Plankton are classified based on their size. There are different types of plankton, such as megaplankton, mesoplankton, and femtoplankton. Femtoplankton can be as small as 2 × 10-8 meter. Mesoplankton can be up to 1 × 106 times bigger than femtoplankton. Megaplankton, such as jellyfish, can have a diameter 1 × 108 times the size of the smallest femtoplankton.

Question 1
Part A
Write an expression to find the size of the largest mesoplankton. Represent the expression in meters as a product of two numbers in scientific notation.

Part B
Apply the Commutative and Associative Properties of multiplication to the expression you found in part A to group the first factors together and the powers of 10 together.

Part C
Now that the first factors are grouped and the powers of 10s are grouped, multiply the first factors in the expression from part B. Then multiply the powers of 10 by using the properties of exponents.

Part D
Make sure the value you found in part C is in scientific notation. Using scientific notation, represent the size of the largest mesoplankton in meters. If the exponent is 0, you can leave out the power of 10.

Question 2

Part A
Write an expression to find size of the largest jellyfish. Represent the expression in meters as a product of two numbers in scientific notation.

Part B
Apply the Commutative and Associative Properties of multiplication to the expression you found in part A.

Part C
Now that the first factors are grouped and the powers of 10s are grouped, multiply the first factors in the expression from part B. Then multiply the powers of 10 by using the properties of exponents.

Part D
Make sure the expression that you found in part C is in scientific notation. Using scientific notation, represent the size of the largest jellyfish in meters. If the exponent is 0, you can leave out the term containing the power of 10.

Answer: Part A: Mesoplankton can be up to 1 × 106 times bigger than femtoplankton. So, find the size of mesoplankton by multiplying the size of femtoplankton by 1 × 106.

The size of femtoplankton is 2 × 10-8 meter. That means the expression for the size of the largest mesoplankton is 1 × 106 • 2 × 10-8 meters.

Part B: The expression found in part A is 1 × 106 • 2 × 10-8. Apply the Commutative and Associative Properties to the expression.

1 × 10^6 • 2 × 10^-8

= 1 • 10^6 • 2 • 10^-8 (using the Associative Property)

= 1 • 2 • 10^6 • 10^-8 (using the Commutative Property)

= (1 • 2) • (10^6 • 10^-8) (using the Associative Property)

Part C: The expression from part B is = (1 • 2) • (106 • 10-8).

Multiply the first factors.

1 • 2 = 2

Multiply the powers of 10 using this property of exponents: a^n a^m = a^n + m.

10^6 • 10^-8 = 10^6 + ^(-8) = 10^-2

The expression is 2 × 10^-2.

Part D: The expression from part C is 2 × 10^-2. This value is in scientific notation. So, the size of the largest mesoplankton is 2 × 10^-2 meter.

Step-by-step explanation: