# Decimal Cubes

In this chapter we will learn to find the cubes of decimal numbers with solved examples.

To understand the chapter, you should have basic knowledge of decimal numbers. Click the red link to review the concept.

## How to represent cube of decimal number ?

To show cube of any number, simply put number inside the bracket and insert exponent 3.

For example, the cube of decimal 6.15 is shown as;

\mathtt{\Longrightarrow \ ( 6.15)^{3}}

## How to find cube of decimal number ?

To calculate the cube of decimal number, follow the below steps;

(i) Convert the decimal into fraction

(ii) Multiply the number by itself thrice

(iii) Multiply the numerators and denominators separately

(iv) If possible, convert the fraction back into decimal.

The above process can be generalized as follows;

Find the cube of decimal x.yz

\mathtt{\Longrightarrow \ ( x.yz)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{xyz}{100}\right)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{xyz\ \times \ xyz\ \times xyz}{100\ \times \ 100\ \times 100}}

I hope you understood the above concept. Let us try to solve some problems.

Example 01
Find the cube of decimal 2.6

Solution
\mathtt{\Longrightarrow \ ( 2.6)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{26}{10}\right)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{26\ \times \ 26\ \times 26}{10\ \times \ 10\ \times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{17576}{1000}}\\\ \\ \mathtt{\Longrightarrow \ 17.576}

Hence, 17.576 is the cube of given decimal.

Example 02
Find the cube of decimal 1.11

Solution
\mathtt{\Longrightarrow \ ( 1.11)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{111}{100}\right)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{111\times 111\times 111}{100\times 100\times 100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1367631}{1000000}}\\\ \\ \mathtt{\Longrightarrow \ 1.367631}

Hence, 1.367631 is the cube of given decimal

Example 03
Find cube of decimal 4.4

Solution
\mathtt{\Longrightarrow \ ( 4.4)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{44}{10}\right)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{44\times 44\times 44}{10\times 10\times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{85184}{1000}}\\\ \\ \mathtt{\Longrightarrow \ 85.184}

Example 04
Find the cube of decimal 0.5

Solution
\mathtt{\Longrightarrow \ ( 0.5)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{5}{10}\right)^{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5\times 5\times 5}{10\times 10\times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{125}{1000}}\\\ \\ \mathtt{\Longrightarrow \ 0.125}

Example 05
Find the cube of -1.2

Solution