Question

Convert the following decimals into fraction in the lowest terms.
(i) \[0.375\] (ii) \[0.444\]
A.(i) \[\dfrac{5}{8}\] (ii) \[\dfrac{{11}}{{25}}\]
B.(i) \[\dfrac{5}{8}\] (ii) \[\dfrac{{111}}{{250}}\]
C.(i) \[\dfrac{3}{8}\] (ii) \[\dfrac{{11}}{{25}}\]
D.(i) \[\dfrac{3}{8}\] (ii) \[\dfrac{{111}}{{250}}\]

Answer 1

Hint: To convert a decimal into a fraction of lowest term, we first assume that every decimal is a fraction with the numerator as decimal itself and denominator as \[1\]. Further we multiply the numerator and denominator with specific power of \[10\] so as to just remove the decimal and convert it into an integer.

Complete step-by-step answer:
The given decimals are \[0.375\] and \[0.444\].
For the first decimal that is \[0.375\] , we can write it in the form of fraction as \[\dfrac{{0.375}}{1}\].
Now, to convert into its lowest form, we have to remove the decimal from the numerator. We can do this by multiplying both the numerator and denominator with \[1000\] as that will shift the decimal after \[5\] which is the last non-zero number in the decimal.
Thus, we get \[\dfrac{{0.375 \times 1000}}{{1 \times 1000}} = \dfrac{{375}}{{1000}}\].
Now this can be easily simplified as both, numerator as well denominator are multiples of \[5\].
Thus, on simplification, we get \[\dfrac{{375}}{{1000}} = \dfrac{{75}}{{200}} = \dfrac{3}{8}\].
So, the lowest form of fraction of decimal \[0.375\] will be \[\dfrac{3}{8}\].
Now, for the decimal \[0.444\], it can also be written in fraction form with denominator as \[1\] and numerator as the decimal itself, which gives \[\dfrac{{0.444}}{1}\].
Here again, if we multiply the numerator as well as the denominator with \[1000\] we can just shift the decimal after the last \[4\] as it is the last non-zero number in the decimal.
This will give us \[\dfrac{{0.444 \times 1000}}{{1 \times 1000}} = \dfrac{{444}}{{1000}}\].
Now, both the numerator and denominator can be simplified as both are multiples of \[4\] so we divide both numerator as well as denominator by \[4\].
This gives us \[\dfrac{{\dfrac{{444}}{4}}}{{\dfrac{{1000}}{4}}} = \dfrac{{111}}{{250}}\].
Now, as it can be observed that the numerator and denominator cannot be simplified further.
So the lowest form of fraction of decimal \[0.444\] is \[\dfrac{{111}}{{250}}\].
Hence, the option (D) is the correct option.

Note: A simpler way of solving this can be individually dividing each option and checking which one of the answers match with the decimal values, however that may not work if options are not given. Students must make sure to divide numerator and denominator as long as they give an integer value up to a point where they cannot be divided further without giving a decimal.