Chapter 4.6, Problem 55E

a.

To determine

To denote $\frac{1}{1,000,000,000}$ square meter as a negative exponent.

Answer to Problem 55E

  ${10}^{-9}$ square meter

Explanation of Solution

Given information: $\frac{1}{1,000,000,000}$ square meter.

  $\frac{1}{1,000,000,000}$ can be written as

  $=\frac{1}{{10}^9}$

  $={10}^{-9}$ square meter. This is written as a negative exponent.

b.

To determine

To find the total area of all the crystals in a brittle star.

Answer to Problem 55E

  ${10}^{-5}$ square meter

Explanation of Solution

Given information:Area of each crystal is $\frac{1}{1,000,000,000}$ square meter and ${10}^4$ crystals are there in each brittle star.

Formula used: The product of powers rule.

Calculation:

  $\frac{1}{1,000,000,000}$ can be written as

  $=\frac{1}{{10}^9}$

  $={10}^{-9}$ square meter. This is the area written in negative exponent.

Total number of crystals $={10}^4$

Hence, total area that the crystals cover is:

  $={10}^4\times {10}^{-9}$ square meter

  $={10}^{4-9}$ square meter

  $={10}^{-5}$ square meter, written with a negative exponent.