Question

Convert 73 degree 25'30" into centesimal system ?

Answer 1

So 73 degree 25'30" in centesimal system is `81^g` `58'` `33.33''`

Explanation:

solution;
we know that,

In sexagesimal system or English system,

`1^o=60' = 3600''`

Therefore

`73^o 25' 30'' = (73*3600)'' + (25*60)''+30''`

.......................`= 262800'' + 1500'' +30''`

.......................`= 264330''`

.......................`= (264330*1/3600)^o [because 1''=(1/3600)^0]`

.......................`= (264330/3600)^o`

.......................`= 73.425^o`

Also we know that,

`pi^c = 180^o = 200^g`

so `1^o=(200/180)^g`
`therefore 73.425^o = (73.425*200/180)^g`

......................`=(14685/180)^g`

......................`=81.58333333^g`

Now in centesimal system

we know that,

`1^g = 100' = 10000''`

Therefore

`81.5833333^g =81^g` `(0.5833333*100)'`

.........................`= 81^g` `58.333333'`

.........................`=81^g` `58'` `(0.3333*100)` `[because 1' =100'']`

.........................`=81^g` `58'` `33.33''`

So 73 degree 25'30" in centesimal system is `81^g` `58'` `33.33''`