Question

Special balances can weigh something like $0.00000001gm$. express this number in standard form.

Answer 1

Hint: The number given is in general form. When we write it in standard form we use powers of 10. All zeros are written in the form of powers of 10. Also sometimes we use decimal also and increase the power of 10 by 1. And this is increased as the decimal shifts to left. But we will shift the decimal to the right. Now let’s solve it!

Complete step by step solution:
Given is a weight of a light thing equals to $0.00000001 gm$
Now in order to write this in standard form we will measure the zeros and that will be written in the power of $10$.
So there are $7$ zeros. So the power of $10$ will be $-7$.
\[0.1 \times {10^{ - 7}}\]
All the zeros are now in the power of $10$.
If we further simplified it and the decimal is to be removed then, \[1 \times {10^{ - 8}}\]
Thus \[0.00000001 = 1 \times {10^{ - 8}}\].

Note:
Note that when we have the numbers in the form $1,00,000$ and are to be expressed in standard form we use the same way but the power of $10$ is positive.
And in the case above, the value is very less because after decimal there are 7 more zeros but we are converting that less into standard form so that is done by power of 10 as minus. Negative power is nothing but lesser value. And we know as the decimal shifts the power increases. Thus it increased by 1 but in negative form.
$0.0000001$ and $1,00,000$ have tremendous differences between them.