Is one divided by 19 a rational number?

Question

How many digits will there be after the . and is it repetitive?

thanks!

Answer 1

Yes. In fact, the word "RATIOnal" means "can be expressed as a ratio of two integers". That ratio is 1/19, with 1 and 19 being the integers.

If you write out 1/19 as a decimal, it will look like this:
0.052631578947368421052631578947368...

After the initial 0.0, there is an 18-digit repeating pattern.

Answer 2

Hey there!

Yes. It IS rational. Rational numbers can be expressed in the form a/b. Since 1/19 can be expressed in this form, it is rational. All fractions are rational numbers and all repeating decimals are rational.

Repeating decimals include 0.11111111111... 0.12121212121212 ... etc.

Also all terminating decimals, like 0.5, are rational numbers.

1/19 is a repeating decimal, with digits like

0.0526315789474

I got only upto these decimal places. Even though they are not repeating, they will repeat, when they are expressed in more digits.

Hope it helps!

Answer 3

Emily, As I comprehend it, indexed right here are some definitions: Integers: ....., -3, -2, -a million, 0, a million, 2, 3, 4, ..... entire Numbers: 0, a million, 2, 3, 4, ..... organic Numbers: a million, 2, 3, 4, 5, ..... So, "2" is an integer, an entire sort, and a organic sort. 0 is an integer, an entire sort, yet no longer a organic sort "-3," or "unfavorable 3" is an integer, and neither an entire sort nor a organic sort. solutions on your questions: a million-Integers incorporate entire numbers, yet in addition incorporate unfavorable numbers 2-The sq. root of 25 is an integer; your reasoning is actual 3- A rational sort is any sort which would be written as a fragment in lowest phrases. Examples: a) 3/4, -2/3, b) terminating decimals, e.g., 0.25, which would be written as 25/one hundred or a million/4 c) integers, e.g., 572, which would be written as 572/a million, or -6, which would be written as -6/a million d) 0.11111111111111.....(or the different repeating decimal), which would be rewritten as a million/9 e) sq. roots of suitable squares, ?sixty 4, ?9, etc. -An irrational sort is any sort that may not rational. some examples are "pi," and sq. roots of numbers which at the instant are not suitable squares. The sq. root of any best sort, as an occasion, is irrational. 4)a real sort is any rational or irrational sort. Examples are integers, organic numbers, entire numbers, any fraction, any decimal, any sq. root of a remarkable sort, "pi," best numbers, etc. Any sort which would be represented on a sort line is a real sort. Examples of numbers which at the instant are not genuine are ?(-a million), and log(-a million). 5)See above sturdy success!

Answer 4

Yes, it's rational. A rational number just means that it can be expressed as a fraction.

I think there will be 18 digits before it starts repeating, but I'm not 100% sure on that.

Answer 5

YES since both 1 and 19 are integers.
16 decimal places.
Not repetitive.

Answer 6

Yes. All numbers that we use daily are rational numbers. They include integer numbers. Integer numbers are 'whole' numbers. 1, 2, 23, -67. Rational numbers are also include fractions of numbers like 1.0. 1.2, -12.2 etc. Irrational numbers are used to solve complex mathemetical problems. An example of an irrational number is the sqaure root of -1, which cannot be expressed using our daily numbers framework, noramlly denoted 'i'.

Answer 7

yes, a rational number is any number that can be describe by one number divided by another non-zero number. 1/19 qualifies as such.

Answer 8

Yes it rational. 18 digits before it repeats
0.05263 15789 47368 421 0526315789 47368 421 05......

Answer 9

no, rational numbers can only be whole numbers.

not sure what you mean by if it is repetitive or not, but if you do 1/19 on the calculator you come out to a decimal that does not have any pattern to the subsequent numbers.

Answer 10

yes,it is .0526315 Ans