The repeating decimal 2.666... (2.6 repeating) converts to the improper fraction 8/3, or the mixed number 2 2/3, which is found by treating it as 2 + 0.666 . . . 2 + 0 . 6 6 6 . . . and converting the repeating part (0.666...) to 2/3.
Yes, 2.6 is a Rational Number, as it can be expressed in fraction or ratio form. Number 13/5 is the ratio of two integers that are 13 integers divided by 5 integers and expressed in fraction form (as p/q where q is not equal to 0). Hence, 2.6 is a rational number.
Both decimals, 2.6 and 2.60, are equal in value, despite the extra zero in 2.60. This is because trailing zeros do not affect the actual value of a decimal number. Thus, 2.6 is not larger than 2.60; they represent the same quantity.
The fraction 7/8 as a decimal is 0.875, which you get by dividing the numerator (7) by the denominator (8).
0.3333 is both recurring and non terminating - it's a rational number . As a sidnote: 0.333333 is terminating (and equals 3333331000000 instead of 13). You mean 0. ¯3.
A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely).
Writing 5/6 as a decimal using division method
To convert any fraction to decimal form, we just need to divide its numerator by denominator. This gives the answer as 0.833... So, 5/6 as a decimal is 0.833... Irrespective of the methods used, the answer to 5/6 as a decimal will always remain the same.
2.6 as a fraction is 2 3/5.
(A fraction can be written as a terminating decimal if the prime factors of the denominator consist of only two's and five's. If the prime factors of the denominator contain other numbers, then the fraction will produce a recurring decimal).
The answer for 2.66666666667 as a fraction is approximately 8/3.
Since both 2 and 6 are even numbers. Therefore, the GCF or the greatest common factor of 2 and 6 is 2. So, to simplify the fraction and reduce it to its simplest form we will divide both numerator and denominator by 2. Both 1/ 3 and 2/ 6 are equivalent fractions having the same value.
To convert 2.13 to a vulgar fraction, write it as 213/100, which is already in simplest form because 213 and 100 share no common factors other than 1, making it an improper fraction. If you meant 2.13 with the '13' repeating (2.13̄), the vulgar fraction is 211/99.
Note that 1 has decimal representation 1.000… which is just 1 + 0/10 + 0/100 + 0/1000 + … so if one realizes that decimal expansions are just a code for an infinite sum, it may be less surprising that two infinite sums can have the same sum. Hence 0.999… equals 1.
Sometimes, when we divide the numerator by the denominator, it becomes clear that the digits will keep repeating. In this case, we write the answer as a repeating decimal. In our answer, we write a bar over the repeating digits to show that they repeat.