Why is any rational number either a terminating or repeating decimal?

Why is any rational number either a terminating or repeating decimal?

It says that between any two real numbers, there is always another real number. So, any terminating decimal is a rational number. A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number.

Is 2/5 a repeating or terminating decimal?

If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.

Is 7/8 a repeating or terminating decimal?

1 Expert Answer To do this without a calculator, divide 7 by 8 longhand. Alas, I can’t really duplicate this, but the answer is . 875. It does not repeat, it terminates.

Is 7/24 a terminating decimal?


How do you know if a decimal is terminating?

Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal.

What do you mean by non terminating decimal?

a decimal numeral that does not end in an infinite sequence of zeros (contrasted with terminating decimal).

What is non terminating number example?

Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals. Non terminating decimals: Non terminating decimals are those which keep on continuing after decimal point (i.e. they go on forever). They don’t come to end or if they do it is after a long interval.

Is 7/9 a terminating decimal?

Answer and Explanation: To convert seven-ninths to a decimal, simply divide 7 by 9. As is evident from the image above, 7/9 is a non-terminating decimal equal to 0….

What is the example of non terminating decimal?

Terminating and Non-Terminating Decimals It is a decimal, which has a finite number of digits(or terms). Example: 0.15, 0.86, etc. Non-terminating decimals are the one that does not have an end term. It has an infinite number of terms.

What do you mean by non terminating?

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Examples. Pi is a non-terminating, non-repeating decimal.

How do you find a non terminating repeating decimal?

When we divide 125 by 99, we get “Non terminating repeating decimal”. It has been explained below. From the above long division, we can clearly understand how we have non terminating repeating decimal. When we divide 125 by 99, the digits after the decimal keep going infinitely and the repeated pattern is 26.

How do you find a number is terminating or non terminating?

6:01Suggested clip 85 secondsTrick to Identify Terminating Rational Numbers & Non-Terminating …YouTubeStart of suggested clipEnd of suggested clip

Is 17 8 has a terminating decimal expansion?

Hence, the decimal expansion of 178 is terminating. Since the denominator is not in the form 2m×5n, 2 m × 5 n , and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.

Is 7/15 a terminating decimal?

Since 7/15 have 15 as its denominator and factorization of 15 is 5×3, which is not in the form of 2^m×5^n. Therefore it will have non terminating repeating decimal expansion.

What is 3/4 as a terminating decimal?


Is 4 a terminating decimal?

To determine whether a given fraction, such as 4/5, can be written as a terminating or repeating decimal, divide the denominator into the numerator of the fraction. Since 5 divided into 4 is 0.8, 4/5 can be written as a terminating decimal.

What is 13 20 as a decimal?

0.65 is a decimal and 65/100 or 65% is the percentage for 13/20.