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Decimals

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Demystifying Decimals: A Comprehensive Guide to Decimal Numbers and Their Significance

Comprehensive Definition, Description, Examples & Rules 

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Introduction to Decimals

Numbers are important mathematical elements that are known and classified into various types like natural numbers, rational, irrational, and more. Decimal numbers are another of the important elements to classify. 

Let’s understand what is a decimal?

Decimals are numbers with a fractional part and a whole number. A dot or point present in between numbers that is a fractional part and a whole part is called a decimal point. Such as 0.8 which can be written as 08/10.

Decimal numbers are highly critical in real-life situations such as property measurements, etc. They are used in varied industries like sports, commerce, science, finance, construction, etc. In many instances where accurate measurement is required, it can result in decimal points or decimal numbers.

Understanding Decimal Numbers

Decimals definition states decimal numbers are important when it comes to accurate measurements for any number. 

The decimal definition  states that these numbers are a part of the whole number and the fraction part. The decimal part of a whole number works when you start with extending the place values to the right making every value on the right 10 times smaller as you place on the right side. This allows number representation that has whole numbers.

Decimal Places

Now that we know what is a decimal, we will discuss decimal places. There are different decimal places in numbers that classify differentiates: 

Decimal places or place values define the positions of decimal places in numbers which determine the value. The position of the digit is important when writing specific measurements. 

The various place values include 

  • Ones (1s) 
  • Tens (10s) 
  • Hundreds (100s) 

Tens are 10 times bigger than 1s, and Hundreds are 10 times 10s. These are the main decimal points. However, place values can go left and right from the decimal point. 

On the left side of the decimal point include ones, tens, hundreds, thousands, ten thousand, hundred thousand, and millions. On the right side also tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths, millionths. 

These values are ranked as it’s written. 

For instance 456.34

  • 6 is one’s decimal place. 
  • 5 is Ten’s decimal place. 
  • 4 is a hundred decimal places. 
  • 3 is the tenth decimal place. 
  • 4 is the hundredth decimal place.

The Decimal Point

The position of the decimal point determines the value of the number. Decimal definition states the decimal points separate the whole number and fraction part. Often when you divide complex numbers, the digits after the decimal increase for more accurate measurement. 

How does the decimal point affect the value of a number? 

The decimal point placed at different positions in a number or digit can increase or decrease its value. The values of decimals are determined or counted from the left and right sides of the point as mentioned in decimal places. 

The decimal values move from right to left. 

Key Concepts:

Decimals and integers are an important part of mathematics. Integers can be positive, negative, zero, or non-zero and do not have decimal places. For instance, 4, 5, 6, 7, etc., are integers. 

Decimals have the whole number and fraction part, the decimal numbers can have many place values or decimal places. Such as 0.4, 56.7, 456.777, 9876.09875, etc., are decimal numbers. 

Decimal representation in comparison to fractions.

Decimals separate the whole number and fraction part, they can be divided and written into fractions. The decimal to fraction and fraction to decimal can be converted easily. The methods are: 

Decimal to fraction 

For instance 0.65 

The expanded form – 0.65 = 65x(1/100)= 65/100=¾.

Fraction to decimal 

For instance, 6/7 when divided you get 0.8571428571

Creating a Visual Aid

Here is the structure of decimal numbers: 

decimal number

Here is the visual representation of decimal places and decimal points:

decimal point

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Key Takeaways

  1. Decimal numbers are an important classification in mathematics. 

  2. They separate the whole number and fraction part by decimal point or dot. 

  3. The decimal numbers are used for accurate measurements in mathematics. 

  4. Decimal numbers are used in varied industries like finance, real estate, science, and more. 

  5. Decimal numbers have various place values to determine the value of numbers. 

  6. Decimal numbers are separated on the right and left sides with a decimal point in the center. The left side of the decimal point is the whole number part and the right of the decimal point is the fraction part.

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Frequently Asked Questions

A decimal point in a number is a dot or point used to separate the whole number part from the fractional part. Such as 12.0, 0.3, 67.8, 45.5, 76.5, etc.

Decimal numbers can be read and interpreted as whole numbers as whole and separately after decimal.

The decimal fractions are written in the form of p/q where p is the numerator and q is the denominator. Decimals can be written with decimal points. Fractions can be converted into decimal points and decimal points can be converted into fractions.

Often people confuse decimal places when writing about various number positions.

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2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers
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