7/6=1.1666. Write it in a non-terminating recurring decimal form.
Answers
Step-by-step explanation:
It is very simple to identify whether the decimals of a fraction will be terminating or not....
Let me explain with a few examples.
Here are a few numbers:
49/3 , 67/5 , 28/6 , 55/7 , 35/2 , 65/10 , 23 / 125
Let's solve these fractions to figure out what their decimals are:
1) 49/3 = 16.3333...
This number has recurring and non-terminating decimals.
2) 67 / 5 = 13.4
This number has terminating decimals.
3) 28 / 6 = 4.6666...
This number has recurring and non-terminating decimals.
4) 55 / 7 = 7.857142857...
This number has recurring and non-terminating decimals.
5) 35 / 2 = 17.5
This number has terminating decimals.
6) 65 / 10 = 6.5
This number has terminating decimals.
7) 23 / 125 = 0.184
This number has terminating decimals.
Did you observe a pattern?
All the numbers in the denominator which are divisible only by 2 and 5 are the terminating fractions....
No matter what the numerator is (but it should be a terminating fraction), if your denominator is in the form (2^x)(5^y), where x and y are whole numbers, the result will be a terminating fraction.
Take example of the number 100. Its prime factors are 2 and 5. (It can be written as (2^2)(5^2). (Here x = 2 and y = 2)
Which means its only factors are 2 and 5. Hence, of the denominator of any fraction is 100, your result will be a number with a terminating decimal.
So our conclusions are:
If the denominator of a fraction has only 2 and 5 as its prime factors, then the fraction will result into a number with terminating decimal.
Just keep a thing in mind....
If the numerator is perfectly divisible by the denominator, then there's no need to think!
66 / 3 = ?
It's not a number with a non terminating decimal! Because 66 is divisible by 3! You result will be 22...
Hope you find this explanation helpful. If there are any mistakes feel free to point out, and I'll be glad to know so. Also please tell me of you have a better explanation... Because I am still a student studying in school, my explanation may be lacking...:)
Thank you!
Step-by-step explanation:
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