Scientific Notation: Multiplication, Division, Addition and Subtraction

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Kwchiro

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Questions: 10 | Attempts: 3,929 | Updated: Oct 13, 2023

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Scientific Notation: Multiplication, Division, Addition And Subtraction - Quiz

Performing mathematical computations with scientific notation.

Questions and Answers

1.

Is the following numbers in proper scientific notation? 23.2 x 10²
- A.
  
  Yes, this is proper scientific notation
- B.
  
  No, this is not proper scientific notation
Correct Answer
B. No, this is not proper scientific notation

Explanation
2.32 x 10^3

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3
0
2.

Do NOT use your calculator. UNDERSTAND how to work with scientific notation!(10¹²is the same as 10^12)(3.0x 10⁷)(4.0 x 10⁵) =
- A.
  
  12.0 x 10^12
- B.
  
  12.0 x 10^35
- C.
  
  1.2 x 10^13
- D.
  
  1.2 x 10^36
Correct Answer
C. 1.2 x 10^13

Explanation
When MULTIPLYING in scientific notation, ADD the exponent.
Make sure you change your answer to proper scientific notation. (3.0x 10^7) (4.0 x 10^5)= (3.0 x 4.0)x 10^(7+5)

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3
0
3.

Find the answer: 9.0 x 10³ 3.0 x 10²
- A.
  
  3.0 x 10^5
- B.
  
  3.0 x 10^6
- C.
  
  3.0 x 10^1
- D.
  
  3
- E.
  
  3.0 x 10^-1
Correct Answer
C. 3.0 x 10^1

Explanation
Dividing scientific notation: SUBTRACT the exponenent in the numerator from the exponent in the demoninator:
9.0 x 10^3 divided by 3.0 x 10^2 =
(9 divided by 3)x 10^(3-2)

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0
2
4.

(8.0 x 10^-2) x (3 x 10^-3) =
- A.
  
  2.4 x 10^-5
- B.
  
  24.0 x 10^-5
- C.
  
  24.0 x 10^-6
- D.
  
  2.4 x 10^-4
Correct Answer
D. 2.4 x 10^-4

Explanation
When multiplying with scientific notation: add the exponents.
(8.0 x 10^-2) x (3 x 10^-3) = (8 x 3)x 10^(-2 + -3) = 24 x 10^-5 = 2.4 x 10^-4

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1
0
5.

(3.0 x 10²) + (4.0 x 10³) =
- A.
  
  4.3 x 10^2
- B.
  
  7.0 x 10^-1
- C.
  
  4.3 x 10^3
- D.
  
  7.0 x 10^5
Correct Answer
C. 4.3 x 10^3

Explanation
Adding and Substracting in Scientific Notation REQUIRES the exponents to be the SAME. EASIEST way to do this problem:
Change into "regular numbers" and then put your answer in proper scientific format:
(3.0 x 10^2) + (4.0 x 10^3) = 300 + 4,000 = 4,300 =
4.3 x 10^3

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2
0
6.

(9.0 x 10³) - (4.0 x 10²)
- A.
  
  5.0 x 10^1
- B.
  
  13.0 x 10^5
- C.
  
  9.4 x 10^3
- D.
  
  5.0 x 10^5
- E.
  
  8.6 x 10^3
Correct Answer(s)
C. 9.4 x 10^3
E. 8.6 x 10^3

Explanation
When substrating in scientific notation, the exponents MUST be the same. EASIEST way to do the problem: Change to "regular numbers", calculate and then change your answer back to scientific notation: (9.0 x 10^3)-(4.0 x 10^2)=
9,000 - 400 = 8,600 = 8.6 x 10^3

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1
0
7.

(6.0 x 10²) x (5.0 x 10⁴) = (2.0 x 10 ³)
- A.
  
  1.5 x 10^4
- B.
  
  1.5 x 10^8
- C.
  
  15 x 10^4
- D.
  
  6.0 x 10^4
Correct Answer
A. 1.5 x 10^4

Explanation
(6 x 5 divided by 2)x 10 ^ (2 + 4 -3)= 15 x 10^3
= 1.5 x 10^4

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1
0
8.

(6.0 x 10²) + (4.0 x 10⁴) = (2.0 x 10²)
- A.
  
  5.0 x 10^4
- B.
  
  2.03 x 10^2
- C.
  
  1.2 x 10^8
- D.
  
  5.0 x 10^5
Correct Answer
B. 2.03 x 10^2

Explanation
Change the numerator into "regular" numbers, calculate and change back to scientific notation (40,000 + 600 = 40,600 = 4.06 x 10^4) then divide by 2.0 x 10^2)

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1
1
9.

(8.0 x 10^-2) = (2 x 10^-3)
- A.
  
  2 x 10^1 = 20
- B.
  
  4 x 10^1 = 40
- C.
  
  4 x 10^-5
- D.
  
  4.0 x 10^-1
Correct Answer
B. 4 x 10^1 = 40

Explanation
Division: Subtract the exponents: (-2) - (-3) = +1

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2
0
10.

What is this equivalent to? 6.2 x 10^-3
- A.
  
  .062
- B.
  
  .62
- C.
  
  0.0062
- D.
  
  6,200
Correct Answer
C. 0.0062

Explanation
The given number, 6.2 x 10-3, is in scientific notation. In scientific notation, the number is expressed as a decimal number multiplied by a power of 10. In this case, 6.2 x 10-3 means 6.2 multiplied by 10 raised to the power of -3. To convert this to a decimal number, we move the decimal point three places to the left, resulting in 0.0062. Therefore, the correct answer is 0.0062.

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Current Version
Oct 13, 2023

Quiz Edited by
ProProfs Editorial Team
Jul 22, 2010

Quiz Created by
Kwchiro

Scientific Notation: Multiplication, Division, Addition And Subtraction

Is the following numbers in proper scientific notation? 23.2 x 102

Do NOT use your calculator. UNDERSTAND how to work with scientific notation!(1012 is the same as 10^12)(3.0x 107) (4.0 x 105) =

Find the answer: 9.0 x 103 3.0 x 102

(8.0 x 10-2) x (3 x 10-3) =

(3.0 x 102) + (4.0 x 103) =

(9.0 x 103) - (4.0 x 102)

(6.0 x 102) x (5.0 x 104) = (2.0 x 10 3)

(6.0 x 102) + (4.0 x 104) = (2.0 x 102)

(8.0 x 10-2) = (2 x 10-3)

What is this equivalent to? 6.2 x 10-3

Is the following numbers in proper scientific notation? 23.2 x 10²

Do NOT use your calculator. UNDERSTAND how to work with scientific notation!(10¹²is the same as 10^12)(3.0x 10⁷)(4.0 x 10⁵) =

Find the answer: 9.0 x 10³ 3.0 x 10²

(8.0 x 10^-2) x (3 x 10^-3) =

(3.0 x 10²) + (4.0 x 10³) =

(9.0 x 10³) - (4.0 x 10²)

(6.0 x 10²) x (5.0 x 10⁴) = (2.0 x 10 ³)

(6.0 x 10²) + (4.0 x 10⁴) = (2.0 x 10²)

(8.0 x 10^-2) = (2 x 10^-3)

What is this equivalent to? 6.2 x 10^-3