Question

Write the following as fractions in their simplest form
A) \[0.4\]
B) \[1.5\]
C) \[25.75\]
D) \[0.072\]
E) \[1.249\]

Answer 1

Hint:Fraction is a number which is of the form \[\;p\] by \[q\] where q is not equal to zero.That is, \[\dfrac{p}{q},(q \ne 0)\] and \[p,{\text{ }}q\] are the whole number.When the numerator and the denominator can no longer be reduced to any smaller number separately, then the fraction is in its simplest form.In decimal form, we observe that in some terms that is if a decimal point after a single (ones) digit we can multiply and divide by \[10\].If the decimal point after \[\;2\] digits we can multiply and divide by \[100\].

Complete step-by-step answer:
A) 0.4
Here \[0.4\] is the decimal number, the first decimal number changes into a fraction.
For that, multiply and divide by \[10\].
$ \Rightarrow 0.4 = \dfrac{{0.4 \times 10}}{{10}}$
Multiply the numerator we get,
$ \Rightarrow 0.4 = \dfrac{4}{{10}}$
On some simplification we get,
$ \Rightarrow 0.4 = \dfrac{4}{{10}} = \dfrac{2}{5}$
It cannot be reduced further, \[0.4\] is a decimal number and its simplest form of fraction is \[\dfrac{2}{5}\].

B) 1.5
Here, \[1.5\] is a decimal number,
For that, multiply and divide by \[10\]
$ \Rightarrow 1.5 = \dfrac{{1.5 \times 10}}{{10}}$
Multiply the numerator we get,
$ \Rightarrow 1.5 = \dfrac{{15}}{{10}}$
On some simplification \[\dfrac{{15}}{{10}}\] as
$ \Rightarrow 1.5 = \dfrac{3}{5}$
It cannot be reduced further, \[1.5\] is a decimal number and its simplest form of fraction is \[\dfrac{3}{5}\].

C) 25.75
Here, \[25.75\] is a decimal number,
For that, multiply and divide by \[100\].
$ \Rightarrow 25.75 = \dfrac{{25.75 \times 100}}{{100}}$
Multiply the numerator and we get,
               $ \Rightarrow 25.75 = \dfrac{{2575}}{{100}}$
On some simplification we get,
$ \Rightarrow 25.75 = \dfrac{{515}}{{20}}$
$ \Rightarrow 25.75 = \dfrac{{103}}{4}$
It cannot be reduced further, \[25.75\] is a decimal number and its simplest form of fraction is \[\dfrac{{103}}{4}\].

D) 0.072
Here, \[0.072\] is a decimal number,
For that, multiply and divide by \[1000\].
\[ \Rightarrow 0.072 = \dfrac{{0.072 \times 1000}}{{1000}}\]
Multiply the numerator term and we get,
$ \Rightarrow 0.072 = \dfrac{{72}}{{1000}}$
On some simplification we get,
$ \Rightarrow 0.072 = \dfrac{{18}}{{250}}$
$ \Rightarrow 0.072 = \dfrac{9}{{125}}$
It cannot be reduced further, \[0.072\] is a decimal number and its simplest form of fraction is \[\dfrac{9}{{125}}\].

E) 1.249
Here, \[1.249\] is a decimal number,
For that, multiply and divide by \[1000\].
$ \Rightarrow 1.249 = \dfrac{{1.249 \times 1000}}{{1000}}$
Multiply by numerator
$ \Rightarrow 1.249 = \dfrac{{1249}}{{1000}}$
It cannot be reduced further, \[1.249\] is a decimal number and its simplest form of fraction is \[\dfrac{{1249}}{{1000}}\].

Note:A fraction is said to be the simplest form as when the numerator and denominator of the fraction cannot be reduced to further. That is, divide the numerator and denominator by the greater number that will divide both numbers.A fraction is not a whole number but a number lies between the two whole numbers.The simplest form is the smallest possible equivalent fraction of the number.