How many decimal places can a rational number have?

How many decimal places can a rational number have?

3 decimal places
Therefore, from the decimal representation of the given rational number we can see that there are only 3 decimal places. Hence, after three decimal places the decimal representation of the given rational number terminates.

Are finite decimals rational numbers?

Numbers with finite (i.e., terminating) decimal expansions, as well as those numbers that are infinite with repeat blocks, are called rational numbers.

Is rational number finite?

The set of rational numbers between 0 and 1 belongs to a finite segment but, in itself, is infinite. Among numbers, the notion of finiteness is an outgrowth of our ability to count. The last number to be called is the cardinality of the set.

Do all rational numbers have a decimal expansion?

The theorem. The content of the theorem is that any rational number, and only a rational number, has a repeating or terminating decimal expansion.

Which describes all decimals that are rational numbers?

All decimals which either terminate or have a repeating pattern after some point are also rational numbers. The number 0.2 is a rational number because it can be re-written as 15 . The number 0. 33333… is a rational number because it can be re-written as 13 .

How do you know if a decimal is rational?

In general, any decimal that ends after a number of digits such as 7.3 or −1.2684 is a rational number. We can use the place value of the last digit as the denominator when writing the decimal as a fraction.

How do you know if a decimal is finite?

A finite decimal is one that stops, like 0.157 ….To answer this question:

1. start by putting the fraction in simplest form;
2. then, factor the denominator into primes.
3. If there are only prime factors of 2 and 5 in the denominator, then the fraction has a finite decimal name.

Is a number that has a finite number of decimals?

A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point. A terminating decimal like 13.2 can be represented as the repeating decimal 13.20000000000000…, but when the repeating digit is zero, the number is usually labelled as terminating.

What is decimal expansion of rational number?

When the numerator of a rational number is divided by its denominator, we get the decimal expansion of the rational number. The decimal numbers thus obtained can be of two types. The decimal numbers having finite numbers of digits after the decimal point are known as the terminating decimal numbers.

What describes all decimals that are not rational numbers?

Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. These numbers include non-terminating, non-repeating decimals, for example , 0.45445544455544445555…, or . Any square root that is not a perfect root is an irrational number.

Can a rational number have an infinite decimal?

9 Answers. Rational numbers can have decimals and even an infinite decimals, BUT any rational number’s decimals will have a repeating pattern at some point whether it be like 2 3 = 0.666… or 92 111000 = 0.000828828828… or 3 2 = 1.500000000… The reason why √45 is not rational is not because it has decimals.

When is a decimal called a rational number?

Any decimal that can be converted to a fraction with an integer numerator and integer denominator is called a rational number; repeating decimals (even though they have an infinite number of decimal places) and decimals with a finite number of decimal places are all rational numbers.

Which is the only rational number that is finite?

Rational numbers are defined as the ratio of two (finite) integers, where the denominator is not 0, so using this definition, all rational numbers are finite. 8 clever moves when you have $1,000 in the bank. We’ve put together a list of 8 money apps to get you on the path towards a bright financial future. , PhD in algebraic topology.

Can a fraction be written as a decimal?

In some instances, a fraction cannot be written as a decimal with a finite (limited) number of decimal places. Consider, for instance, . Let’s look at a portion of the long division for this fraction. Clearly, the long division will continue indefinitely, adding additional sixes to the decimal without end.