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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: 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.

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!