Question

Convert 1.44999... into a vulgar fraction.
(a) $\dfrac{29}{20}$
(b) $\dfrac{29}{30}$
(c) $\dfrac{29}{40}$
(d) None

Answer 1

Hint: We will use the rules of converting a mixed recurring decimal number into a vulgar fraction. We start by separating the whole number from the decimal if any. Then there is an explicit way to write the numerator and denominator of the fraction by looking at the digits to the right of the decimal. We will then add the whole number back to this fraction and get the desired vulgar fraction representing the given decimal number.

Complete step-by-step solution
The given number $1.449999...$ can be written as $1.44\overline{9}$. Now, we will separate the whole number from the given decimal number as follows,
$1.44\overline{9}=1+0.44\overline{9}$
Now we will represent $0.44\overline{9}$ in its fractional form. The numerator of this fraction is the difference between the number formed by all digits after the decimal while including the repeated digits only once and the number formed by the non-repeating digits. The number formed by all digits after the decimal while including the repeated digits only once is $449$. And the number formed by the non-repeating digits is $44$. So, the numerator is $449-44=405$.
The denominator of this fraction has as many 9's as the number of repeating digits followed by as many zeros as the number of non-repeating digits. We have one repeating digit and two non-repeating digits. So the denominator is $900$.
Hence, we get the fraction as $\dfrac{405}{900}$. Now, we will add the whole number that we separated in the first step back to this fraction, as follows,
$1+\dfrac{405}{900}=\dfrac{900+405}{900}$
So, the given number can be represented as a fraction as
$1.449999...=\dfrac{1305}{900}$
Reducing the above fraction, we get
$1.449999...=\dfrac{29}{20}$
Hence, the correct option is (a).

Note: Students might get confused if they do not know what vulgar fraction means. It is another name for a normal fraction or just fraction, where a part of the whole unit is expressed. It is essential that we are familiar with the rules for converting any type of decimal number to a fraction. We cannot miss any of the steps given in the rules. Otherwise, we will not be able to obtain the correct fraction that represents the given decimal number. While reducing a fraction, we divide the numerator and denominator by the same number.