Conversion & Finding Percentage

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Unit: Basic Algebra

Chapter: Conversion & Finding Percentage

Reference: – Introduction to Percentage, Converting Fractions to Percentages, Converting Decimals to Percentages, Converting Percentages to Fractions and Decimals, Finding Percentage of a Number, Finding What Percent One Number Is of Another, Real-Life Applications

After studying this chapter, you should be able to understand:

• Introduction to Percentage & Its Meaning
• Converting Fractions to Percentages
• Converting Decimals to Percentages
• Converting Percentages to Fractions and Decimals
• Finding Percentage of a Number
• Finding What Percent One Number Is of Another
• Real-Life Applications of Percentage

What is Percentage?

Let’s try to understand this by taking few live examples-

• We all often go for shopping and see discount offers that always attract us. We have seen “50% off” or similar offers written across many outlets.

Source: Kapdec.com

• We also take loans for homes or cars and the banks charge a certain rate of interest like 5.8% p.a. against houses or 7% p.a. against cars. (p.a. : per annum)

• We look at our cellphones and the screen displays the percentage (%) of battery left.

If we look at the examples above, the symbol “%” is used frequently.

So, what does it mean or represent?

Percent as the name says basically means out of 100 (per cent). It is simply a fraction with 100 as its denominator and is expressed as the numerator part followed by the symbol %.

Examples-

1. 22100
   

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    = 22%

where 22% means 22 out of 100.

1. 85100
   

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    = 85%

where 85% means 85 out of 100.

When we express a number in per cent form, it is called percentage.

Examples-

1. 63100
   

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    = 63%

1. 29100
   

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    = 29%

1. 15% = 15100
   

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1. 52% = 52100
   

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Conversions

• Conversion of Fractions into Percentage

• First, we convert the fraction into an equivalent fraction with denominator as 100.

• Then, we write the numerator of the new fraction followed by ‘%’ symbol to express it in percentage terms.

Examples-

1. Convert 510
   

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    into percentage.

510=5 ×1010 ×10 = 50100

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  = 50%

1. Convert 125
   

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    into percentage.

125=75 =7 ×205 ×20 = 140100

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  = 140%

1. Convert 13
   

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    into percentage.

13 = 13 ×1001 × 100

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  = 1300100

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  = 1300%  (Every whole number is also a fraction with denominator as 1)

Or

• We multiply the fraction by 100% (As 100% = 100100
  

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   = 1. So, the value of the fraction does not change)

• We then reduce the ‘fraction multiplied by 100’ into lowest terms and write the final number followed by a ‘%’ symbol.

Examples-

1. Convert 910
   

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    into percentage.

910=9 10×100% = 90010%= 90%

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1. Convert 625
   

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    into percentage.

625=325= 325 ×100% =32005% =

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 640%

1. Convert 13
   

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    into percentage.

2.  

13 = 13 × 100% = 1300%

• Conversion of Decimals into Percentage

• We can convert any decimal into percentage simply by multiplying it by 100%.

• Here, we first multiply the decimal by 100 i.e. the decimal point is shifted two places towards right and then the new number is written followed by % symbol.

Examples-

1. Convert 0.25 into a percentage.

0.25 = 0.25 × 100% = 25%

1. Convert 6.82 into a percentage.

6.82 = 6.82 × 100% = 682%

1. Convert 3.451 into a percentage.

3.451 = 3.451 × 100% = 345.1%

• Conversion of Percentage into Fractions

• We divide the fraction by 100 and remove the % symbol so the value remains the same (Since % = out of 100 = 100
  

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  )

• We then reduce this new fraction into lowest terms.

Examples-

1. Express 20% as a fraction.

20% = 20100=20 ÷ 20100 ÷ 20 = 15

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  (As GCF of 20 and 100 is 20)

1. Express 64% as a fraction.

64% = 64100=64 ÷ 4100 ÷ 4 = 1625

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  (As GCF of 64 and 100 is 4)

1. Express 234
   

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   % as a fraction.

234%=114%=114

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 × 1100= 11400

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  (As GCF of 11 and 400 is 1)

• Conversion of Percentage into Decimals

• We can convert any percentage into decimal simply by dividing it by 100 and removing the % symbol

• Here, we first divide the number by 100 i.e. the decimal point is shifted two places towards left and then the new number is written without % symbol.

Examples-

1. Convert 15% into a decimal.

15% = 15100

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 = 0.15

1. Convert 22.5% into a decimal.

22.5% = 22.5100

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 = 0.225

1. Convert 22.5% into a decimal.

155% = 155100

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 = 1.55