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Question
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.
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Solution
From the question,
The overall width in cm of several wide screen television are,
97.28 cm = `9728/100` ...[∵ By the decimal removing method]
By dividing both numerator and denominator by 4 we get,
= `2432/25` cm
By converting mixed fraction into improper fraction we get,
`98 4/9` cm = `886/9` cm
By converting mixed fraction into improper fraction we get,
`98 1/25` cm = `2451/25` cm
97.94 cm = `9794/100` ...[∵ By the decimal removing method]
By dividing both numerator and denominator by 2 we get,
= `4897/50` cm
Now, we have to 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 xx 18)/(25 xx 18)]`
= `43776/450`
`886/9 = [(886 xx 50)/(9 xx 50)]`
= `44300/450`
`2451/25 = [(2451 xx 18)/(25 xx 18)]`
= `44118/450`
`4897/50 = [(4897 xx 9)/(50 xx 9)]`
= `44073/450`
Then,
Now, 43776 < 44073 < 44118 < 44300
Hence, in ascending order = `2432/25 < 4897/50 < 2451/25 < 886/9`
∴ `97.28 < 97.94 < 98 1/25 "cm" < 98 4/9 "cm"`.
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