## Decimals

 2.2 Decimals

We will learn to do basic operations for decimal numbers.

Decimals represent fractions with the denominators $$10, 100, 1\,000$$ and so on.

• When adding decimals in vertical form, make sure that the decimal points are aligned vertically.

Then, add from the right to the left as in adding the whole numbers.

As example,

$$0.18+4.59=\underline{\hspace{1cm}}$$

$$\begin{array}{rr} \small{\color{green}{1}}\space\space\space\space \\0\space.\space1\space8 \\+\quad4\space.\space5\space9 \\\hline4\space.\space7\space7 \\\hline \end{array}$$

• When subtracting decimals in vertical form, make sure that the decimal points are aligned vertically.

Subtract the numbers from the right to the left.

As example,

$$8.322-2.7=\underline{\hspace{2cm}}$$

$$\begin{array}{rr} \small{\color{red}{7}}\space\space\small{\color{green}{13}\space\space\space\space\space\space\space} \\\cancel{8}\space.\space\cancel{3}\space2\space2 \\-\quad\quad2\space.\space7\space0\space0 \\\hline5\space.\space6\space2\space2 \\\hline \end{array}$$

• Multiplication of a decimal by a whole number is adding up the repeating decimal.

To find the product of a decimal and a whole number, multiply the digits in the same way as for whole numbers.

The decimal point is placed as in the multiplied number.

As example,

$$6.4\times6=\underline{\hspace{2cm}}$$

$$\begin{array}{rr} \small{\color{red}{2}}\quad\space\space\space \\6\space.\space4 \\\times\quad\quad\quad6 \\\hline3\space8\space.\space4 \\\hline \end{array}$$

• Divide decimals as in whole numbers.

The decimal point is placed as in the divided number.

Note that the decimal point is aligned vertically to that in the dividend.

As example,

$$18.768\div6=\underline{\hspace{2cm}}$$

\begin{aligned}\color{red}{3\space.\space1\space2\space8} \\6\space\overline{)1\space8\space.\space7\space6\space8} \\\underline{-\space1\space8}\space\space\space\space\space\quad\space\space \\7\quad\space\space \\\underline{-\space6}\space\space\quad \\1\space6\space\space\space \\\underline{-\space1\space2}\space\space\space\\4\space8 \\\underline{-\space4\space8} \\0 \end{aligned}