Percentage
Percentage is basically a fraction or ratio of two values scaled by a factor of 100 so that a fractional value of 1 is equivalent to the percentage of 100. The term ‘percent’ is represented by the symbol %. Mathematically, one percent means one one-hundredth.
To convert a fractional value to a percent, multiply the fractional value by 100. If the fractional value is expressed as a decimal number, simply move the decimal point two positions to the right. Then add the percent symbol (%).
To convert a percent to a decimal number, simply move the decimal point two positions to the left. Then, drop the percent symbol.
Example 1: Express 34% as a decimal number.
Solution: since the decimal point is understood to follow the 4 (that is, 34 is 34.), we move the decimal point two positions to the left and drop the % symbol, so that 34% is equivalent to the decimal number 0.34.
Example 2: Express 1.375% as a decimal number.
Solution: we move the decimal point two positions to the left and drop the % symbol. Since there are no digits to the left of the 1, we add a zero to count our two positions to the left and drop the % symbol, so that 1.375% is equivalent to the decimal number 0.01375.
Example 3: Express 135% as a decimal number.
Solution: since the decimal point is understood to follow the 5 (that is, 135 is 135.), we move the decimal point two positions to the left and drop the % symbol, so that 135% is equivalent to the decimal number 1.35.
Example 4: Express the decimal number 0.685 as a percentage.
Solution: we move the decimal point two positions to the right and add the % symbol, so that 0.685 is equivalent to 68.5%.
Example 5: Express the decimal number 2.46 as a percentage.
Solution: we move the decimal point two positions to the right and add the % symbol, so that 2.45 is expressed as 245%.
Example 6: Express the fraction as a percentage.
Solution: we first calculate the decimal value of the fraction as 0.35. We then move the decimal point two positions to the right and add the % symbol, so that is expressed as 35%.
Now, try these problems:
Express the following percentages as a decimal number and as a fraction and simplify: (a) 1.25%, (b) 12.5%, (c) 125%
Express the following numbers and fractions as percentages: (a) 1/4, (b) 0.059, (c) 1.254
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