Chapter SH, Problem 9.2MPS

To determine

To calculate: To find the prime factorization of the distances.

Answer to Problem 9.2MPS

The distances after prime factorization are

  $Distanc{e}_1={\left(2\right)}^4\left(3\right){\left(5\right)}^2$

  $Distanc{e}_2=\left(2\right){\left(5\right)}^2\left(7\right)\left(11\right)$

Explanation of Solution

Given: The state of Hawaii is located approximately $2400$ miles from the California coast and $3850$ miles from Japan

Formula Used:

Prime Factorization is finding the prime numbers that multiply together to make the original number

Calculation:

Given the distance between the state of Hawaii and California coast is as follows:

  $Distanc{e}_1=2400$

On prime factorization,

  $\begin{array}{l}Distanc{e}_1=2\times 2\times 2\times 3\times 5\times 2\times 5\times 2\\ Distanc{e}_1={\left(2\right)}^4\times 3\times {\left(5\right)}^2\\ Distanc{e}_1={\left(2\right)}^4\left(3\right){\left(5\right)}^2\end{array}$

Also, given the distance between the state of Hawaii and Japan is as follows:

  $Distanc{e}_2=3850$

On prime factorization,

  $\begin{array}{l}Distanc{e}_2=2\times 5\times 5\times 7\times 11\\ Distanc{e}_2=2\times {\left(5\right)}^2\times 7\times 11\\ Distanc{e}_2=\left(2\right){\left(5\right)}^2\left(7\right)\left(11\right)\end{array}$

Conclusion:

Hence, distances after prime factorization are

  $Distanc{e}_1={\left(2\right)}^4\left(3\right){\left(5\right)}^2$

  $Distanc{e}_2=\left(2\right){\left(5\right)}^2\left(7\right)\left(11\right)$