# Scientific Notation: Multiplication, Division, Addition And Subtraction

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Performing mathematical computations with scientific notation.

• 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

B. No, this is not proper scientific notation
Explanation
2.32 x 10^3

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• 2.

### 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)  =

• A.

12.0 x 10^12

• B.

12.0 x 10^35

• C.

1.2 x 10^13

• D.

1.2 x 10^36

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.

### 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

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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• 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

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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• 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

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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• 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

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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• 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

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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• 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

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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• 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

B. 4 x 10^1 = 40
Explanation
Division: Subtract the exponents: (-2) - (-3) = +1

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• 10.

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

• A.

.062

• B.

.62

• C.

0.0062

• D.

6,200

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

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