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The digits to the right of the decimal point indicate division by a power of 10:diegocuenca wrote:If t = 1/2^9 * 5^3 is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point? Any theories?
I read the problem as "One half to the power of 9 multiplied by five cubed." Did I make a fundamental mistake somewhere, or is this an issue where the questions on the site are not as easy to read as the questions from official materials?GMATGuruNY wrote:The digits to the right of the decimal point indicate division by a power of 10:diegocuenca wrote:If t = 1/2^9 * 5^3 is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point? Any theories?
.1 = 1/10 = 1/10¹.
.01 = 1/100 = 1/10².
.001 = 1/1000 = 1/10³.
To determine the number of zeros that will appear to the right of the decimal point when 1/(2�5³) is put into decimal notation, factor out as many 10's as possible from the denominator:
2�5³
=2� * (2³5³)
= 64 * (2*5)³
= 64 * 10³
= 64000.
Thus, 1/(2�5³) = 1/64000 = .00001...
There are 4 zeros to the right of the decimal point.
Ha, well actually, as it's written, it should technically be taken as "one divided by (2 to the 9th) -- all that times (5 to the third)." But the solutions above all assume that everything after the / is in the denominator of one single fraction (with a numberator of 1). So I think it is an issue of what you said. Technically, for onto-screen transfer (assuming our interpretation is correct, we'd need parentheses around (2^9 * 5^3). (And technically, had it intended to be "one half to the power of 9," it would've needed parentheses around the (1/2).) Order of operations tends to make us insert parentheses quite often when we translate once-vertical problems into strictly-horizontal problems!edvhou812 wrote:I read the problem as "One half to the power of 9 multiplied by five cubed." Did I make a fundamental mistake somewhere, or is this an issue where the questions on the site are not as easy to read as the questions from official materials?diegocuenca wrote:If t = 1/2^9 * 5^3 is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point? Any theories?
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