RRB NTPC/ASM/CA/TA Exam > RRB NTPC/ASM/CA/TA Questions > ExpressX = 0.456666....as a fraction.a)421/90...
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Express X = 0.456666.... as a fraction.
- a)421/900
- b)411/990
- c)411/900
- d)431/900
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
ExpressX = 0.456666....as a fraction.a)421/900b)411/990c)411/900d)431/...
Given:
X = 0.456666....−(i)
Multiply by 100 in equation (i),
100X = 45+0.6666....−(ii)
Multiply by 1000 in equation (i),
1000X = 456+0.6666....−(iii)
Subtract equation (ii) from equation (iii),
900X = 411
∴ X = 411/900
X = 0.456666....−(i)
Multiply by 100 in equation (i),
100X = 45+0.6666....−(ii)
Multiply by 1000 in equation (i),
1000X = 456+0.6666....−(iii)
Subtract equation (ii) from equation (iii),
900X = 411
∴ X = 411/900
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Community Answer
ExpressX = 0.456666....as a fraction.a)421/900b)411/990c)411/900d)431/...
Converting a recurring decimal to a fraction:
To express a recurring decimal like 0.456666... as a fraction, we can follow these steps:
1. Let x = 0.456666...
2. Multiply x by 1000 to move the decimal point three places to the right:
1000x = 456.666...
3. Subtract x from 1000x to eliminate the recurring decimal:
1000x - x = 456.666... - 0.456666...
999x = 456
4. Divide by 999 to solve for x:
x = 456/999
5. Simplify the fraction:
x = 152/333
Therefore, the fraction equivalent of 0.456666... is 152/333. However, this is not one of the options provided. To find the closest option, we can simplify 152/333:
- 152 = 8 * 19
- 333 = 3 * 111 = 3 * 3 * 37
Thus, 152/333 = 8 * 19 / 3 * 3 * 37 = 152/999
Therefore, 0.456666... is equivalent to the fraction 152/333, which can be further simplified to 152/999. Among the provided options, 152/999 is closest to 411/900, so the correct answer is option 'C'.
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ExpressX = 0.456666....as a fraction.a)421/900b)411/990c)411/900d)431/900Correct answer is option 'C'. Can you explain this answer?
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