# What is a decimal that has one or more digits that repeat forever?

1/3(.3 repeated), 2/3(.6 repeated), 1/9(.1repeated), 2/9(.2 repeated), etc. There are billions of repeating decimals.

### Is 5.7777 A rational number?

Yes. If you mean 5.7777 as a terminating decimal it is 57777/10000 If you mean 5.7777... as a recurring decimal where the 7 repeats forever it is 57/9 If a decimal number terminates or repeats one or more digits forever it is a rational number. Otherwise if a decimal number goes on forever but does not repeat any digits (eg √2 = 1.41421356...) then it is an irrational number.

### Are decimals rational?

Some are, some aren't. If the portion after the decimal point: terminates (eg 0.125); does not terminate, but repeats one or more digits (eg 0.333..., 0.181818...) does not terminate, but has one or more digits followed by one or more further digits that repeat (eg 0.16666..., 0.258373737...) then the decimal is rational. otherwise, if the decimal does not terminate and does not repeat any digits (eg π = 3.1415726..., √2 = 1.41421...) then the decimal…

### Is 0.01011011101111011111 rational or irrational?

All numbers with a finite number of decimal digits are rational. Some that infinitely many decimal digits are rational as well. If you mean to repeat the pattern, adding one more "1" every time, then no, it is not rational - rational numbers repeat the SAME sequence of digits over and over (for example, 0.1515151515...), at least eventually (they may start with some digits that are not part of the repeating part, such as 3.87112112112...).

### What makes a decimal repeating?

When you divide a number (like in long division) and end up with a remainder that keeps coming up the same remainder as you carry the numbers into the decimal portion. For example: 1 divide by 3: You start out 1.000 divide by 3, and 1 divided by 3 is zero, bring down the 1 and a zero and then you have 10 divided by 3 is 3 remainder 1, so now you have 0.3…

### Is 4.680 a rational number?

A rational number is any number that can be written in the form of one integer over another integer; all rational numbers have a decimal form that either terminates or repeats one, or more, digits forever. 4.680 is a terminating decimal, therefore it is a rational number. 4.680 = 4680/1000 = 468/100 = 117/25 -------------------------- The decimal form of a rational number will repeat forever if the prime factorization of the denominator contains any prime…

### What does a point over a number mean in mathematics?

that dot means reccurent, its usually above a decimal number, & means that digit continues on forever. E.g. put 1/3 as a decimal. this wouldn't be 0.3 it would be 0.3 (with the dot above the 3) so for the example above the answer is 0.333333333333333333333333333(continues on forever) By the way, the number can have a dot on more than one of its digits

### What is 2352 divided by .083?

According to the calculator built-in to Windows... 28337.34939759036144578313253012 -------------------------------------------------------------------- More accurately: 2352 ÷ 0.083 = 2352 ÷ 83/1000 = 2352 × 1000/83 = 28337 29/83 ≈ 28337.3494 (as the decimal is a non-terminating decimal repeating the 41 digits 34939759036144578313253012048192771084337 forever)

### Which is greater of two positive numbers?

It's the number that has more digits to the left of the decimal point (if there is no decimal point, it's the number with more digits). If the number of digits to the left of the decimal point is the same, find the position farthest to the left where the digits are different. The number with the greater of those two digits is the greater number. For example, 10000 is greater than 9999 because 10000…

### What is a recurring decimal?

A recurring decimal is a number which is written in decimal notation and in which, after a finite number of digits, a string of digits repeats for ever more. The repeating string need not start straight after the decimal point. For example, 5/26 = 0.1923076923076... with the string 923076 (but not the 1 at its start) repeating for ever.

### How can you find the repeating digits of a decimal when the calculator display is not long enough to show the repeating digits?

You can try to subtract the first few digits that are displayed from the answer, but note that calculators work to a limited precision so you may not be able to get much more than 10 to 12 digits this way and if the decimal has more than 12 digits you will not be able to find all the digits. The only solution is to do the long division (by hand, using the digits displayed…

### What is the decimal expansion of an irrational number?

A decimal expansion means to write out the base 10 digits of a number. Because irrational numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion: 3.14159265... Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if…

### 414 million in digits is there a simple way to do these conversions?

Just add 6 zeroes. Also, for readability, add commas: 414,000,000. For a number like "4.32 millions", you have to add 6 digits to the right of the decimal point - and eliminate the decimal point. Keep the existing digits, and if you need more digits, fill out with zeroes. This is the result: 4,320,000.

### What is repeating as an fraction?

A decimal fraction is said to be repeating if, after a finite number of digits, there is a string of a finite number of digits which repeats itself for ever more. For example, 1537/700 = 2.19571428571428... The first three digits in the decimal representation are not part of the repeating pattern. After that, however, the string "591428" repeats endlessly.

### Does pi ever repeat or end?

The decimal digits of Pi never end; they continue infinitely. The digits also will never repeat. These are characteristics of irrational numbers. Rational numbers have decimal fractions that either come to an exact end, or they fall at some point into an infinitely repeating pattern. 1/5 equals .25 exactly, and 1/3 has a repeating decimal fraction of .3333_. So far pi has been calculated out to at least 2.7 trillion decimal places, and since irrational…

### What is the Alphanumeric and Decimal System?

The decimal system is based on the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. For systems whose bases are greater than 10, you need more "digits" and, since there are no more single digits, you use these 10 digits together with some alphabetic characters. So, for base 12, you use A and B; for base 16 you use A, B, C, D, E and F and so on.

### What is the earliest occurrence of six consecutive decimal digits in pi?

The probability of a specific sequence of six consecutive decimal digits occurring early in the decimal representation of pi is usually only about 0. 08% (or more precisely, about 0. 0762%). However, if the sequence can overlap itself (such as 123123 or 999999) then the probability is less. The Feynman point is the first occurrence of four and five consecutive identical digits, but not six.

### Does the numbers of pi ever repeat themselves in any pattern?

For short stretches, yes, certainly. For example, there are 9 stretches of a number repeating 6 or more times (eg 333333) in the first million digits. Similarly, you can get 212121. But sooner or later the pattern and its repeat diverge. For short stretches, yes, certainly. For example, there are 9 stretches of a number repeating 6 or more times (eg 333333) in the first million digits. Similarly, you can get 212121. But sooner or…

### Is 9.565565556 rational?

9.565565556 = 9565565556/1000000000 = 2391391389/250000000 So it is rational. However, if you mean 9.565565556... where it continues with one more 5 than last time followed by a 6 and so on forever, then no, it is not a rational. ----------------------------------------------------------------------------------------- The decimal form of a rational number either terminates or continues with the same one or more digits repeating, eg 1.5, 1.333..., 1.1818181..., 1.1666..., 1.1565656... are all rational numbers. If the decimal does not terminate…