Question

Question 147
The overall width in cm of several wide-screen televisions are 97.28 cm, $98\frac{4}{9}cm,98\frac{1}{25}cm$ and 97.94 cm. Express these numbers as rational numbers in the form $\frac{p}{q}$ and arrange the widths in ascending order.

Answer 1

We have, width of televisions screen are $97.28cm,98\frac{4}{9}cm,98\frac{1}{25}cm$ and 97.94 cm.

Then, firstly, we convert all widths in the rational numbers.

i) $97.28cm=\frac{9728}{100}cm$ [remove decimal]

$\therefore \frac{p}{q}=\frac{2432}{25}cm$ [numerator and denominator both dividing by 4]

ii) $98\frac{4}{9}cm=\frac{886}{9}cm$ [convert mixed fraction into simple fraction]

$\therefore \frac{p}{q}=\frac{886}{9}cm$

iii) $98\frac{1}{25}cm=\frac{2451}{25}cm$ [convert mixed fraction into simple fraction]

$\therefore \frac{p}{q}=\frac{2451}{25}cm$

iv) $97.94cm=\frac{9794}{100}$ [remove decimal]

$\therefore \frac{p}{q}=\frac{4897}{50}cm$ [numerator and denominator both dividing by 2]

To arrange in ascending order, firstly we convert all the denominators same, then we get

$\begin{array}{ccccc}2& 25& 9& 25& 50\\ 25& 25& 9& 25& 25\\ 9& 1& 9& 1& 1\\ & 1& 1& 1& 1\end{array}$

$\therefore$ LCM of 25, 9, 50 $=2\times 25\times 9=450$

So, 97.28 cm = $\frac{2432}{25}=\frac{2432\times 18}{25\times 18}=\frac{43776}{450}$

$98\frac{4}{9}cm=\frac{886}{9}=\frac{886\times 50}{9\times 50}=\frac{44300}{450}$

$98\frac{1}{25}cm=\frac{2451}{25}=\frac{2451\times 18}{25\times 18}=\frac{44118}{450}$

$97.94cm=\frac{4897}{50}=\frac{4897\times 9}{50\times 9}=\frac{44073}{450}$

In ascending order, $\frac{43776}{450}<\frac{44073}{450}<\frac{44118}{450}<\frac{44300}{450}$

i.e. $97.28cm<97.94cm<98\frac{1}{25}cm<98\frac{4}{9}cm$