Question

The city of San Diego used an average of 1380 acre-feet of water per day during January of this year. Given that 1 acrefoot \(=1.233 \times 10^{6} \mathrm{~L}\), (a) Calculate the kL of water used every day. (b) Calculate the number of gallons of water used by San Diego last January.

Short answer

San Diego used 1,701,540 kL of water per day and 13,822,011,742.8 gallons of water in January.

Step-by-step solution

- Convert acre-feet to liters

We know that San Diego used 1380 acre-feet of water per day. To convert this into liters, use the given conversion factor: \[ 1 \text{ acre-foot} = 1.233 \times 10^{6} \text{ L} \] Therefore, the daily water usage in liters is: \[ 1380 \text{ acre-feet/day} \times 1.233 \times 10^{6} \text{ L/acre-foot} = 1,701,540,000 \text{ L/day} \]

- Convert liters to kiloliters

To find the volume in kiloliters (kL), we need to convert liters to kiloliters. We know that: \[ 1 \text{ kL} = 10^{3} \text{ L} \] Therefore, divide the volume in liters by 1000: \[ 1,701,540,000 \text{ L/day} \times \frac{1 \text{ kL}}{10^{3} \text{ L}} = 1,701,540 \text{ kL/day} \]

- Calculate total gallons for January

First, find the total volume in liters for January: \[ 1,701,540,000 \text{ L/day} \times 31 \text{ days} = 52,347,740,000 \text{ L} \] Now, convert liters to gallons using the conversion factor: \[ 1 \text{ L} \times 0.264172 \text{ gal/L} \] Therefore, the number of gallons: \[ 52,347,740,000 \text{ L} \times 0.264172 \text{ gal/L} = 13,822,011,742.8 \text{ gallons} \]

Key concepts

Unit Conversion

Unit conversion is a fundamental skill in science and daily life. It involves changing measurements from one unit to another. This is crucial when working with different measurement systems, such as the metric system and the imperial system. For example, converting from meters to feet or from liters to gallons. To convert units, you multiply or divide by a conversion factor, which is a known relationship between two units. In the San Diego water usage example, we converted between acre-feet, liters, and kiloliters. Understanding these conversions helps ensure we use consistent units in calculations and communicate measurements accurately.

Volume Measurement

Volume measurement is the process of quantifying the amount of space that a substance (like water) occupies. Common units of volume in the metric system include liters (L), milliliters (mL), and kiloliters (kL). In the imperial system, common units include gallons, quarts, and pints. Accurate volume measurement is essential in fields like chemistry, engineering, and environmental science. The given problem measures water usage in acre-feet, which can be converted to other units to understand and compare volumes more easily. Volume measurements allow us to manage resources, design systems, and conduct scientific research effectively.

Liters to Gallons Conversion

Converting liters to gallons is a typical example of unit conversion between the metric and imperial systems. The conversion factor for liters to gallons is approximately 0.264172. This means that 1 liter is equivalent to about 0.264172 gallons. To convert a volume in liters to gallons, you multiply the volume in liters by this conversion factor. For instance, in the San Diego water usage problem, after converting the total water usage to liters, we multiplied by 0.264172 to get the volume in gallons. This step helps us understand the quantity in a more familiar unit for those using the imperial system.

Kiloliters (kL)

Kiloliters (kL) are a unit of volume in the metric system. One kiloliter equals 1,000 liters (10³ L). Kiloliters are used for measuring large volumes of liquid. For example, water usage in a city is often measured in kiloliters. When we converted San Diego's daily water usage from liters to kiloliters, we divided the number of liters by 1,000. Using kiloliters makes it easier to work with large volumes without dealing with incredibly high numbers. This simplification is useful for calculations, reporting, and understanding significant amounts of liquid.