you need the following basic knowledge: Decimal Numbers
$\to$ Since each subtracted term is a tenth of its predecessor, the result must be $3 - 0. 2$ .
$\frac{25}{9}$ is the fraction corresponding to $3 - 0. 2$ .

$1.04 - \frac{1}{2}$	$=$
	↓	Convert into a fraction.
	$=$	$\frac{104}{100} - \frac{1}{2}$
	↓	Calculate the common denominator (100).
	$=$	$\frac{104}{100} - \frac{50}{100}$
	$=$	$\frac{54}{100}$
	$=$	$\frac{27}{50}$
	$=$	$0.54$

$\frac{6}{3} - 0.23$	$=$
	$=$	$\frac{6}{3} - \frac{23}{100}$
	$=$	$\frac{600}{300} - \frac{69}{300}$
	$=$	$\frac{531}{300}$
	$=$	$\frac{177}{100}$
	$=$	$1.77$

$0.94 - \frac{4}{11}$	$=$
	↓	As $\frac{4}{11}$ is a periodic fraction, you should convert the decimal number into a fraction.
	$=$	$\frac{94}{100} - \frac{4}{11}$
	↓	Calculate the common denominator and subtract the fractions.
	$=$	$\frac{1034}{1100} - \frac{400}{1100}$
	$=$	$\frac{634}{1100}$
	$=$	$\frac{317}{550}$

$2.98 - \frac{4}{11}$	$=$
	↓	As $\frac{4}{11}$ is a periodic fraction, you should convert the decimal number into a fraction.
	$=$	$\frac{298}{100} - \frac{4}{11}$
	↓	Calculate the common denominator (1100).
	$=$	$\frac{3278}{1100} - \frac{400}{1100}$
	$=$	$\frac{2878}{1100}$
	$=$	$\frac{1439}{550}$