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If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
 21 Mar 2012, 09:04
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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 fist nonzero digit to the right of the decimal point? A. Three B. Four C. Five D. Six E. Nine bunnel , can you please explain this problem
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TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B.
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Re: If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
21 Mar 2012, 10:56
Bunuel: Good approach!
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Re: If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
23 Mar 2012, 04:36
nice approach Bunuel. It shortens the long process and makes it less error prone. 
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Bunuel wrote: TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B. Can someone please explain how is multiplying 5^6 to the denominator (2^9 * 5^3) get 10^9?
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catty2004 wrote: Bunuel wrote: TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B. Can someone please explain how is multiplying 5^6 to the denominator (2^9 * 5^3) get 10^9? 5^6*(2^9*5^3) = 2^9*5^(6+3)= 2^9 *5^9 = (2*5)^9 = 10^9 Hope this helps...!!!
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Bunuel wrote: TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B. 1st method is really awasome to follow...thanks Bunuel
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Re: If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
16 Apr 2012, 06:14
Wow Bunuel, that was really good! 
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Re: If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
29 Apr 2012, 10:34
Please I would like to know why you multiplied by 5^6. and I did not understand your second approach.
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Re: If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal [#permalink]
29 Apr 2012, 13:08
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Terminating decimal OG [#permalink]
20 Oct 2012, 01:31
If t = 1 / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the first nonzero digit to the right of the decimal point? (A) Three (B) Four (C) Five (D) Six (E) Nine
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Re: Terminating decimal OG [#permalink]
20 Oct 2012, 02:25
t= 1 / (2^9 * 5^3) or t=1/(2^3*5^3)*2^6 t=1/(10^3)*64 1/64 will be 0.01 and shifting the decimal point by three places to account for 1/10^3.. we get 4 zeros followed by 1.. Ans:B)
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Re: Terminating decimal OG [#permalink]
20 Oct 2012, 02:58
With a question like this always try to convert the numbers to 10^(x) times something so that you can see the shift of the decimal point. As stated above, the answer is B.
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Re: Terminating decimal OG [#permalink]
20 Oct 2012, 04:19
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Hi, I still dont understand why we have to multiply by 5^6/5^6 i understand that this equals one but what is the general rule for this? how did you know to pick 5^6? Thanks Bunuel wrote: TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B. |
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shahir16 wrote: Hi, I still dont understand why we have to multiply by 5^6/5^6 i understand that this equals one but what is the general rule for this? how did you know to pick 5^6? Thanks Bunuel wrote: TomB wrote: If t = (1) / (2^9 * 5^3) is expressed as a terminating decimal, how many zeros will it have between the decimal point and the fist nonzero digit to the right of the decimal point?
A. Three
B. Four
C. Five
D. Six
E. Nine
bunnel , can you please explain this problem Given: t=\frac{1}{2^9*5^3}. Multiply by \frac{5^6}{5^6} --> t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625. Hence t will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}. Now, \frac{1}{64,000} is greater than \frac{1}{100,000}=0.00001 and less than \frac{1}{10,000}=0.0001, so \frac{1}{64,000} is something like 0.0000xxxx. Answer: B. Welcome to GMAT Club shahir16. We want the denominator of the fraction to be written as some power of 10. We need that in order to transform the fraction into decimal easily. Now, the denominator = 2^9 * 5^3, hence we need to multiply it by 5^6 to get 10^9. Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
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Can you please show me step-by-step how to convert 2^9 * 5^3 to a power of 10? I am unclear on the concept of converting an expression with exponents to a power of 10. I appreciate your help
Answer: B.[/quote][/quote]
Welcome to GMAT Club shahir16.
We want the denominator of the fraction to be written as some power of 10. We need that in order to transform the fraction into decimal easily.
Now, the denominator = 2^9 * 5^3, hence we need to multiply it by 5^6 to get 10^9.
Hope it's clear.[/quote]
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