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प्रश्न
Find the greatest and the smallest rational number among the following.
`(-2)/(3) , (-7)/(9) and (-5)/(6)`
उत्तर
Given numbers : `(-2)/(3) , (-7)/(9) and (-5)/(6)`
The L.C.M. of 3, 9 and 6 is 18.
Thus, numbers are :
`(-2)/(3) = (-2 xx 6)/(3 xx 6)`
= `(-12)/(18); (-7)/(9)`
= `(-7 xx 2)/(9 xx 2)`
= `(-14)/(18); (-5)/(6)`
= `(-5 xx 3)/(6 xx 3)`
= `(-15)/(18)`
Since -12 > -14 > -15, we have `(-2)/(3) > (-7)/(9) > (-5)/(6)`.
Hence, the greatest rational number is `(-2)/(3)` and the smallest rational number is `(-5)/(6)`.
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The average life expectancies of males for several states are shown in the table. Express each decimal in the form `p/q` and arrange the states from the least to the greatest male life expectancy. State-wise data are included below; more indicators can be found in the “FACTFILE” section on the homepage for each state.
| State | Male | `bb(p/q)` form | Lowest terms |
| Andhra Pradesh | 61.6 | ||
| Assam | 57.1 | ||
| Bihar | 60.7 | ||
| Gujarat | 61.9 | ||
| Haryana | 64.1 | ||
| Himachal Pradesh | 65.1 | ||
| Karnataka | 62.4 | ||
| Kerala | 70.6 | ||
| Madhya Pradesh | 56.5 | ||
| Maharashtra | 64.5 | ||
| Orissa | 57.6 | ||
| Punjab | 66.9 | ||
| Rajasthan | 59.8 | ||
| Tamil Nadu | 63.7 | ||
| Uttar Pradesh | 58.9 | ||
| West Bengal | 62.8 | ||
| India | 60.8 |
Source: Registrar General of India (2003) SRS Based Abridged Lefe Tables. SRS Analytical Studies, Report No. 3 of 2003, New Delhi: Registrar General of India. The data are for the 1995-99 period; states subsequently divided are therefore included in their pre-partition states (Chhatisgarh in MP, Uttaranchal in UP and Jharkhand in Bihar)
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