The overall width in cm of several wide-screen televisions are 97.28 cm, 98(4/9) cm, 98(1/25) cm and 97.94 cm. Express these numbers as rational numbers in the form p/q and arrange the widths in ascending order.

Given

The overall width in cm of several wide-screen televisions are 97.28 cm, [latex]98\frac{4}{9}[/latex] cm, [latex]98\frac{1}{25}[/latex] cm and 97.94 cm.

Find out

We have to express the given numbers in rational numbers in the form p/q and arrange the widths in ascending order.

Solution

97.28 cm on converting into fraction using decimal method we get

= 9728/100 

On dividing both numerator and denominator by 4 we get,

= 2432/25cm

[latex]98\frac{4}{9}[/latex] cm 

On converting mixed fraction into improper fraction we get,

= 886/9 cm

[latex]98\frac{1}{25}[/latex]cm 

On converting mixed fraction into improper fraction we get,

= 2451/25 cm

97.94 cm

on converting into fraction using decimal method we get

= 9794/100 

On dividing both numerator and denominator by 2 we get,

= 4897/50cm

Let us take the LCM of denominators to arrange them in ascending order.

The LCM of the denominators 25, 9, 25 and 50 is 450

∴ 2432/25= [(2432×18)/ (25×18)] = (43776/450)

(886/9) = [(886×50)/ (9×50)] = (44300/450)

(2451/25) = [(2451×18)/ (25×18)] = (44118/450)

(4897/50) = [(4897×9)/ (50×9)] = (44073/450)

43776/450, 44300/450, 44118/450, 44073/450

Now, 43776 < 44073 < 44118 < 44300

On arranging in ascending order = (2432/25) < (4897/50) < (2451/25) < (886/9)

∴97.28 < 97.94 <[latex]98\frac{1}{25}[/latex] cm<[latex]98\frac{4}{9}[/latex]cm

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