Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 0

SCIENTIFIC

ERROR ANALYSIS

NOTATION

Scientific Notation

Comparing Numbers in Scientific Notation

Multiplication & Division with Scientific Notation

Addition & Subtractions with Scientific Notation

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 1

Error Analysis – SCIENTIFIC NOTATION

Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

An album receives an award when it sells 10,000,000 copies. An album has sold 7,680,000 copies. How many more copies does it need to sell to receive the award? Write your answer in scientific notation.

Incorrect Work/Solution Identify and Explain the Error

10,000,000 - 7,680,000 = 2,320,000

2,320,000 4 zeroes

2.32 x 104

The album must sell 2.32x104 more copies to receive the award.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 2

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

In 2006 Google purchased YouTube for $1,650,000,000. Write this number in scientific notation.

Incorrect Work/Solution Identify and Explain the Error

1,650,000,000 = 16.5 x 108

move 8 places

The number 1,650,000,000 is written in scientific notation as 16.5 x 108.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 3

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

A female flea can consume about 1.4 x 10-5 liter of blood per day. If a dog has 100 female fleas, how much blood do the fleas consume per day? Write your answer in standard form.

Incorrect Work/Solution Identify and Explain the Error

1.4 x 10-5 = 0.000014 move 5 places

= 0.000014 ● 100 = 0.00001400 The fleas consume about 0.00001400 per day.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 4

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

The diameter of a human hair is 0.000099 meter. What is this number written in scientific notation?

Incorrect Work/Solution Identify and Explain the Error

0.000099 = 9.9 x 106 move 6 places

The number 0.000099 written in scientific notation is 9.9 x 106.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 5

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

A dime is 0.135 cm thick. The thickness of a dollar bill is 1.0922 x 10-2 cm. How many times greater is the thickness of a dime than the thickness of a dollar bill?

Incorrect Work/Solution Identify and Explain the Error

0.135 = 1.35 x 10-1

1.35 × 10−1

1.0922 × 10−2 =1.35

1.0922 ×

10−1

10−2

1.236 × 10−3 = 123.6 ≈ 124

The thickness of a dime is 124 times greater than the thickness of a dollar bill.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 6

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

A patient has 0.0000081 gram of irons in 1 liter of blood. The normal level of iron in 1 liter of blood is between 6 x 10-7 gram and 1.6 x 10-5 gram. Is the patients iron level normal? Write the patient’s amount of iron in scientific notation.

Incorrect Work/Solution Identify and Explain the Error

0.0000081 = 8.1 x 10-6 8.1 > 6 8.1 > 1.6

No the patient’s iron is not normal. It is 8.1 x 10-6.

0.00001

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 7

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

In 2011 the population in the United States was 3.1 x 108. The population in Canada was 3.38 x 107. Find the total population of these countries. Write your answer in scientific notation.

Incorrect Work/Solution Identify and Explain the Error

United States 3.1 x 108 Canada 3.38 x 107

3.1 + 3.38 = 6.48 108+107 = 1015 The total population of the United States and Canada in 2011 was 6.48 x 1015.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 8

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

The area of a rectangle is 5.612 x 1014 cm2. The length of the rectangle is 9.2 x 107cm. Find the perimeter of the rectangle.

Incorrect Work/Solution Identify and Explain the Error

width = 5.612 × 1014

9.2 × 107 = 0.61 × 107

total width 2(0.61 × 107) = 1.22 × 107 total length2(9.2 × 107) = 18.4 × 107 perimeter (1.22 × 107) + (18.4 × 107) = 19.62 × 1014 19.62 × 1014 = 1.962 × 1015 The perimeter of the rectangle is 1.962 × 1015cm.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 9

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

Each store manager at D&G Electronics makes an annual salary of $2.68 × 104. If there are a total of 2.2 × 102 store managers in the company, how much do they make in all? Write your answer in scientific notation.

Incorrect Work/Solution Identify and Explain the Error

(2.68 × 104)(2.2 × 102)

= (2.68 × 2.2) × (104 × 102) = 5.896 × 108

The store managers make $5.896 × 108 in all.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 10

Error Analysis – SCIENTIFIC NOTATION Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

The diameter of the Sun is 1,400,000 km. The diameter of Earth is 1.28 x104 km. How many times greater is the diameter of the Sun than the diameter of Earth?

Incorrect Work/Solution Identify and Explain the Error 1,400,000 = 1.4 x 106 (1.4 × 106)(1.28 × 104) = (1.4 × 1.28)(106 × 104) = 1.792 × 1010

1.792 × 1010 = 17,920,000,000

The diameter of the Sun is about 17,920,000,000 times greater than the diameter of Earth.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 11

Error Analysis – SCIENTIFIC NOTATION Answer Key

Error Correct Sample Work Correct Answer 1. The error is the number of zeroes is

used as the exponent instead of the number of places the decimal is moved

10,000,000-7,680,000 2,320,000 2.32x106

The album must sell 2.32x106 more copies to receive the award.

2. The error is the decimal is only moved 8 places. The final answer is not written in scientific notation.

1,650,000,000=1.65 x 109

The number 1,650,000,000 is written in scientific notation as 1.65 x 109.

3. Two zeroes are incorrectly annexed to the end of the number. The decimal should be moved two places to the right.

1.4 x10-5●100 0.000014●100 0.0014

The fleas consume about 0.0014 per day.

4. The number of places that the decimal is moving is incorrect.

0.000099 = 9.9 x 105

The number 0.000099 written in scientific notation is 9.9 x 105.

5. The error is the sum of the exponents are found instead of the difference.

0.135=1.35 x 10-1 1.35 × 10−1

1.0922 × 10−2 =1.35

1.0922 ×

10−1

10−2

1.236 × 101 = 12.36 ≈ 12

The thickness of a dime is 12 times greater than the thickness of a dollar bill.

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 12

6. The powers of 10 must be the same before comparing the multipliers.

6 x 10-7 = 0.0000006 1.6 x 10-5 = 0.000016 0.000016 > 0.0000081 > 0.0000006

Yes the patient’s iron is normal. It is 8.1 x 10-6.

7. The powers of 10 must be the same before adding the multipliers.

United States : 3.1 x 108 Canada: 3.38x107=0.338x108 3.1+0.338=3.438

The total population of the United States and Canada in 2011 was 3.438 x 108.

8. The error is the exponent for each power is added. The exponent should stay the same.

5.612 × 1014

9.2 × 107 = 0.61 × 107

2(0.61 × 107) = 1.22 × 107 2(9.2 × 107) = 18.4 × 107 (1.22 × 107) + (18.4 × 107) = 19.62 × 107 19.62 × 107 = 1.962 × 108

The perimeter of the rectangle is 1.962 × 108cm.

9. The error is the product of the exponents are found instead fo the sum.

(2.68 × 104)(2.2 × 102) = (2.68 × 2.2) × (104 × 102) 5.896 × 106

The store managers make $5.896 × 106 in all.

10. The value of the diameters are multiplied instead of divided.

1,400,000 = 1.4 x 106 1.4 × 106

1.28 × 104 =1.4

1.28×

106

104

1.09375 × 102 = 109.375

The diameter of the Sun is about 109 times greater than the diameter of Earth.

Name (s) ______________________________________ Class_______________ Date_______________________________

©Exceeding the CORE Question # 13

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