Question

ActivityPlankton 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 1Part AWrite 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 BApply 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 CNow 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 DMake 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.

Answer 1

A) The mesoplankton is 1 x 10^6m x the femtoplankton which is 2 x 10^-8m

So an expression in meters as a product of two numbers in scientific notation for the largest mesoplankton is

(1 x 10^6 x 2 x 10^-8)m

B) Applying the commutative and associative property of multiplication we have

(1 x 10^6 x 2 x 10^-8)m = ((1 x 2 )x (10^6 x 10^-8))m

C) (1x2) (10^6 x 10^-8) = 2 x 10^6+-8 m

`D)2*10^(6+(-8))m`

`\begin{gathered} 2\text{ }*10^(6-8)m \\ 2*10^(-2)m \\ \text{The largest mesoplankton in meters is 2 x 10}^(-2)m \end{gathered}`