If an object went from #0.96g " to " 0.69g# would the percent change be #-28# or #-39# and why?

Always remember that a percentage change of two different values is the difference over the original.

The difference in the change is #0.69g-0.96g=-0.27g#.

Now, divide this value by the original value: #(-0.27g)/(0.96g)=-28.125%~~-28%# to get the percentage change.

(Note, usually, the percentage change is taken to be the absolute value, i.e. ignore the sign to get #28%#.)

#0.96 - 0.69 = 0.27 #

#0.27# = the change
#x# = the change in percent
#0.96# = the total starting value.
#100# = the total percent.

The ratio is

#"change"/" total" = "percent" /100#

putting these values into the equation gives

# 0.27/0.96 = x/100#

Multiplying both sides by #100# and dividing by #0.96# gives

#x = (0.27 xx100)/0.96#

# x = 28.125 ~~28#

Because the #0.96# is the starting value it is the base of the ratio.

The first clue is the negative sign, which indicates a decrease.

The mass changed from #0.96g# to #0.69g#

This means that the #0.96g# is the starting value. Any change, whether an increase or decrease, is calculated as a percentage of the original amount.

The amount of the decrease is #0.96g-0.69g= 0.27g#

Determine what percent this is of the original amount.

#0.27/0.96 xx 100%#

#= 28.125 ~~ 28%#

As the change is a decrease this can be shown as #-28%#

If the change was calculated using the final amount the answer is #39%#

#0.27/0.69 xx 100% = 39%#

However, this is incorrect.