SOLUTION: express the foloowing recurring decimals as an infinite G.P. and then find out their values as a rational number. the *x* refer to the recurring part
(a)0.*7*
(b)0.3*15*
Algebra.Com
Question 1122513: express the foloowing recurring decimals as an infinite G.P. and then find out their values as a rational number. the *x* refer to the recurring part
(a)0.*7*
(b)0.3*15*
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
(a) x = 0.*7* = 7/10 + 7/100 + 7/1000 + ...
This is a geometric progression with first term 7/10 and common ratio 1/10; the infinite sum is
Answer: 0.*7* = 7/9
(b) x = 0.3*15* = 3/10 + 15/1000 + 15/100000 + 15/10000000 + ...
After the first term, the rest is a geometric progression with first term 15/1000 and common ratio 1/100; its infinite sum is
Then the entire decimal number is
Answer: 0.3*15* = 312/990; simplify if required.
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