Question

Find the scientific notation of \[0.025\] .

Answer 1

Hint: 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 or, \[1 \leqslant \left| a \right| < 10\] . Here “b” is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

Complete step-by-step answer:
To write a number in scientific notation, we can write as follows:
 \[a \times {10^n}\] , where \[0 < a < 10\] and “n” is an integer.
In this question, the most probable value of “a” would be 2.5.
We can write 2.5 as, \[2.5 = 0.025 \times 100\]
Now to obtain the value we can multiply and divide the number by 100 hence we have,
 \[
  0.025 \times 100 \div 100 \\
   \Rightarrow 2.5 \div 100 \\
   \Rightarrow 2.5 \times {10^{ - 2}} \;
  \]
Since, \[\dfrac{1}{{{{10}^n}}} = {10^{ - n}}\]
 \[0.025\] Will shift to two decimal places when multiplied by 100 and by again dividing we have \[2.5 \times {10^{ - 2}}\] .
So, the correct answer is “ \[2.5 \times {10^{ - 2}}\] ”.

Note: Scientific Notation is a standard way of writing very large and very small numbers so that they are easier to both compare and use in computations. To write in scientific notation \[N \times {10^a}\] form can be followed. Where \[N\] is a number between 1 and 10, but not 10, and “a” is an integer. The decimal point of a number is moved until the new form is a number from 1 up to 10 and then the exponent is recorded as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether we move the decimal to the right or to the left.