Question

Express \[250\% \] as a decimal and a fraction.

Answer 1

Hint: In decimal form of a number the whole number is separated from the fractional part by a decimal point and a fraction represents a part of a whole.

Complete step-by-step answer:
In the decimal form the whole number and the fractional part are separated by a decimal point. In our case we have \[250\% \]. If we can express any number in the fraction form as \[\dfrac{x}{{100}}\] then it is equal to \[x\% \].
\[\therefore 250\% \] \[ = \] \[\dfrac{{250}}{{100}}\]
\[ \Rightarrow \] \[250\% \] \[ = \] \[\dfrac{{25 \times 10}}{{10 \times 10}}\]
Cancel out the common factor of \[10\]:
\[ \Rightarrow \] \[250\% \] \[ = \] \[\dfrac{{25}}{{10}}\]
\[ \Rightarrow \] \[250\% \] \[ = \] \[2.5\]

A fraction is the expression of a part of a whole thing. The following fraction \[\dfrac{a}{b}\] represents that \[a\] is a part of the whole system \[b\].
From the previous step:
\[250\% \] \[ = \] \[\dfrac{{250}}{{100}}\]
\[ \Rightarrow \] \[250\% \] \[ = \] \[\dfrac{{25 \times 10}}{{10 \times 10}}\]
Cancel out the common factor of \[10\]:
\[ \Rightarrow \] \[250\% \] \[ = \] \[\dfrac{{25}}{{10}}\]
\[ \Rightarrow \] \[250\% \] \[ = \]\[\dfrac{{5 \times 5}}{{5 \times 2}}\]
Cancel out the common factor of \[5\]:
\[ \Rightarrow \] \[250\% \] \[ = \] \[\dfrac{5}{2}\]

Additional information:
Any fraction has two parts: a numerator and a denominator. That is for any fraction \[\dfrac{a}{b}\] the numerator is \[a\] and the denominator is \[b\]. For example for the fraction \[\dfrac{5}{9}\], the numerator is \[5\] and the denominator is \[9\].

Note: The fraction \[\dfrac{5}{2}\] can also be expressed as \[2\dfrac{1}{2}\], this form is known as a mixed fraction. A mixed fraction is the combination of a whole number and a proper fraction.
To convert an improper fraction to mixed fraction follow the following method taking the example of the above conversion:
Divide the numerator of the fraction by the denominator to obtain a quotient and a remainder:
Fraction: \[\dfrac{5}{2}\], dividing \[5\] by \[2\], the quotient obtained is \[2\] and the remainder obtained is \[1\].
Next, note that the quotient represents the whole number part and the remainder divided by the denominator of the original fraction denotes the fractional part of the mixed fraction:
Quotient: \[2\], Remainder divided by denominator : \[\dfrac{1}{2}\]
\[\therefore \] Mixed fraction form \[ = \] \[2\dfrac{1}{2}\].