Percent Error

P re - R e q ui si te 7.RP.2: Recognize and represent proportional relationships between quantities. c. Represent proportional relationships by equations. St 7.RP.3: Use proportional relationships to solve multistep ratio and percent a problems. n 7.EE.3: Solve multi-step real-life and mathematical problems posed with positive d and negative rational numbers in any form (whole numbers, fractions, and ar decimals), using tools strategically. Apply properties of operations to calculate d with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies C Lesson 7.4.8 C L e ss o n St  Given the exact value, x, of a quantity and an approximate value, a, of the u quantity, students use the absolute error |a – x|, to compute the percent error d by using the formula e  Students understand the meaning of percent error as the percent the absolute n t value is of the exact value. L  Students understand that when an exact value is not known, an estimate of the e percent error can still be computed when given a range determined by two ar inclusive value (eg: if there are known to be between 6,000 and 7,000 black bears ni in New York, but the exact number is not known, the percent error can be n estimated to be at most which is %. g G o al Percent Error

M e di a H #88 W Spiral Review #24 W K S P

You want to buy a new computer screen. The following students used a ruler (inch side) to measure the length of the diagonal. The box says the size of the screen is 15-inches. Who is the best guesser?

Student Measurement Error

Taylor

Jordan

Connor

Absolute Error

Even though Taylor overestimated and Jordan underestimated the length of the diagonal, the distance from the actual value is the same for both!

Given the exact value, x, of a quantity and an approximate value, a, of the quantity,

Exercise 1 The actual length of a field is 500 feet. A measuring instrument shows the length . to be 508 feet. Find the absolute error in the measured length of the field. Percent Error

2 Find the absolute error of the approximation 3.14 to the true , using the pi button . on the calculator as the actual value. Round your final answer to the nearest thousandths.

3 I know that I have between $100 and $110 in my wallet. I estimate that I have . $103. What is the most my absolute error can be?

Percent Error

Guessing is relative to the starting amount!

Taylor’s Percent Error:

Connor’s Percent Error:

Who is the better guesser, Taylor or Connor? Explain.

Exercise: Find the percent error for each situation.

4 A realtor expected 18 people to show up for an open house, but 25 attended. .

5 In science class, Mrs. Moore’s students were directed to weigh a 300-gram mass on . the balance scale. Tina weighed the object and reported 328 grams. Percent Error

6 Darwin’s coach recorded that he had bowled 250 points out of 300 in a bowling . tournament. However the official scoreboard showed that Darwin actually bowled 225 points out of 300.

Estimating Percent Error

You know that you have between $100 and $110 in your wallet.

What is the most percent error you could make?

What is the maximum percent error you can make if you estimate that you have $103?

What is the least (minimum) percent error that can be made?

You find out you have $107 in your wallet. What percent error did you make guessing you had $103? (Round your final answer to the nearest tenth.)

Exercise 7 The attendance at a musical event was counted several times. All counts were . between 573 and 589. If the actual attendance number is between 573 and 589, what is the most the percent error could be? (Round your answer to the nearest tenth.)

8 You know you can save anywhere from $300 to $500 each year. What is the Percent Error

. maximum your percentage of error can be?

9 The estimated deer population for Suffolk county is 105,000 to 107,000. What is . the most percent error that can be made? (Round your answer to the nearest tenth.) Percent Error

Name: ______Date: ______Pre-Algebra Exit Ticket

The odometer in Mr. Washington’s car does not work correctly. The odometer recorded 13.2 miles for his last trip to the hardware store, but he knows the distance traveled is 15 miles. What is the percent error?

Connor and Angie helped take attendance during their school’s practice fire drill. The actual count was between 77 and 89. What is the most the percent error could be? (Round your answer to the nearest tenth.)

Name: ______Date: ______Pre-Algebra Exit Ticket

The odometer in Mr. Washington’s car does not work correctly. The odometer recorded 13.2 miles for his last trip to the hardware store, but he knows the distance traveled is 15 miles. What is the percent error?

Connor and Angie helped take attendance during their school’s practice fire drill. The actual count was between 77 and 89. What is the most the percent error could be? (Round your answer to the nearest tenth.) Percent Error

Name: ______Date: _____ Pre-Algebra HW #88

1. The Veterinarian weighed Oliver’s new puppy, Boaz, on a defective scale. He weighed 36 pounds. However, Boaz weighs exactly 34.5 pounds.

What is the absolute error?

What is the percent of error in measurement of the defective scale to the nearest tenth?

2. The actual length of a rectangular soccer field is 500 feet. A measuring instrument shows the length to be 493 feet. The actual width of the field is 250 feet, but the recorded width is 246.5 feet. Answer the following questions based on this information. Round all decimals to the nearest tenth.

a. Find the percent error for the length of the soccer field.

b. To the nearest tenth, find the percent error of the area of the soccer field.

over 

Review: 3 The Lions won 16 games last year. This year the Lions won 20 games. What is the . percent increase in the number of games the Lions won from last year to this year?

a. 20% b. 25% c. 80% d. 125% Percent Error

4 In Town A, there was a 60% turn out for an election of 400 eligible voters. How . many of the town’s eligible voters voted?

In Town B, we were told that 280 people represents 70% of the population. How many people live in Town B?

In Town C, we are told that 320 out of 500 people voted. What percent of the people voted?