Real Numbers: Intro & Decimal Place Value

Introduction

Real numbers are the set of numbers that include both the rational and irrational numbers.

The rational numbers are numbers that can be written in the form of a fraction such as a/b where a and b are integers, but b is not equal to 0. This includes integers, terminating decimals, and repeating decimals as well as fractions.

Irrational numbers are numbers whose decimal form is nonterminating and nonrepeating. Irrational numbers cannot be written in the form a/b, where a and b are integers (b cannot be zero). So all numbers that are not rational are irrational. π is a well known irrational number.

Decimal Place Value 

The decimal place value chart shows the place value of decimal numbers. We know that place value is the numerical value represented by a digit in a number. Therefore, just like the whole number place value chart, decimal place value charts are used to identify the correct position of all the digits in a decimal number. This chart indicates the place value of the digits that are given before the decimal point and after the decimal point.

The place value to the right of the decimal point represents the fractional part of the number. For example, the number 0.56 is made up of 5 tenths and 6 hundredths. This can also be written as 0.56 = 0.5 + 0.06. In other words, it means, 0.56 = 5/10 + 6/100.

Reference:

Cuemath:Representation of Real Numbers on Number Line

Cuemath: Decimal Place Value