# Decimal

**Decimal number system**

Hello ScienceBee, lets learn about the decimal number system.

**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*/10^{n}, 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**

**Rational numbers**

**Video: What 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,

**Estimating decimal additions**

**Estimating decimal additions**

This video shows how to estimate decimal additions.

**Adding three decimals**

**Adding three decimals**

This video shows how to add three decimals.

**Converting decimals into fractions**

**Converting decimals into fractions**

This video shows how to convert decimals into fractions.

**Multi-digit division of decimals**

**Multi-digit division of decimals**

This video shows Multi-digit division of decimals,

**Calculate numbers with decimal exponents**

**Calculate numbers with decimal exponents**

This video shows how to calculate numbers with decimal exponents.

**Converting decimals to fractions**

**Converting decimals to fractions**

This video shows how to convert decimals to fractions.

**Converting decimals to percent**

**Converting decimals to percent**

This video shows how to convert decimals to percent.

**Converting decimals to mixed numbers**

**Converting decimals to mixed numbers**

This video shows how to convert decimals to mixed numbers.

**Converting decimals to binary**

**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

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