The aim of this question is to learn **unit conversions** between different **customary units** in use in the **United States of America**.

**Rhode Island** is the** smallest state** out of all the states within **mainland** of the United States of America. Its area is **776,960 acres**. Although the **international unit** of area is **square meters,** there are many units that are used in the United States. These include **square miles, square kilometers, square foot, and square yards**. The** interconversion of these units** is essentially required during any **engineering** project, therefore it’s necessary to understand these **area unit conversions**.

Different **units of area are related** with each other as follows:

\[ 1 \ \text{ square yards } \ = \ 9 \ \text{ square foot } \]

\[ 1 \ acre \ = \ 43560 \ \text{ square foot } \]

\[ 1 \ \text{ square miles } \ = \ 2.78 \times 10^{ 7 } \ \text{ square foot } \]

\[ 1 \ \text{ square kilometers } \ = \ 1.076 \times 10^{ 7 } \ \text{ square foot } \]

## Expert Answer

The **area of Rhode Island in acres** is given as follows:

\[ \text{ Area of Rhode Island } \ = \ 776960 \ acres \]

**Since:**

\[ 1 \ acre \ = \ 43560 \ \text{ square foot } \]

**Substituting this value in the above equation:**

\[ \text{ Area of Rhode Island } \ = \ 776960 \ ( \ 43560 \ \text{ square foot } \ ) \]

\[ \text{ Area of Rhode Island } \ = \ 33844377600 \ \text{ square foot } \ ) \]

**In scientific notation:**

\[ \text{ Area of Rhode Island } \ = \ 3.38 \ \times \ 10^{ 10 } \ \text{ square foot } \ ) \]

Which is the **required answer**.

## Numerical Result

\[ \text{ Area of Rhode Island } \ = \ 3.38 \ \times \ 10^{ 10 } \ \text{ square foot } \ ) \]

## Example

Given the area of Rhode Island as calculated in the above question, Find the **area of Alaska** (the largest state in the United States of America)** in square feet, acres, square miles, and square kilometers** given that it is $ 5.5 \times 10^{ 2 } $ **times larger than Rhodes Island** (the smallest state in the United States of America).

\[ \text{ Area of Alaska } \ = \ 776960 ( 5.5 \times 10^{ 2 } ) \ acres \ = \ 4.27 \times 10^{ 7 } \ acres \]

\[ \text{ Area of Alaska } \ = \ ( 3.38 \times 10^{ 10 } ) ( 5.5 \times 10^{ 2 } ) \ \text{ square foot } \ = \ 1.86 \times 10^{ 12 } \ \text{ square foot } \]

\[ \text{ Area of Alaska } \ = \ \dfrac{ 1.86 \times 10^{ 12 } }{ 2.78 \times 10^{ 7 } } \ \text{ square mile } \ = \ 6.69 \times 10^{ 4 } \ \text{ square mile } \]

\[ \text{ Area of Alaska } \ = \ \dfrac{ 1.86 \times 10^{ 12 } }{ 1.076 \times 10^{ 7 } } \ \text{ square yards} \ = \ 1.73 \times 10^{ 5 } \ \text{ square yards } \]