Question

How do you write \[0.00001\] in scientific notation?

Answer 1

Hint: In order to convert \[0.00001\] into scientific notation, first move the decimal point in the number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number will be $ a $ . Count how many places we move the decimal point. This number will be $ b $ . Here we will move the decimal to the right, thus $ b $ is negative. Write the scientific notation number as $ a \times {10^b} $ , which is the required solution.

Complete step-by-step answer:
Now, we need to write \[0.00001\] in scientific notation.
Scientific notation is a special way of writing big and small numbers as small decimal values.
Here, the proper format for scientific notation is $ a \times {10^b} $ , where $ a $ is a number or decimal number such that the absolute value of $ a $ is greater than or equal to one and less than ten. $ b $ is the power of ten required so that the scientific notation is mathematically equivalent to the original number.
When we move the decimal point in the given number until there is only one non-zero digit to the left of the decimal point, then the number will be $ 1 $ . Hence, $ a = 1 $ .
And this number will be obtained when we move the decimal point to the right for $ 5 $ places. We know that when we move the decimal to the right then $ b $ is negative. Thus,
 $ b = - 5 $ .
Now let us substitute the values in $ a \times {10^b} $ , we have,
 $ = 1 \times {10^{ - 5}} $
Hence, the scientific notation of \[0.00001\] is $ 1 \times {10^{ - 5}} $ .
So, the correct answer is “ $ 1 \times {10^{ - 5}} $ ”.

Note: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or scientific index form or standard form. The base ten notations is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.