A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 - 10^2) (0.0012)?
Note: There is a bar over "12" in 0.0012. Couldn't figure out how to insert it.
(A) 0
(B) 0.12 (with the bar on 12)
(C) 1.2
(D) 10
(E) 12
A bar over
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The repeating digits beyond the bar represent values that are EXTREMELY SMALL relative to the other values.shahfahad wrote:A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 - 10^2) (0.0012)?
Note: There is a bar over "12" in 0.0012. Couldn't figure out how to insert it.
(A) 0
(B) 0.12 (with the bar on 12)
(C) 1.2
(D) 10
(E) 12
Thus, we can safely ignore the repeating digits beyond the bar.
(10� - 10²)(.0012)
= (10²)(10² - 1)(12/(10�)
≈ (10²)(10²)(12/10�)
= 12.
The correct answer is E.
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Another approach:
If xy is a two digit number (i.e. x = tens digit, y = units digit), then xy/99 = .xyxyxy...
We want this to be moved two places to the right, so we have xy/9900 = .00xyxyxy...
Hence .00121212... is 12/9900.
From there, we have (10� - 10²) * 12/9900, or 9900 * 12/9900, or 12.
If xy is a two digit number (i.e. x = tens digit, y = units digit), then xy/99 = .xyxyxy...
We want this to be moved two places to the right, so we have xy/9900 = .00xyxyxy...
Hence .00121212... is 12/9900.
From there, we have (10� - 10²) * 12/9900, or 9900 * 12/9900, or 12.