Question

The decimal form of : $ - \dfrac{5}{6} $ is
A.-0.833
B.-0.8
C.-0.811
D.-0.888

Answer 1

Hint: Decimal numbers are the number in which number is written in two parts which are separated by decimal. One part is the whole number and the other part is the fractional part. In this question we will convert the fraction given into decimal form by multiplying with the numerator and denominator which converts the denominator in the power of 10.

Complete step-by-step answer:
Given:
The given fraction is $ - \dfrac{5}{6} $ .
We are required to convert this fraction into decimal form. Hence, to convert the given fraction into decimal form, we will need to make the denominator in the power of 10. This can be easily done when the denominator has the prime factor 2 and 5. Then we can multiply the denominator with 2 and 5 to get the power of 10. When 3 is the factor we can multiply the denominator with 333 so that it will become 999 which is nearly 1000.
In our question denominator is 6 which has the factors as 2 and 3. We need to multiply the denominator with 333 and 5. We will also multiply the numerator with 333 and 5. This can be expressed as:
 $ \begin{array}{c}
 - \dfrac{5}{6} = \dfrac{5}{{2 \times 3}}\\
 - \dfrac{5}{6} = \dfrac{{5 \times 5 \times 333}}{{2 \times 3 \times 5 \times 333}}
\end{array} $
We will rewrite the above expression as,
 $ - \dfrac{5}{6} = \dfrac{{8325}}{{10 \times 999}} $
Since 999 is nearly 1000 we can write the above expression as,
 $ \begin{array}{c}
 - \dfrac{5}{6} = - \dfrac{{8325}}{{10 \times 1000}}\\
 = - 0.8325\\
 \approx - 0.83
\end{array} $
Hence the decimal form of the fraction $ - \dfrac{5}{6} $ is $ - 0.83 $ and option (E) is the correct answer.
So, the correct answer is “Option E”.

Note: There are certain tricks to find the decimal of the fractions according to the factors of the denominator. In this question, the factors are 3 and 2. Hence we have multiplied with 333 and 5 but if the factors were different we can multiply the denominator with the terms which convert the denominator in the power of 10.