# Find the cubes of 10,30,100,1000. What can we say about the zeros at the end?

Last updated date: 17th Mar 2023

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**Hint**: We will find the cubes of the numbers and then will observe the things. Is there any pattern or any trick that relates to the cubing method. Finding a cube is nothing but multiplying the number with itself thrice.

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__Complete step-by-step answer__Given the numbers are 10,30,100 and 1000.

We can see that the first two numbers have only one zero. So their cubes are,

\[\begin{gathered}

{10^3} = 10 \times 10 \times 10 = 1,000 \\

{30^3} = 30 \times 30 \times 30 = 27,000 \\

\end{gathered} \]

Now the second number has two zeros. Its cube is,

\[{100^3} = 100 \times 100 \times 100 = 10,00,000\]

The last number has three zeros. The cube will be,

\[{1000^3} = 1000 \times 1000 \times 1000 = 1,00,00,00,000\]

Like in 10 and 30 there became 3 zeros. In the case of 100 there are 6 zeros and in 1000 there are 9 zeros.

Thus we conclude that “the number of zeros in a number after cubing becomes three times they are present”.

**Note**: Students cubing and squaring are the frequently used processes in mathematics. In squaring a number becomes double and in cubing becomes triple. For zeros in a square they become doubl in number unlike in cube they become triple.

For example, \[{10^2} = 10 \times 10 = 100\]

\[{10^3} = 10 \times 10 \times 10 = 1,000\]

Hope this clears the concept!

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