# Math 115

posted by .

Every fraction has a decimal equivalent that either terminates (for example,1/4=0.25 ) or repeats (for example,2/9=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.
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 and which 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 or has a terminating decimal or a repeating decimal. Then confirm your prediction.

• Math 115 -

You posted this questin twice.

• Math 115 -

1/2=0.5
1/3=0.333333333333333
1/4=0.25
1/5=0.2
1/6=0.166666666666667
1/7=0.142857142857143
1/8=0.125
1/9=0.111111111111111
1/10=0.1
1/11=0.090909090909091
1/12=0.083333333333333

• Math 115 -

1/2=0.5
1/3=0.333333333333333
1/4=0.25
1/5=0.2
1/6=0.166666666666667
1/7=0.142857142857143
1/8=0.125
1/9=0.111111111111111
1/10=0.1
1/11=0.090909090909091
1/12=0.083333333333333
fractions with denominators of 3,6,7,9,11,12 (or multiples of these numbers) have decimal forms that repeat, while fractions with denominators of 2,4,5,8,10 (or multiples of these numbers)have decimal forms that terminate.

i predict that 1/25 has a terminating decimal
reason: 25 is a multiple of 5, which has a terminating decimal
1/25=.04 correct
Any power of 10 only has 2 and 5 as prime factors. So if the reduced fraction has a denominator with factors other than 2 or 5, those factors will always be there, and there will be no way to get the fraction expressed with a power of 10 for the denominator. So in conclusion: if the reduced form of the fraction has only 2 and 5 for prime factors in its denominator, then the decimal terminates.

## Similar Questions

1. ### Math 115

Every fraction has a decimal equivalent that either terminates (for example,1/4=0.25 ) or repeats (for example,2/9=0.2 ). Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You …
2. ### math

ACTIVITY 12: TERMINATE OR REPEAT? Every fraction has a decimal equivalent that either terminates (for example, ) or repeats (for example, ). Work with a group to discover which fractions have terminating decimals and which have repeating
3. ### Math

Can someone help me with this problem? A) Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two categories: those that can be written as a terminating decimal and those of non-terminating. Write an explanation of how
4. ### math

Separate the fractions 2/6,2/5,6/13,1/25,7/8and 9/29into two categories: those that can be written as a terminating decimal and those that cannot. Write an explanation of how you made your decisions. b. Form a conjecture about which …
5. ### Math

A terminating decimal ends after a certain finite number of decinal places, and does not have to be rounded off. An example would be 378 = 0.875 Your selfterminating decimal fractions are: 2/5, 1/25, and 7/8 So how would I form a conjecture …
6. ### math

How do you write repeating decimals as fractions?
7. ### math,algebra,fractions, decimals

Find 1 terminating decimal and 1 repeating decimal between 1/2 and 2/3.
8. ### Math

Need help with adding subtracting decimals. In this unit, you learned about fractions that can be written as terminating decimals and fractions that can be written as nonterminating decimals. Create an addition word problem and a subtraction …
9. ### Math

Need help with adding subtracting decimals. In this unit, you learned about fractions that can be written as terminating decimals and fractions that can be written as nonterminating decimals. Create an addition word problem and a subtraction …
10. ### CAN SOMEBODY HELP MEEEEEEE!!!!!!!!!!!

Need help with adding subtracting decimals. In this unit, you learned about fractions that can be written as terminating decimals and fractions that can be written as nonterminating decimals. Create an addition word problem and a subtraction …

More Similar Questions