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Expressing a Mixed Number as a Decimal Number and Vice Versa
Concept sheet | Mathematics
Secondary
1-2
In some situations, it may be useful to convert a mixed number to a decimal number or vice versa. The following concept sheet shows several methods that can be used to do this.
Expressing a Mixed Number in Decimal Notation
It is possible to express a mixed number directly as a decimal number.
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Identify the integer of the mixed number. This integer will be the whole number in the decimal notation.
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Divide the numerator by the denominator of the fraction in the mixed number.
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Add the integer and the result of the division to get the number in decimal notation.
Express |3\;\dfrac{2}{5}| in decimal notation.
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Identify the integer of the mixed number
The integer is |3.| The integer in decimal notation will also be |3.|
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Divide the numerator by the denominator of the fraction
The fraction is equal to |0.4.|
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Add the integer and the result of the division to obtain the number in decimal notation
||3+0.4=3.4||
Thus, ||3\dfrac{2}{5}=3.4||
Expressing a Decimal Number as a Mixed Number
It is possible to express a number written in decimal notation as a mixed number. Follow these steps.
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Identify the integer of the number written in decimal notation. This integer will be the whole number in the mixed number.
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Identify the decimal part of the number written in decimal notation and express it as a fraction.
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Write the mixed number composed of the integer followed by the fraction.
To express the decimal part as a fraction, we can simply read it.
For example, the decimal part |0.42| can be read as: "forty-two hundredths".
The fraction representing the decimal part is therefore |\dfrac{42}{100}.| The fraction can be expressed as “forty-two hundredths ”.
Once the decimal part is expressed as a fraction, the only remaining step is to simplify it!
Express |14.65| as a mixed number.
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Identify the integer of the number written in decimal notation
The integer is |14| . The integer of the mixed number will also be |14.|
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Determine the decimal part of the number written in decimal notation and express it as a fraction
The decimal part of the number is |0.65| and it reads as "sixty-five hundredths." It can be expressed as a fraction. For example: ||\dfrac{65}{100}||
Simplifying the fraction results in the following: ||\dfrac{65\color{green}{\div 5}}{100\color{green}{\div 5}}=\dfrac{13}{20}|| -
Write the mixed number composed of the integer followed by the fraction
So,||14.65=14\;\dfrac{13}{20}||