free physics video tutorials for all

 

Coursework Notes - Number

 

Percentages

 

[ fractions to %'s ][ %'s to fractions ][ decimals to %'s ][ %'s to decimals ]

 

[ % of a quantity ][ % increase ][ % decrease ][ reversed % ]

 

 

The concept of percentages depends on the principle that '1'(a whole) is represented by 100 percentage points(100%). That is, 1% =1/100 th of the whole.

 

 

Converting a fraction to a % - To do this simply multiply the fraction by 100 and cancel.

 

fractions to percentages

 

back to top

 

 

Converting a % to a fraction - For a whole number % divide by 100 and cancel. If the % has one decimal place, divide by 1000 and cancel, two decimal places, 10000, and so on.

 

percentages to fractions

 

 

 

Converting a decimal to a % - Multiply the decimal number by 100.

 

decimals to percentage

 

back to top

 

 

Converting a % to a decimal - Divide the decimal number by 100. This has the effect of moving the decimal point two places to the left.

 

percent to decimal

 

 

back to top

 

 

Calculating the % of a given quantity - Simply multiply by the % and divide by 100. If the % has one decimal place, divide by 1000, two places, divide by 10000 and so on.

 

 

example #1 - what is 25% of £360?

 

percent of #1

 

 

example #2 - what is 17.5% of £3000?

 

percent of #2

 

 

example #3 - what is 1.25% of £800?

 

percent of #3

 

 

back to top

 

 

Calculation of % increase - Add 100 to the % increase. Express this figure as a fraction of 100. Then multiply out with the given quantity.

 

 

example #1 - what is the final figure when a sum of £2000 is increased by 18%?

 

percentage increase #1

 

 

example #2 - what is the new salary if the old salary of £30,000 is increased by 5%?

 

percentage increase #2

 

 

example #3 - A car costing £12,000 has its price increased by 3%. What is its new price?

 

 

percentage increase #3

 

 

back to top

 

 

Calculation of % decrease - The % decrease is subtracted from 100, converted to a decimal, then multiplied by the original quantity.

example #1 - A car costing £5000 has its price reduced by 5%. What is its new price?

 

percent decrease #1

 

 

example #2 - An old house originally valued at £85,000 has its price reduced by 10%. What is its new price?

 

percent decrease #2

 

 

example #3 - Workers at a factory earn £12,000 per annum. If their wages are cut by 2.5%, what is their new wage?

 

percentage decrease #3

 

 

back to top

 

 

Calculation of 'reversed' percentages - The key to solving this type of problem is to work out the value of one percentage point(1%). This done by dividing the original quantity by 100 plus the % increase. Then multiply this value by 100 to obtain the original number.

 

 

example#1 - A foreign car costs 15,000 euros including 8% tax. What is the price of the car without the tax added?

 

value of 1 % point is :

 

reversed% #1

 

to get the original cost we multiply the 1% point by 100

 

 

reversed % #2

 

 

 

example#2 - A factory worker receives a salary of £18,000 after a 5% pay rise. What was the salary of the worker before?

 

value of 1 % point is :

 

revers % #3

 

to get the original salary we multiply the 1% point by 100

 

 

reversed percentage

 

 

 

example#3 - A farmer has a flock of 1210 sheep that have increased their number by 10% over the year. How many sheep were there the year previous?

 

value of 1 % point is :

 

reverse % #5

 

to get the original number of sheep we multiply the 1% point by 100

 

 

reverse % #6

 

 

 

back to top

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright gcsemathstutor.com 2024 - All Rights Reserved