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Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL PDF Download

Definition

Decimal fractions are a fundamental aspect of mathematics, representing numbers that are less than one but more than zero. They are expressed with a decimal point, where the denominator is typically a power of 10. 

Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL

Let's explore decimal fractions in detail.

Understanding Decimal Fractions

Decimal fractions are numbers that include a decimal point to indicate values smaller than a whole unit. For example, numbers like 0.1 (one tenth), 0.25 (twenty-five hundredths), 0.008 (eight thousandths), and 0.333 (three hundred thirty-three thousandths) are all decimal fractions. The digits to the right of the decimal point represent parts of a whole, such as tenths, hundredths, thousandths, and so forth.


Decimal Fractions:

Decimal fractions are numbers less than one that are expressed using a decimal point. They are fractions where the denominator is a power of 10. Here are some examples:
Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL

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What is a decimal fraction?
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Conversion of Decimal to Vulgar Fraction:

To convert a decimal into a vulgar fraction:

  1. Put 1 in the denominator under the decimal point and add zeros equal to the number of decimal places.
    Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGLAnnexing Zeros and Removing Decimal Signs:
    • Annexing zeros to the right of a decimal fraction doesn't change its value. For example, 0.8=0.80=0.8000.8 = 0.80 = 0.8000.8=0.80=0.800.
    • When the numerator and denominator have the same number of decimal places, the decimal point can be removed.
      Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL

Question for Decimal Fractions: Notes and Important Formulas
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How can a decimal be converted into a vulgar fraction?
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Operations on Decimal Fractions

  • Addition and Subtraction: Align decimals and perform as usual.

    • Example: 5.9632+0.073=6.03625.9632 + 0.073 = 6.03625.9632+0.073=6.0362
  • Multiplication: Multiply without the decimal point, then place the decimal in the product according to the total decimal places.

    • Example: 0.2×0.02×0.002=0.0000080.2 \times 0.02 \times 0.002 = 0.0000080.2×0.02×0.002=0.000008
  • Division: Divide as normal and place the decimal in the quotient corresponding to the decimal places in the dividend.

    • Example: 0.0204÷17=0.00120.0204 \div 17 = 0.00120.0204÷17=0.0012
  • Comparison: Convert to decimal form to compare values.

Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL

Recurring Decimals:

  • If figures or sets of figures repeat indefinitely, it's a recurring decimal.
    • Example: 0.333...=0.30.333... = 0.\overline{3}0.333...=0.3, 3.142857142857...=3.1428573.142857142857... = 3.1428573.142857142857...=3.142857

Question for Decimal Fractions: Notes and Important Formulas
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Which operation should be used to align decimals and perform addition and subtraction?
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Pure and Mixed Recurring Decimals:

  • Pure Recurring Decimal: All figures after the decimal point repeat.
    Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGLMixed Recurring Decimal: Some figures repeat while others don't.

    • Example: 0.173333...=0.1730.173333... = 0.1730.173333...=0.173

Decimal fractions are essential in mathematics for precise representation of values less than one. They're used in everyday calculations, finance, science, and more. Understanding their conversion, operations, and recurring nature is crucial for mastering mathematical concepts and applications.

The document Decimal Fractions: Notes and Important Formulas | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
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FAQs on Decimal Fractions: Notes and Important Formulas - Quantitative Aptitude for SSC CGL

1. What are decimal fractions?
Ans. Decimal fractions are fractions where the denominator is a power of 10. They can be represented in decimal form, such as 0.5 or 0.75.
2. How do you convert a decimal fraction to a common fraction?
Ans. To convert a decimal fraction to a common fraction, you can write the decimal as a fraction with the decimal part as the numerator and the place value as the denominator. For example, 0.25 can be written as 25/100, which simplifies to 1/4.
3. What are some important formulas related to decimal fractions?
Ans. Some important formulas related to decimal fractions include converting fractions to decimals by dividing the numerator by the denominator, adding and subtracting decimals, multiplying decimals, and dividing decimals.
4. How do you compare decimal fractions?
Ans. To compare decimal fractions, you can align the decimal points and then compare digit by digit from left to right. If the digits are the same, move to the next digit until you find a difference.
5. How do you round decimal fractions to a certain place value?
Ans. To round a decimal fraction to a certain place value, identify the digit at the desired place value and look at the digit to its right. If that digit is 5 or greater, round up the digit at the desired place value; if it is less than 5, keep the digit at the desired place value the same.
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