After how many decimal places will the decimal representation of the rational number 229 / 2²x5³ terminate ?
Answers
Answer:
after three places it will terminate
Answer:
To find : After how many decimal places will the decimal representation of the rational number 22922×57\frac{229}{2^2\times 5^7}
2
2
×5
7
229
terminate ?
Solution :
The rational number is represented as 22922×57\frac{229}{2^2\times 5^7}
2
2
×5
7
229
Multiply the numerator and denominator by 252^52
5
,
=229×2522×25×57=\frac{229\times 2^5}{2^2\times 2^5\times 5^7}=
2
2
×2
5
×5
7
229×2
5
=229×3227×57=\frac{229\times 32}{2^7\times 5^7}=
2
7
×5
7
229×32
=7328(2×5)7=\frac{7328}{(2\times 5)^7}=
(2×5)
7
7328
=7328(10)7=\frac{7328}{(10)^7}=
(10)
7
7328
=0.0007328=0.0007328=0.0007328
After 7 decimal places will the decimal representation of the rational number 22922×57\frac{229}{2^2\times 5^7}
2
2
×5
7
229
terminate.
#Learn more
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Step-by-step explanation:
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