Respuesta :
Answer:
Here, we use an underscore preceding the repeating digit(s).
1/3 = 0.3_3
1/6 = 0.16_6
1/7 = 0.142857_142857
1/9 = 0.1_1
Step-by-step explanation:
You want the four largest unit fractions that are repeating decimals, and their decimal equivalents.
Repeating decimal
The decimal equivalent of a fraction will repeat if the denominator of that fraction has factors other than 2 and 5.
Larger fractions
A fraction with a given numerator will be larger if its denominator is smaller.
Largest repeating decimals
The fractions of interest will have denominators that are the smallest integers greater than 1 that have factors other than 2 and 5. Consider the integers:
2 . . . . factor is 2
3 . . . . suitable denominator
4 = 2² . . . . factors are 2
5 . . . . factor is 5
6 = 2·3 . . . . suitable denominator
7 . . . . suitable denominator
8 = 2³ . . . . factors are 2
9 = 3² . . . . suitable denominator
Using an overline to signify the repeating digits, the fractions of interest are ...
[tex]\dfrac{1}{3}=0.\overline{3}\\\\\text{ }\dfrac{1}{6}=0.1\overline{6}\\\\\dfrac{1}{7}=0.\overline{142857}\\\\\text{ }\dfrac{1}{9}=0.\overline{1}[/tex]
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Additional comment
The number of repeating digits may be as many as one less than the denominator. This is the case for 1/7, which has 6 repeating digits. 1/17 is another example, with 16 repeating digits.
The four unit fraction that has its numerator as 1 and a repeating decimal is
- 1/3, 1/6, 1/7, and 1/9
What are repeating decimals?
A repeating decimal are also called recurring decimal, is a time of decimal number with only digits that repeat after the decimal at regular intervals.
In mathematics, a repeating decimal is written in short form with an overline on the number that repeats
In the problem, the repeating fraction requires to have a unit numerator and the greatest. from knowledge of fractions, the ones with lesser numerators are the greatest.
The greatest is 1/3 = 0. 333.....
others are
1/6 = 0.166.....
1/7 = 0.142957142957.......
1/9 = 0.111111.........
Learn more about repeating decimals:
https://brainly.com/question/30144995
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