Exercises: decimal numbers (mixed)

Compute

$17.17+0.3$

$18.7-1.87$

$1.2\cdot0.12$

$0.8:0.32$

$0.32:0.6$

$0.5\overline{3}$
$5.\overline{3}$
1.875

$0.0123:1000$

$0.0123\cdot100$

$5.5\cdot0.12:0.1$

$\left(2.08+9.2\right)-6.99$

$\left(9\cdot0.8-0.70\right):\left(0.6+0.5\right)$

$5.\overline{90}$
$0.0\overline{18}$
$0.\overline{81}$

For this task you need the following basic knowledge: Decimal fractions

$\displaystyle \left(9\cdot0.8-0.70\right):\left(0.6+0.5\right)$	$=$
	↓	Pay special attention to the operator hierarchy. Calculate first $9\cdot0.8$ .
	$=$	$\displaystyle \left(7.2-0.70\right):\left(0.6+0.5\right)$
	↓	Add/subtract the numbers in the parentheses.
	$=$	$\displaystyle 6.5:1.1$
	↓	The value does not change when the numerator and denominator are multiplied by 10. Now use the written method of division.
	$=$	$\displaystyle 65:11$

$\def\arraystretch{1.25} \begin{array}{l}\hphantom{-}65:11=5{.}9090\ldots=5{.}\overline{90}\\\underline{-55}\\\hphantom{-}100\\\underline{-\hphantom{1}99}\\\hphantom{-10}10\\\hphantom{11}\underline{-\hphantom{1}0}\\\hphantom{-10}100\\\hphantom{11}\underline{-\hphantom{1}99}\\\hphantom{-1000}10\\\hphantom{1111}\underline{-\hphantom{1}0}\\\hphantom{-1000}100\\\hphantom{1000000}\vdots\end{array}$

$\Rightarrow\left(9\cdot0.8-0.70\right):\left(0.6+0.5\right)=5.\overline{90}$

Alternative way

$\displaystyle \left(9\cdot0.8-0.70\right):\left(0.6+0.5\right)$	$=$
	↓	Convert decimal numbers into fractions.
	$=$	$\displaystyle \left(\frac{9}{1}\cdot\frac{8}{10}-\frac{70}{100}\right):\left(\frac{6}{10}+\frac{5}{10}\right)$
	↓	Multiply and add the fractions.
	$=$	$\displaystyle \left(\frac{72}{10}-\frac{70}{100}\right):\frac{11}{10}$
	↓	Get everything on a common denominator; subtract.
	$=$	$\displaystyle \left(\frac{720-70}{100}\right):\frac{11}{10}$
	↓	Divide the fractions.
	$=$	$\displaystyle \frac{650}{100}\cdot\frac{10}{11}$
	$=$	$\displaystyle \frac{6500}{1100}$
	↓	Shorten the fraction.
	$=$	$\displaystyle \frac{65}{11}$
	↓	You may still convert the fraction into a periodic decimal number.
	$=$	$\displaystyle 5.\overline{90}$

Do you have a question?

Write it here 👇

$\displaystyle 17.17+0.3$	$=$	$\displaystyle \frac{1717}{100}+\frac{30}{100}$
	↓	Add the fractions.
	$=$	$\displaystyle \frac{1747}{100}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 17.47$

$\displaystyle 18.7-1.87$	$=$	$\displaystyle \frac{1870}{100}-\frac{187}{100}$
	↓	Subtract fractions.
	$=$	$\displaystyle \frac{1683}{100}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 16.83$

$\displaystyle 1.2\cdot0.12$	$=$	$\displaystyle \frac{12}{10}\cdot\frac{12}{100}$
	↓	Multiply the fractions.
	$=$	$\displaystyle \frac{144}{1000}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 0.144$

$\displaystyle 0.32:0.6$	$=$	$\displaystyle \frac{\displaystyle\frac{32}{100}}{\displaystyle\frac{60}{100}}$
	↓	Convert the decimal numbers into fractions.
	$=$	$\displaystyle \frac{32}{100}\cdot\frac{100}{60}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\displaystyle \frac{3200}{6000}$
	↓	Shorten by 100.
	$=$	$\displaystyle \frac{8}{15}$
	↓	You may still be able to convert the fraction to a periodic decimal fraction.
	$=$	$\displaystyle 0.5\overline{3}$

$\displaystyle 0.8:0.32$	$=$
	↓	Form a fraction.
	$=$	$\displaystyle \frac{\frac{8}{10}}{\frac{32}{100}}$
	↓	Divide by $\frac{32}{100}$ .
	$=$	$\displaystyle \frac{8}{10}\cdot\frac{100}{32}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\displaystyle \frac{800}{320}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 2.5$

$\displaystyle 0.0123:1000$	$=$
	↓	Convert into fractions.
	$=$	$\displaystyle \frac{\displaystyle\frac{123}{10000}}{\displaystyle\frac{1000}1}$
	↓	Divide by $\frac{1000}1$ .
	$=$	$\displaystyle \frac{123}{10000}\cdot\frac{1}{1000}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\displaystyle \frac{123}{10000000}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 0.0000123$

$\displaystyle 0.0123\cdot100$	$=$
	↓	Convert the decimal numbers into fractions.
	$=$	$\displaystyle \frac{123}{10000}\cdot\frac{100}{1}$
	↓	Multiply the fractions.
	$=$	$\displaystyle \frac{12300}{10000}$
	↓	Shorten the fractions.
	$=$	$\displaystyle 1.23$

$\displaystyle 5.5\cdot0.12:0.1$	$=$
	↓	Convert into fractions.
	$=$	$\displaystyle \frac{\frac{550}{100}\cdot\frac{12}{100}}{\frac{10}{100}}$
	↓	Divide by $\frac{10}{100}$ .
	$=$	$\displaystyle \frac{550}{100}\cdot\frac{12}{100}\cdot\frac{100}{10}$
	↓	Multiply the fractions.
	$=$	$\displaystyle \frac{660000}{100000}$
	↓	Shorten the fraction.
	$=$	$\displaystyle \frac{66}{10}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 6.6$

$\displaystyle \left(2.08+9.2\right)-6.99$	$=$
	↓	First, compute $2.08+9.2$ .
	$=$	$\displaystyle 11.28-6.99$
	$=$	$\displaystyle 4.29$

$\displaystyle \left(2.08+9.2\right)-6.99$	$=$
	↓	Convert the decimal numbers into fractions.
	$=$	$\displaystyle \frac{208}{100}+\frac{92}{10}-\frac{699}{100}$
	↓	Get everything on a common denominator.
	$=$	$\displaystyle \frac{208}{100}+\frac{920}{100}-\frac{699}{100}$
	↓	Compute.
	$=$	$\displaystyle \frac{429}{100}$
	↓	Convert into a decimal number.
	$=$	$\displaystyle 4.29$