 % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇 𝒑 𝟏𝟎𝟎 = 𝒂 𝒃 7.2 Percentages: You can represent “ a is p percent of b” using the percent proportion:  % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇 𝒑 𝟏𝟎𝟎 = 𝒂 𝒃 Ex: what percent of 56 is 42? % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇  𝒙 𝟏𝟎𝟎 = 𝟒𝟐 𝟓𝟔 cross multiply  56(x) = 100(42) divide by 56  x = 4200/56

𝒑 𝟏𝟎𝟎 = 𝒂 𝒃  % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇 % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇  𝟏𝟐𝟓 𝟏𝟎𝟎 = 𝟏𝟕.𝟓 𝒙 𝒑 𝟏𝟎𝟎 = 𝒂 𝒃  % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇 Ex: 125% of what number is 17.5? % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇  𝟏𝟐𝟓 𝟏𝟎𝟎 = 𝟏𝟕.𝟓 𝒙 cross multiply  125(x) = 100(17.5) divide by 125  x = 1750/125

𝒑 𝟏𝟎𝟎 = 𝒂 𝒃  % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇 Ex: A family sells a car to a dealership for 60% less than they paid for it. They paid $9000? For the car. What was the price they sold it the car for? % 𝟏𝟎𝟎 = 𝒊𝒔 𝒐𝒇  𝟔𝟎 𝟏𝟎𝟎 = 𝒙 𝟗𝟎𝟎𝟎 cross multiply  60(9000) = 100(x) divide by 100  x = 540000/100

CLASSWORK: Page 141-142 Problems: 9, 14, 17, 21, 23, 29, 47, 49

2.10 Change Expressed as Percent: Percent change is the ratio of the amount of change to the original amount: Percent Change: 𝒂𝒎𝒐𝒖𝒕 𝒐𝒇 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒓 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 Amount of Increase: new amount – original amount Amount of decrease: original amount – new amount

The average monthly precipitation of Chicago, Illinois, peaks in June at 4.1 in. The average monthly precipitation in December is 2.8 in. What is the percent decrease from June to December? Percent Change: 𝒂𝒎𝒐𝒖𝒕 𝒐𝒇 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 Percent Change: 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 −𝒏𝒆𝒘 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 Percent Change: 𝟒.𝟏 −𝟐.𝟖 𝟒.𝟏 = 𝟏.𝟑 𝟒.𝟏 = 0.317 = 32%

In one year the toll for the passenger cars to use a tunnel rose from $3 to $3.50. What was the percent increase? Percent Change: 𝒂𝒎𝒐𝒖𝒕 𝒐𝒇 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 Percent Change: 𝒏𝒆𝒘 −𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 Percent Change: 𝟑.𝟓𝟎 −𝟑 𝟑 = 𝟎.𝟓𝟎 𝟑 = 0.166 = 17%

|𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒐𝒓 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆| 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 RELATIVE ERROR: |𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒐𝒓 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆| 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 PERCENT ERROR: relative error in percent You think that the distance between your house and a friend’s house is 5.5 mi. The actual distance is 4.75 mi. What is the percent error in your estimation?

RELATIVE ERROR: |𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒐𝒓 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒗𝒂𝒍𝒖𝒆 − 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆| 𝒂𝒄𝒕𝒖𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 You think that the distance between your house and a friend’s house is 5.5 mi. The actual distance is 4.75 mi. What is the percent error in your estimation? RELATIVE ERROR: |𝟓.𝟓 𝒎𝒊 − 𝟒.𝟕𝟓 𝒎𝒊| 𝟒.𝟕𝟓 𝒎𝒊 |𝟎.𝟕𝟓 𝒎𝒊| 𝟒.𝟕𝟓 𝒎𝒊 = 0.157 = 16%

CLASS WORK: Pages: 148-149 Problems: 7, 17, 19, 28

MAXIMUM & MINIMUM:The most any measurement can be off by is one half of the unit used in measuring. Ex: A student’s height is measured as 66 in. to the nearest in. What are the student’s maximum and minimum possible heights? Maximum: (half of the unit more) Since the height is 66 in. and we are using inches, then maximum is .5 in more.  66in. + 0.5 in.= 66.5 in Minimum: (half of the unit less) Since the height is 66 in. and we are using inches, then maximum is .5 in less.  66in. - 0.5 in.= 65.5 in.

MAXIMUM & MINIMUM:The most any measurement can be off by is one half of the unit used in measuring Ex: An ostrich egg has a mass of 1.1 kg. to the nearest tenth of a kg. Find the minimum and maximum possible measurements. Maximum: (half of the unit more) Since the mass is 1.1 kg and and we are using decimal, then maximum is .05 more since ½ of 0.1 is 0.05  1.1 kg. + 0.05 kg= 1.15 kg. Minimum: (half of the unit less) Since the mass is 1.1 kg and and we are using decimal, then minimum is .05 less since ½ of 0.1 is 0.05  1.1 kg. - 0.05 kg= 1.05 kg.

Problem: Finish the homework problems CLASS WORK: Pages: Homework Problem: Finish the homework problems