Metric Units of Length: 동영상 및 연습문제

The metric system uses the meter (m) as its basic unit of length. Other units are formed by adding prefixes that represent powers of ten. For example, a kilometer (km) is 1000 meters, a hectometer (hm) is 100 meters, and a decameter (dam) is 10 meters. On the smaller side, a decimeter (dm) is 0.1 meters, a centimeter (cm) is 0.01 meters, and a millimeter (mm) is 0.001 meters. These relationships can be expressed as: $1\mathrm{km}=1000m$, $1\mathrm{cm}=0.01m$, and $1\mathrm{mm}=0.001m$. This decimal-based system makes conversions straightforward by scaling units up or down by factors of ten.

To convert between metric units of length using the prefix line, first identify the starting and target units on the line of prefixes: kilo, hecto, deka, (meter), deci, centi, milli. Count the number of steps between the units. Moving from a smaller unit to a larger unit means moving the decimal point to the left; moving from a larger unit to a smaller unit means moving it to the right. For example, converting 250 meters to kilometers involves moving three places left (since kilo is three steps above meter), resulting in 0.25 km. Conversely, converting 23.6 hectometers to centimeters involves moving four places right, giving 236,000 cm. This method leverages the base-10 nature of the metric system, making conversions as simple as shifting the decimal point.

The mnemonic to remember the order of metric prefixes is "King Henry Doesn't Usually Drink Chocolate Milk." Each initial corresponds to a prefix: K for kilo, H for hecto, D for deka, U for unit (meter), D for deci, C for centi, and M for milli. This helps you quickly identify the relative size of units and how many steps apart they are on the prefix line. Knowing this order allows you to determine how many decimal places to move when converting between units. For example, converting from centimeters (C) to meters (U) involves moving two steps left, so you move the decimal point two places to the left. This mnemonic simplifies remembering the sequence and facilitates accurate and efficient conversions.

When adding or subtracting metric units of length, you must first convert all measurements to the same unit. Unlike US customary units, metric units are not expressed as mixed units, which simplifies calculations. For example, to subtract 560 meters from 2.5 kilometers, convert 2.5 km to meters by moving the decimal three places to the right, resulting in 2500 m. Then subtract: 2500 m - 560 m = 1940 m. Similarly, to add 1.6 meters and 12 centimeters, convert 12 cm to meters by moving the decimal two places left, giving 0.12 m. Then add: 1.6 m + 0.12 m = 1.72 m. Always ensure units match before performing operations to maintain accuracy.

Converting metric units is often easier because the metric system is decimal-based, meaning all conversions involve multiplying or dividing by powers of ten. This allows conversions to be done simply by moving the decimal point left or right, depending on whether you are converting to a larger or smaller unit. In contrast, US customary units involve irregular conversion factors (e.g., 12 inches in a foot, 3 feet in a yard), requiring more complex calculations. The metric system's consistent base-10 structure and the use of prefixes like kilo, centi, and milli make conversions straightforward and less error-prone, especially when using tools like the prefix line or mnemonic devices.