Question

Express \[1.27\] in the form of \[\dfrac{p}{q}.\]

Answer 1

Hint: Here, we will remove the decimals to convert the decimal into fraction. Then we will simplify further (if possible) to get it in the simplified fraction form. A fraction is defined as a part of the whole number or a whole divided into equal parts.

Complete step-by-step answer:
Here we will follow the rules while converting a decimal number into a fraction.
First, we will rewrite the decimal as a fraction by writing the decimal number as the numerator and the number 1 as the denominator. Then we will multiply the numerator and the denominator by the number 10 raised to the power of \[n\] where \[n\] is the number of digits after the decimal point. Now, we will express into a fraction which can be reduced into its simplest form.
Let \[x\] be the given number.
So, we get \[x = \dfrac{{1.27}}{1}\]
By multiplying and dividing by \[100\], we get
\[ \Rightarrow x \times \dfrac{{100}}{{100}} = \dfrac{{1.27}}{1} \times \dfrac{{100}}{{100}}\]
Thus, we get
\[ \Rightarrow \dfrac{{100x}}{{100}} = \dfrac{{127}}{{100}}\]
By cancelling common terms from both the sides, we get
\[ \Rightarrow 100x = 127\]
Dividing both side by 100, we get
\[ \Rightarrow x = \dfrac{{127}}{{100}}\]
Thus the decimal \[1.27\] can be expressed into a fraction \[\dfrac{{127}}{{100}}\] .
Therefore, the decimal \[1.27\] can be expressed in the form of fraction as \[\dfrac{{127}}{{100}}\] .

Note: We know that the number which can be expressed as the ratio of two integers, then the number is said to be a rational number. Therefore the given number is a rational number. A decimal point is said to be a terminating decimal if it has no repeating digits. We should also know that if a decimal number is multiplied by the powers of 10, then the decimal moves towards the right and if a decimal number is divided by the powers of 10, then the decimal moves towards the left. The number of digits moved is according to the powers of 10.