any decimal that has only a finite number of nonzero digits is a terminating decimal. for example, 24, 0.82, and 5.096 are three terminating numbers. If r and s are positive integers and the ratio is r/s is expressed as a decimal, is r/s a terminating decimal?
1. 90<r< 100
2. s = 4
Thanks
terminating decimal
Would anyone be willing to elaborate on this a little for me? I think I get the explanation, but on a broader scope, Im not sure that Im grasping the concept, and what I would do if the answer set were different. Thanks for anyone that can help!chidcguy wrote:Answer is B
If we can express the denominator in the form of 2^x X 5^y the decimal will terminate.
4 is 2 ^ 2 X 5 ^ 0
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man think of 1/4, 2/4, 3/4. 4/4 ....etc, have you ever seen decimals recurring for this fractions ?
Hopefully, got the point.
Hopefully, got the point.
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I'll try. Think first of how you would write a terminating decimal as a fraction. If you saw, for example:phumbert wrote:Would anyone be willing to elaborate on this a little for me? I think I get the explanation, but on a broader scope, Im not sure that Im grasping the concept, and what I would do if the answer set were different. Thanks for anyone that can help!chidcguy wrote:Answer is B
If we can express the denominator in the form of 2^x X 5^y the decimal will terminate.
4 is 2 ^ 2 X 5 ^ 0
0.203
you'd write that as 203/1000. That is, any terminating decimal can be written with a power of 10 in the denominator. Here, we've used 10^3; prime factorize 10^3 and you have (2^3)*(5^3). That is, any terminating decimal can be written with only 2s and 5s in the prime factorization of the denominator. Some of the 2s and 5s might cancel; using a different example:
0.204 = 204/1000 = 51/250 = 51/[(2^1)*(5^3)]
but the point is, if you only see 2s and/or 5s in the denominator of a completely reduced fraction, the fraction definitely represents a terminating decimal, because you could multiply the numerator and denominator by 2s or 5s to get a power of 10 in the denominator. For example, if you had 11/125, which is 11/5^3, you could multiply by 2^3 to get 1000 in the denominator:
11/125 = 11/(5^3) = [11*(2^3)]/[(2^3)(5^3)] = 88/1000 = 0.088
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Im not sure if this rule applies here ( im too sleepy to solve this ) but anything that is divided by a power of 5 or 2 in the denominator will ALWAYS terminate.
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When I say a power of 5 or 2, I mean 2^X or 5^Y for all x, y E integers && X, Y != 0
so basically A/(2^X) would be terminating and B/(5^X) would be terminating.
so basically A/(2^X) would be terminating and B/(5^X) would be terminating.
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1/(3^2) is not equal to 0.1111111111.pepeprepa wrote:Can you explain further your tip because
1/(3^2)= 0.1111111111
1/(3^2) is equal to 0.11111111111111111111............, repeating forever. It is not a terminating decimal; it is what is called a 'recurring' or 'repeating' decimal. You can tell, by looking at the fraction 1/(3^2), that it will be a repeating decimal, because it is a reduced fraction, and there is a prime different from 2 or 5 in the denominator.
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ah! reduced was the key word. So basically if you have a fraction
ABC / XYZ, reduce it and now, if we have p/q and q is solely a power of 5 or 2 or both ( and nothing else - so eg p/15 wont make a terminating decimal) then its terminating.
Gurus - correct me if im wrong
ABC / XYZ, reduce it and now, if we have p/q and q is solely a power of 5 or 2 or both ( and nothing else - so eg p/15 wont make a terminating decimal) then its terminating.
Gurus - correct me if im wrong
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Yep Ian I am ok that's a non terminating decimal.
It was a counter-example to what I understood wrongly of sumithshah property.
Indeed what sumithsha told was: A/(2^X) would be terminating and B/(5^X) would be terminating.
Finally, any reduced fraction which has a prime at the denominator is a non terminating, am I right?
For example,
1/3
2/3
1/7
8/9
It was a counter-example to what I understood wrongly of sumithshah property.
Indeed what sumithsha told was: A/(2^X) would be terminating and B/(5^X) would be terminating.
Finally, any reduced fraction which has a prime at the denominator is a non terminating, am I right?
For example,
1/3
2/3
1/7
8/9
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6/3 will terminate, 14/7 will terminate toopepeprepa wrote:Yep Ian I am ok that's a non terminating decimal.
It was a counter-example to what I understood wrongly of sumithshah property.
Indeed what sumithsha told was: A/(2^X) would be terminating and B/(5^X) would be terminating.
Finally, any reduced fraction which has a prime at the denominator is a non terminating, am I right?
For example,
1/3
2/3
1/7
8/9
but it will not be decimal
if denumerator can be expressed in prime factorisation of 2 and 5 it is always terminal dicimal
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Ok for your principle:
"if denumerator can be expressed in prime factorisation of 2 and 5 it is always terminal dicimal"
But I don't understand what you mean by 6/3 and 14/7 I talk about reduced fractions...
"if denumerator can be expressed in prime factorisation of 2 and 5 it is always terminal dicimal"
But I don't understand what you mean by 6/3 and 14/7 I talk about reduced fractions...
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I'll try to state the rule as unambiguously as possible. If you need to know whether a fraction represents a terminating decimal:
1) Reduce the fraction completely;
2) Prime factorize the denominator;
3) Look at this prime factorization, and ignore the exponents. If there is a prime besides 2 or 5 in the denominator, the fraction represents a recurring (non-terminating) decimal. If the only primes in the denominator are 2, 5, or both, the fraction represents a terminating decimal.
So 9/125, 3/32, 7/80 and 3/30 are all terminating decimals (when you look at 3/30, you must reduce the fraction first, of course), while 7/121, 5/33, 7/60 and 19/99 all represent recurring decimals.
1) Reduce the fraction completely;
2) Prime factorize the denominator;
3) Look at this prime factorization, and ignore the exponents. If there is a prime besides 2 or 5 in the denominator, the fraction represents a recurring (non-terminating) decimal. If the only primes in the denominator are 2, 5, or both, the fraction represents a terminating decimal.
So 9/125, 3/32, 7/80 and 3/30 are all terminating decimals (when you look at 3/30, you must reduce the fraction first, of course), while 7/121, 5/33, 7/60 and 19/99 all represent recurring decimals.
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