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Question 108912: Can someone PLEASE HELP me with this problem, I really do NOT understand any of this problem , if someone could please explain and help me with all these questions to this problem I would so much appreciate it.
THANK YOU!!!!
Every fraction has a decimal equivalent that__either terminates (for example, 1/4 = 0.25) or repeats (for example,2/9 = 0.2). (The line is above the 2 of the 0.2) Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You may assume that the numerator of each fraction you consider is and focus your attention on the denominator. As you complete
the table below, you will find that the key to this question lies with the prime factorization of the denominator.
Prime Factorization
Fraction Decimal Form Terminate? of the Denominator _______________________________________________________________________________
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11
1/12
State a general rule describing which fractions have decimal forms that terminate andwhich have decimal forms that repeat.
Now test your rule on at least three new fractions. That is, be able to predict whether a fraction such as 1/25 or 1/30 has a terminating decimal or a repeating decimal. Then confirm your prediction.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Can someone PLEASE HELP me with this problem, I really do NOT understand any of this problem , if someone could please explain and help me with all these questions to this problem I would so much appreciate it.
THANK YOU!!!!
Every fraction has a decimal equivalent that__either terminates (for example, 1/4 = 0.25) or repeats (for example,2/9 = 0.2). (The line is above the 2 of the 0.2) Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You may assume that the numerator of each fraction you consider is 1 and focus your attention on the denominator. As you complete the table below, you will find that the key to this question lies with the prime factorization of the denominator.
Prime Factorization
Fraction Decimal Form Terminate? of the Denominator
_______________________________________________________________________________
1/2 = .5 so it is terminating
1/3 = .33333··· so it is repeating
1/4 = .25 so it is terminating
1/5 = .2 so it is terminating
1/6 = .166666··· so it is repeating
1/7 = .142857142857142857··· so it is repeating
1/8 = .125 so it is terminating
1/9 = .11111··· so it is repeating
1/10 = .1 so it is terminating
1/11 = .09090909··· so it is repeating
1/12 = .0833333··· so it is repeating
State a general rule describing which fractions have
decimal forms that terminate and which have decimal forms
that repeat.
The denominators of the fractions above whose decimal form
terminates are 2, 4, 5, 8, and 10. Each of these either has
prime factors 2 and/or 5, and ONLY those.
The denominators of the fractions above whose decimal form
is repeating are 3, 6, 7, 9, and 11. These all have at least
one prime factor which is neither 2 nor 5.
General rule: If the denominator of a common fraction which is
in lowest terms has no prime factor other than 2 or 5, its decimal
form terminates.
If the denominator of a common fraction which is in lowest terms
has any prime factor other than 2 or 5, its decimal form is a
repeating decimal.
Now test your rule on at least three new fractions. That is, be
able to predict whether a fraction such as 1/25 or 1/30 has a
terminating decimal or a repeating decimal. Then confirm your
prediction.
The denominator of 1/25 is 25, and 25 has no other prime factor
but 5, so its decimal form terminates as .04
The denominator of 1/30 is 30, and 30 has the prime factor 3
which is neither 2 nor 5, so its decimal form is the repeating decimal .033333···
The denominator of 3/16 is 16, and 16 has no prime factor other
than 2, so its decimal form terminates as .1875.
The denominator of 5/26 is 26, and 26 has the prime factor 13
but 5, so its decimal form is the repeating decimal
.1923076923076923076···
The denominator of 119/125 is 125, and 125 has no prime factor other
than 5, so its decimal form terminates as .952.
The denominator of 17/28 is 28, and 28 has the prime factor 7
which is neither 2 nor 5, so its decimal form is the repeating
decimal .60714285714285714285···
Edwn
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