# Decimal

## Decimal number system

Hello ScienceBee, lets learn about the decimal number system.

## Decimal number system

Video: Introduction To Decimal Numbers / What Is A Decimal Point?

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.
It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as Decimal notation.
A decimal numeral, or just decimal, or, improperly decimal number, refers generally to the notation of a number in the decimal system, which contains a decimal separator (for example 10.00 or 3.14159). Sometimes these terms are used for any numeral in the decimal system. A decimal may also refer to any digit after the decimal separator, such as in "3.14 is the approximation of π to two decimals".
The numbers that may be represented in the decimal system are the decimal fractions, that is the fractions of the form a/10n, where a is an integer, and n is a nonnegative integer.
The decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator (see Decimal representation). In this context, the usual decimals are sometimes called terminating decimals. A repeating decimal, is an infinite decimal, that, after some place repeats indefinitely the same sequence of digits (for example 5.123144144144144... = 5.123144). An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits.

### Rational numbers

VideoWhat are Rational Numbers?

The long division allows computing the infinite decimal expansion of a rational number. If the rational number is a decimal fraction, the division stops eventually, producing a decimal numeral, which may be prolongated into an infinite expansion by adding infinitely many 0. If the rational number is not a decimal fraction, the division may continue indefinitely. However, as all successive remainder are less than the divisor, there are only a finite number of possible remainders, and after some place, the same sequence of digits must be repeated indefinitely in the quotient. That is, one has a repeating decimal. For example,
1/81 = 0.012345679012... (with 012345679 repeating).
Conversely, every eventually repeating sequence of digit is the infinite decimal expansion of a rational number. This is a consequence of the fact that the recurring part of a decimal representation is, in fact, an infinite geometric series which will sum to a rational number. For example,

This video shows how to estimate decimal additions.

This video shows how to add three decimals.

### Converting decimals into fractions

This video shows how to convert decimals into fractions.

### Multi-digit division of decimals

This video shows Multi-digit division of decimals,

### Calculate numbers with decimal exponents

This video shows how to calculate numbers with decimal exponents.

### Converting decimals to fractions

This video shows how to convert decimals to fractions.

### Converting decimals to percent

This video shows how to convert decimals to percent.

### Converting decimals to mixed numbers

This video shows how to convert decimals to mixed numbers.

### Converting decimals to binary

This video shows how to convert decimals to binary.

### Simplifying Ratios Involving Decimals and Fractions

This video shows how to simplify ratios involving decimals and fractions