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

Last updated date: 24th Jul 2024
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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.

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,
  {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!