Subtract the old from the new, then divide by the old value. Show that as a Percentage. Show
Comparing Old to New
Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options. How to CalculateHere are two ways to calculate a percentage change, use the one you prefer: Method 1
Method 2
ExamplesExample: A pair of socks went from $5 to $6, what is the percentage change?Answer (Method 1):
Answer (Method 2):
Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage change?Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease. Answer (Method 2): Compare today's
value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value. Why Compare to Old Value?Because you are saying how much a value has changed. Example: Milk was $2, now it is $3, did it rise $1 compared to $2 or $3 ?We compare to the original $2 value, so we say the change is $1/$2 = 0.5 which is a 50% increase. The FormulaYou can also put the values into this formula: New Value − Old Value |Old Value| × 100% (The "|" symbols mean absolute value, so negatives become positive) Example: There were 200 customers yesterday, and 240 today:240 − 200 |200| × 100% = 40 200 × 100% = 20% A 20% increase. Example: But if there were 240 customers yesterday, and 200 today we would get:200 − 240 |240| × 100% = −40 240 × 100% = −16.6...% A 16.6...% decrease. How to Reverse a Rise or FallSome people think that a percentage increase can be "reversed" by the same percentage decrease. But no! Example: 10% of 100A 10% increase from 100 is an increase of 10, which equals 110 ... ... but a 10% reduction from 110 is a reduction of 11 (10% of 110 is 11) So we ended up at 99 (not the 100 we started with) What happened?
Because the percentage rise or fall is in relation to the old value:
How to do it properlyTo "reverse" a percentage rise or fall, use the right formula here:
What will be the percentage of increase in the area of a square?Hence, the area of the square gets increased by 21% if its side is increased by 10%.
How do you calculate percentage change in area?Initial area = 8000. New length = 120 and new breadth = 72. Therefore, new area = 8640. The percentage change in the area = ((8640 – 8000) / 8000) * 100 = 8.
What will be the percentage increase in the area of a square if its side is increased by 10%?=0.21×100%=21%
What is the percentage change in the area of a square when each side is increased by 20 %?percentage increase in are =44%
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