Question

How do you write \[0.000000001\] in scientific notation?

Answer 1

Hint:To solve this problem, we have to understand the concept of scientific notation of a number. We know that the scientific notation is a method of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Complete step by step answer:
We know that all numbers in scientific notation or standard form are written in the form \[m \times {10^n}\], where \[m\] is a number between 1 and 10 which means that \[1 \leqslant \left| m \right| < 10{\text{ }}\]and the exponent n is a positive or negative integer.

Thus, we can convert \[0.000000001\] into scientific notation by using the following steps:
We will first move the decimal nine times to right in the number so that the resulting number will be \[m = 1\] which is equal to 1 but less than 10.Here, we have moved the decimal to the right, as a result the exponent \[n\] is negative.
\[n = - 9\]
Now, if we will write in the scientific notation form \[m \times {10^n}\], we get
$1 \times {10^{ - 9}}$
We can also write it as only ${10^{ - 9}}$

Thus, $1 \times {10^{ - 9}}$or ${10^{ - 9}}$ is the scientific notation form of \[0.000000001\] number.

Note:While solving this type of problem, one important thing to keep in mind is the direction in which we move the decimal. If we move the decimal in the right direction, the exponent value will be negative. And when we move the decimal in the left direction the exponent value will be positive. If we forget to consider this, the answer obtained will be wrong because of the wrong sign of the exponent.