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Percentage as fraction or decimals

- Calculus
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Did you know that **percentages** can also be represented **as fractions or decimals**? Herein, you would know how **percentages** can be **changed** to **fractions and decimals.**

Equivalent fractions, decimals, and percentages are fractions, decimals, and percentages that are of the same value regardless of the way they are being expressed.

This means that if converted from one mathematical form (such as fraction, decimal, and percentages) to another, It would be the same.

To illustrate further, the fraction, the decimal 0.5 as well as 50% are all equivalent. To determine if they are equivalent, try converting from one form to another. Therefore,

Afterward, we would go into detail as to how to make these conversions.

Fractions are expressed as percentages by multiplying them by 100%.

Effectively, multiplying the fraction by 100% does not change its value rather the form is changed because 100% is actually 1.

Note that,

Convert the following from fractions to percentages.

a)

b)

**Solution:**

a) To convert to percentage, multiply it by 100%.

b) To convert to percentage, you have to begin by converting the mixed fraction to an improper fraction. Therefore,

Now, you can multiply the resulting improper fraction by 100%.

Just as fractions can be converted to percentages, percentages can be converted to fractions. This is achieved by dividing the percentage by 100% to arrive at the equivalent fraction.

Convert the following percentages to fractions.

a) 75%

b) 260%

**Solution:**

a) To convert 75% to fraction, divide 75% by 100%.

b) To convert 260% to fraction, divide by 100%

Decimals are converted to percentages by multiplying the decimal by 100%.

Convert the following to percentage.

a) 0.7

b) 1.6

**Solution:**

a) Multiply the decimal by 100%.

b) Multiply the decimal by 100%.

Percentages can be converted to decimals by dividing the percentage by 100%. Note that a fraction is initially arrived at, afterward, you are to convert the fraction to decimal following the steps earlier explained herein.

Convert the following to decimals.

a) 70%

b) 160%

**Solution:**

a) Divide by 100%;

Convert the fraction to decimal using the steps explained earlier.

b) Divide by 100%;

Convert the fraction to decimal using the steps explained earlier.

Decimals are converted to fractions by following the following steps:

Determine how many decimal places (d.p) - this is done by counting the numbers after the decimal point.

The number of decimal places will determine how many 0s, 1 d.p would be 10, 2 d.p is 100, 3 is 1000, and so on.

Remove the decimal point and divide the number by 10, 100, 1000 etc. depending on the d.p.

Convert the following to a fraction.

a) 0.2

b) 0.125

**Solution:**

a) The d.p of 0.2 is 1 because there is only one number that comes after the decimal point.

Recall that 1 d.p means 10.

Remove the decimal point and the number you have is 02, but the 0 is actually omitted so you have 2. Now divide 2 by 10.

b) The d.p of 0.125 is 3 because there are three numbers that come after the decimal point.

3 d.p means 1000.

Remove the decimal point and the number you have is 0125, but the 0 is actually omitted so you have 125. Now divide 125 by 1000.

Divide by 5;

Continue dividing until you can no longer divide.

Fractions are easily converted to decimals by dividing directly with the appropriate placement of decimal points or through the use of the long division method.

In this approach, when the numerator is less than the denominator and it is divided by a decimal a 0 is written and a decimal point is placed after it with the placement of a 0 in front of the numerator. Thereafter, the division continues in that manner. However, once the decimal point is placed, you cannot have another decimal point placed again peradventure you divide another number less than the denominator. All you should do is add a 0 in front each time this happens.

Convert the following to decimal.

a)

b)

**Solution:**

a)

The numerator 1 is less than the denominator 5. So you add a 0 in front of 1 making it 10 but place a 0 and decimal point after it above the fraction as seen below;

Now the numerator is large enough to be divided by the denominator, hence you can divide;

Place your answer after the decimal point. Continue dividing if there is a remainder, but in this case, there is no remainder. Therefore;

So our answer is 0.2.

b)

The numerator 1 is less than the denominator 5. So you add a 0 in front of 1 making it 10 but place a 0 and decimal point after it above the fraction as seen below.

10 divided by 8 is 1 remainder 2; write the 1 after the decimal point and leave the remainder on top of 10.

Next, you divide the remainder 2 by 8, 2 is less than 8 so you add another 0 beside it making it 20 and divide by 8.

Next, you divide the remainder 4 by 8, 4 is less than 8, so you add another 0 beside it making it 40, and divide by 8.

There is no remainder anymore, thus;

So our answer is 0.125.

Using long division is similar to the method just explained except with the use of the long division sign and rule. We shall apply long division to the examples just treated.

Convert the following to decimal.

a)

b)

**Solution:**

a)

Apply long division;

b)

Apply long division;

To best understand percentages as fractions or decimals we would look into further examples.

If a man on a project has completed 15% of the task.

a) What fraction is left?

b) If the total task was to be reduced by 30%, what fraction of the new volume expressed in decimal would he have left to do?

**Solution:**

a) Knowing that the total task is 100% and he has completed 15% it means that the fraction left is;

b) Let the new volume of the total task be x, this means that to compare it with the original volume of the task, you would have to add 30% to it. Therefore an expression for the original volume of task in respect of the new volume of task is.

Recall that he has already done 15% of the former volume, thus he has done;

Simplify the fraction using the Lowest Common Denominator (LCD) and you will get,

Now, we know the fraction of work he has done with respect to the new volume, therefore, what he has yet to be done after the reduction is

Simplify the algebraic fraction

Recall that x is the new task, so to complete the task he would have done 100% of the project. Thus substitute x for 100% to know the fraction of the job left undone with respect to the new volume, x

Your answer is required in decimal, thus

Write YES if the fraction, decimal or percentages are equivalent or NO if not equivalent from the table below;

Fraction | Decimal | YES/NO | |

0.33 | 33.3% | ||

0.3 | 32% | ||

0.2 | 40% |

Fraction | Decimal | YES/NO | |

0.33 | 33.3% | YES | |

0.3 | 32% | NO | |

0.2 | 40% | NO |

- Equivalent fractions, decimals, and percentages are fractions, decimals, and percentages that are of the same value regardless of the way they are being expressed.
- Just as fractions can be converted to percentages, percentages can be converted to fractions.
- Decimals are converted to percentages by multiplying the decimal by 100%.
- Fractions are easily converted to decimals by dividing directly with the appropriate placement of decimal points or through the use of the long division method.

You calculate fractions as percentages by multiplying them by 100%.

Percentages can expressed as decimals by dividing the percentage by 100%.

You work out fractions as percentages by multiplying them by 100%.

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