How do you find the percent change if original: $3.78 and new: $2.50?

Question

How do you find the percent change if original: $3.78  and new: $2.50?

Genesis Allen · Accepted Answer

#=-33.862#% to 3 decimal places

Full 'teach in' given about percentages

#color(blue)("Preamble")# In percentage the symbol % may be viewed as a unit of measurement that is worth #1/100# As and example #60% # is the same as #60xx1/100=60/100# It is customary in questions of this kind to express the change in terms of a fraction, with the original value serving as the reference point: #("change")/("reference point value") -> ("changed value- original value")/("original value")# If changed value - original value is negative then it indicates a reduction. As is the case in this question. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering the question")# #color(brown)("Starting point:")# #("changed value- original value")/("original value") -> ($2.50-$3.78)/($3.78)# #=-($1.28)/($3.78)# By the way; like in numbers the $ symbols cancel out in the same way numbers do. This is a useful trick when doing higher mathematics or physics So we have #(-cancel($)1.28)/(cancel($)3.78) = -1.28/3.78# .............................................................................................. #color(brown)("Converting this into percentage")# Remember that #1/100->%# #color(green)((1.25)/(3.78)color(red)(xx1)" "->" "(1.25/3.78color(red)(xx100/100))# #(-1.28/3.78color(red)(xx100xx1/100))# #(-1.28/3.78color(red)(xx100xx%))# #(-1.28/3.78color(red)(xx100))%# #=-33.862#% to 3 decimal places

Avery Alexander · Answer

undefined To find the percent change between $3.78 and $2.50, you use the formula:

Percent Change = [(New Value - Original Value) / Original Value] * 100

Substituting the values:

Percent Change = [($2.50 - $3.78) / $3.78] * 100 = -34.92%

So, the percent change is approximately -34.92%.