Chapter 4.7, Problem 53E

a.

To determine

To find the number of plankton a whale consumes in a second.

Answer to Problem 53E

  $2.07*{10}^4$

Explanation of Solution

Given information: In 1 second, 2.3 cubic meters of waters passes through the whale. Each cubic meter contains 9000 plankton.

Formula used:Using the scientific notations of the said figures, after multiplying them with product of powers rule.

Calculation: $9000$ plankton can be written as $9\times {10}^3$

Amount of water passing through the whale in 1 second $=2.3$ cubic meter

Hence, total number of plankton consumed by the whale in 1 second

  $=2.3\times 9\times {10}^3$

Multiplying non exponential parts

  $=20.7\times {10}^3$

Changing this to scientific notation.

  $=2.07\times {10}^4$ plankton. Using the scientific notation.

b.

To determine

To find the number of plankton a whale consumes in 1 hour.

Answer to Problem 53E

  $1.242\times {10}^6$

Explanation of Solution

Given information: In 1 second, 2.3 cubic meters of waters passes through the whale. Each cubic meter contains 9000 plankton.

Formula used: using the scientific notations of the said figures, after multiplying them with product of powers rule.

Calculation: $9000$ plankton can be written as $9\times {10}^3$

Amount of water passing through the whale in 1 second $=2.3$ cubic meter

Hence, total number of plankton consumed by the whale in 1 second

  $=2.3\times 9\times {10}^3$

Multiplying the non-exponent parts.

  $=20.7\times {10}^3$

Changing to scientific notation.

  $=2.07\times {10}^4$ plankton.

Number of plankton consumed by the whale in 1 hour

  $=2.07\times {10}^4\times 60$

Since an hour has 60 seconds.

  $=124.2\times {10}^4$

Changing the expression to scientific notation.

  $=1.242\times {10}^6$ In scientific notation.

c.

To determine

To obtain the number of plankton consumed by a right whale consumed in a day.

Answer to Problem 53E

  $1.863\times {10}^7$

Explanation of Solution

Given information: In 1 second, 2.3 cubic meters of waters passes through the whale. Each cubic meter contains 9000 plankton. Each day, the right whale consumes for 15 hours

Formula used: using the scientific notations of the said figures, after multiplying them with product of powers rule.

Calculation: $9000$ plankton can be written as $9\times {10}^3$

Amount of water passing through the whale in 1 second $=2.3$ cubic meter

Hence, total number of plankton consumed by the whale in 1 second

  $=2.3\times 9\times {10}^3$

Multiplying the non-exponent terms.

  $=20.7\times {10}^3$

Changing to scientific notation.

  $=2.07\times {10}^4$ plankton.

Number of plankton consumed by the whale in 1 hour

  $=2.07\times {10}^4\times 60$

Since an hour has 60 seconds.

  $=124.2\times {10}^4$

Changing the term to scientific notation.

  $=1.242\times {10}^6$ plankton.

Each day, the whale consumes for 15 hours.

  $=15\times 1.242\times {10}^6$

Multiplying using calculator.

  $=18.63\times {10}^6$

Changing to scientific notation.

  $=1.863\times {10}^7$ plankton, in scientific notation.

d.

To determine

To find the amount of calories a plankton contains.

Answer to Problem 53E

  $37.26$ calories

Explanation of Solution

Given information: Number of plankton consumed by the right whale in a day $1.863\times {10}^7$ , as found in sub-part c.Total calories consumed in a day by the whale is 500,000 calories.

Formula used: using the scientific notations of the said figures. For division, the quotient of powers.

Calculation: $500,000$ can be written as $5\times {10}^5$

And, total calories consumed in a day $=1.863\times {10}^7$ calories.

Hence, each calorie contains.

  $\frac{1.863\times {10}^7}{5\times {10}^5}$

Using product of powers rule

  $=0.3726\times {10}^{7-5}$

Obtaining the exponent.

  $=0.3726\times {10}^2$

Changing the number from scientific notation to number.

  $=37.26$ calories.