Simplification of Decimals


 
 
Concept Explanation
 

Simplification of Decimals

Simplification of Decimals: To simplify an expression containing symbols such as +, -, X, / and brackets we will follow the rule of BODMAS that is  Brackets, Off, Division, Multiplication, Addition and then Subtraction.

Rules to simplify a ratio of decimals

  • To simplify a ratio of decimals we remove the decimal point and reduce the ratio to a ratio of whole numbers.

  • We multiply the numerator and denominator of the ratio in fraction form by a 10, 100, 1000 i.e., a power of ten to eliminate the decimal.

  • Then the fraction is simplified to be in its lowest terms.

  • This gives simplified ratio of decimals as a ratio of whole numbers in simplest form.

  • Illustration: Simplify the ratio 4.8:5.6

    Solution: To simplify the ratios we will follow the following steps:

    Step;1:The ;ratio; 4.8:5.6=frac{4.8}{5.6}

    Step 2 : We multiply and divide the fraction by 10

    frac {4.8}{5.6} = frac{4.8times10} {5.6times10} = frac{48}{56}

    Step 3: HCF of 48 and 56 is 8. Simplifying

    frac{48 div 8}{56div 8}=frac{6}{7}

    Step 4: So, the simplified ratio of 4.8:5.6 is 6:7

    Illustration 2: Simplify the ratio 6.3:1.89

    Solution: To simplify the ratios we will follow the following steps:

    Step;1:The ;ratio; 6.3: 1.89=frac{6.3}{1.89}

    Step 2: We multiply and divide the fraction by 100

    frac {6.3}{1.89} = frac{6.3times100} {1.89times100} = frac{630}{189}

    Step 3: HCF of 630 and 189 is 63. Simplifying

    frac{630 div 63}{189div 63}=frac{10}{3}

    Step 4: So, the simplified ratio of 6.3:1.89 is 10:3

    Illustration 3: Simplify the following decimals: 17.709 + 9.001 - 10.02

    Solution: According to BODMAS: First do the addition: 17.709 + 9.001 = 26.710 or 26.71

    Now do the subtraction 26.71 - 10.02 = 16.69.

    Illustration 4: Simplify 1.6 × (0.5 + 0.3)

    Solution: First simplify the brackets:0.5 + 0.3 = 0.8

    Now multiply 0.16 x 0.8 = 1.28

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Which number is equal to:

    frac{0.1}{0.01} + frac{0.01}{0.1} ?

    Right Option : A
    View Explanation
    Explanation
    Question : 2

    Choose the correct option.

    Right Option : C
    View Explanation
    Explanation
     
     


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