Chapter 7.2, Problem 3P

To determine

To Find: How many molecules of water are there in a swimming pool that holds $200m^3$ of water and to write the answer in scientific notation.

Answer to Problem 3P

The required answer is $6.67\times {10}^{30}$ molecules of water.

Explanation of Solution

Given information:

The swimming pool holds $200m^3$ of water.

Calculation:

One cubic meter of water has a mass of about $9.98\times {10}^{5}g$ .

Each gram of water contains about $3.34\times {10}^{22}$ molecules of water.

Molecules of water $=\left(200\right)\cdot \left(9.98\times {10}^5\right)\cdot \left(3.34\times {10}^{22}\right)$

(Substitute)

  $=\left(2\cdot 9.98\cdot 3.34\right)\times \left({10}^2\cdot {10}^5\cdot {10}^{22}\right)$

(Commutative and associative properties of multiplication)

  $=66.7\times {10}^{2+5+22}$

(Multiply the coefficients. Add the exponents)

  $=66.7\times {10}^{29}$

(Simplify)

  $=6.67\times {10}^{30}$

(Write in scientific notation)

Therefore, the swimming pool has about $6.67\times {10}^{30}$ molecules of water.