Scientific Notation: Multiplication, Division, Addition and Subtraction

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

Yes, this is proper scientific notation

No, this is not proper scientific notation

2.32 x 10^3

Explanation

2.32 x 10^3

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

.062

.62

0.0062

6,200

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.

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.

3) Find the answer: 9.0 x 10³
3.0 x 10²

3.0 x 10^5

3.0 x 10^6

3.0 x 10^1

3

3.0 x 10^-1

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)

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)

4) 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) =

12.0 x 10^12

12.0 x 10^35

1.2 x 10^13

1.2 x 10^36

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)

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)

5) (3.0 x 10²) + (4.0 x 10³) =

4.3 x 10^2

7.0 x 10^-1

4.3 x 10^3

7.0 x 10^5

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

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

6) (8.0 x 10^-2) x (3 x 10^-3) =

2.4 x 10^-5

24.0 x 10^-5

24.0 x 10^-6

2.4 x 10^-4

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

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

7) (6.0 x 10²) x (5.0 x 10⁴) =
(2.0 x 10 ³)

1.5 x 10^4

1.5 x 10^8

15 x 10^4

6.0 x 10^4

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

8) (6.0 x 10²) + (4.0 x 10⁴) =
(2.0 x 10²)

5.0 x 10^4

2.03 x 10^2

1.2 x 10^8

5.0 x 10^5

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)

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)

9) (8.0 x 10^-2) =
(2 x 10^-3)

2 x 10^1 = 20

4 x 10^1 = 40

4 x 10^-5

4.0 x 10^-1

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

Explanation

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

10) (9.0 x 10³) - (4.0 x 10²)

5.0 x 10^1

13.0 x 10^5

9.4 x 10^3

5.0 x 10^5

8.6 x 10^3

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

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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Scientific Notation: Multiplication, Division, Addition And Subtraction