Unit 3 sec 2.1

Unit 3 sec 2.1 what is a rational number

05 November 2015

23:03

A rational number is a number that can be written in the form of

 

The following numbers can be written in this form

Ø   any fraction fractions such as  and  are already written in the form above and so they are rational numbers.

Ø   Any mixed number mixed numbers like  can be written as top-heavy fractions, though they are rational numbers. For example,  =.

Ø   Any whole number. For example, 7 =  and 0 = .

Ø Decimal number with a finite number of digits after the decimal point. For example, 0.23 = and 41.2058 = .

Ø Some decimal numbers but infinitely many digits after the decimal point. For example, 0.333333 = .

Ø The negative number of any number above. For example, -4 =  and - = .

Perhaps you are now wondering whether there are any numbers that are not rational numbers. Some decimal numbers with infinitely many digits after the decimal point are not rational numbers.

Rational numbers as decimals

every rational number can be written as it decimal. To do this, you divide the integer on the top of the fraction by the integer on the bottom.

When you find it decimal in this way, there are 2 possibilities for the outcome. You might get a decimal number that has only a finite number of digits after the decimal point. This is called a terminating decimal. Alternatively, you might get the decimal number with a block of 1 or more digits after the decimal point that repeats indefinitely.

Decimal way. This is called a recurring decimal. There are 2 alternative notations for indicating a recurring decimal. If you would like to know why you always get either terminating or recurring decimal when you write a rational number as a decimal. You need to think about one division. So every rational number, when written in decimal form, is it a terminating or recurring decimal. But is the reverse true? That is, is every decimal rational number? Certainly every terminating decimal is a rational number, since it can be written in the form of an integer divided by and integer, as you saw at the beginning of this subsection.

The rational numbers are the decimal numbers that determine a tame draw recurring.

It has an infinite number of digits after the decimal point. The number is a recurring decimal as it does not have a fixed number of digits that keep repeating. So it is not a rational number. 1^st, however, it is important to make sure that you are proficient with arithmetical operations on fractions.