1) Write 0.78787878787878.... (recurring) as a percentage.
2) The price of petrol increased by 10%.
Six months later it increases again by 10%
There was no other price changes.
What was the total percentage increase in the price of the petrol.
At school yo increase something we would multiply it by 10 so I have no idea what you are talking about sorry please could you show it in an easier way.
let x = .787878...
multiply by 100, (there are 2 digits repeating, if there had been 3 digits repeating, I would have multiplied by 1000)
100 x = 78.787878..
subtract them: notice the decimals line up nicely to get
99x = 78.0000...
x = 78/99 = 26/33
(check with your calculator)
What is (1.1)(1.1) ??
understood question 1 but i don't really understand what you said for question 2. Please can you explain?
To increase something by 10% , multiply by (1 + 10/100)
= 1 + .1
= 1.1
so you are doing this a second time ----> (1.1)(1.1) = 1.21 = 1 + .21 = 1 + 21/100
so the net increase is 21%
check:
suppose an article costs $250 , increase it by 10% -----> 1.1(250) = $275.00
increase it again by 10$ ----> 1.1(275) = $ 302.50
single increase of 21% ----> 1.21(250) = $302.50
1) To write 0.78787878787878... as a percentage, you can express it as a fraction first. Let's call this number x:
x = 0.78787878787878...
To convert a decimal to a fraction, we can use the following trick:
1) Multiply x by a power of 10 such that the repeated part (78) is directly to the left of the decimal point:
100x = 78.78787878787878...
2) Subtract the two equations to eliminate the repeating part:
100x - x = 78.78787878787878... - 0.78787878787878...
99x = 78
Now, divide both sides of the equation by 99:
x = 78/99
To convert this fraction to a percentage, we need to multiply by 100:
x = (78/99) * 100
x ≈ 78.79%
Therefore, 0.78787878787878... is approximately equal to 78.79% as a percentage.
2) To find the total percentage increase in the price of petrol, we need to calculate the compound increase due to two consecutive 10% increments.
Let's assume the original price of petrol is represented by P.
The first increase of 10% can be calculated by multiplying P by 1 + (10/100):
New price after first increase = P * (1 + 10/100) = P * 1.1
After six months, the price increases again by 10%, but this increase is applied to the new price obtained after the first increase. To calculate the second increase, we multiply the new price by 1 + (10/100) again:
New price after second increase = (P * 1.1) * (1 + 10/100) = P * 1.1 * 1.1
The percentage increase is the difference between the new price and the original price divided by the original price, multiplied by 100:
Percentage increase = ((P * 1.1 * 1.1) - P) / P * 100
= (1.21P - P) / P * 100
= 0.21P / P * 100
= 0.21 * 100
= 21
Therefore, the total percentage increase in the price of petrol after two 10% increments is 21%.