Question

How do you convert 0.00008 into scientific form?

Answer 1

Hint: Take the decimal point next to the digit 8 by multiplying the given decimal number with \[{{10}^{5}}\]. To balance the relation divide the obtained result with \[{{10}^{5}}\]. Now, use the formula: - \[\dfrac{1}{{{a}^{m}}}={{a}^{-m}}\] to get the required expression in scientific form.

Complete step by step answer:
Here, we have been provided with the decimal number 0.00008 and we are asked to write it in the scientific form. But first we need to understand the meaning of ‘writing a number in scientific form’.
A scientific form is a way of writing down a very large or a very small number easily. For example: - let us consider a very large number like: - 50000000, so we can write this number in scientific form by considering a decimal point after the digit 5 and writing the number of places we have jumped as the positive exponent of 10. So, we have,
\[\Rightarrow 50000000=5.0\times {{10}^{7}}\]
Here, exponent is 7 because we jumped 7 places to the left to move the decimal point.
Small numbers are also written in scientific form. However, instead of the index being positive, it will be negative. This is because here the number will be very small in comparison to 1 and we will jump the decimal point to the right. Let us consider the number given in the question. As we can see that 0.00008 is very small in comparison to 1, so to move the decimal point to the right we need to multiply it with a larger number. Since, we need to shift the decimal point after 8, i.e., five place to the right, so we need to multiply it with \[{{10}^{5}}\] and to balance the result we need to divide it with \[{{10}^{5}}\], so we have,
\[\Rightarrow 0.00008=\dfrac{{{10}^{5}}\times 0.00008}{{{10}^{5}}}\]
\[\Rightarrow 0.00008=\dfrac{8.0}{{{10}^{5}}}\]
Using the formula: - \[\dfrac{1}{{{a}^{m}}}={{a}^{-m}}\], we get,
\[\Rightarrow 0.00008=8\times {{10}^{-5}}\]
Here, \[8\times {{10}^{-5}}\] is the scientific representation of 0.00008.

Note:
One may note that the scientific form of a number is also known as standard form or standard index form. We generally use these representations to make our calculations easy. Certain formulas of exponents and powers are used in scientific calculations and the concept of rounding off is introduced.