Question

How do you write \[0.82\] as a fraction in its lowest form?

Answer 1

Hint: In the given question, we have been asked to convert a decimal number as a fraction. To do that, we first count the number of digits after the decimal point; let it be ‘c’. Then we just remove the dot and treat the new (dot-free) number as the numerator. The denominator is equal to the digit \[1\] followed by ‘c’ zeroes. Then we just reduce the obtained fraction into the lowest form if possible.

Complete step-by-step answer:
Given a decimal number, \[n = 0.82\].
Number of digits after decimal, \[c = 2\].
So, numerator \[ = 82\] and denominator \[ = {10^2} = 100\]
Hence, \[0.82 = \dfrac{{82}}{{100}}\]
Now we convert to the lowest form by dividing by the number which is a common divisor to both the numerator and denominator – here it is \[2\].
Thus, \[0.82 = \dfrac{{82}}{{100}} = \dfrac{{41}}{{50}}\]

Note: To convert a decimal to fraction, we just count the number of digits after the decimal point. Then, we make our denominator of the fraction by putting a number of zeroes equal to the number of counted digits, and the denominator as the whole number without the point. Then, if possible, we reduce the fraction to the lowest term. We must be careful while reducing the fraction into the lowest term as it is the place where a lot of error occurs.