Metric Units of Length: 동영상 및 연습문제

The basic unit of length in the metric system is the meter (m). 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 by factors of ten.

Converting between metric units of length involves moving the decimal point based on the difference in prefixes. Since the metric system is base 10, moving from a smaller unit to a larger unit means moving the decimal point to the left, making the number smaller. Conversely, moving from a larger unit to a smaller unit means moving the decimal point to the right, making the number larger. For example, to convert 250 meters to kilometers, you move the decimal three places left (because 1 km = 1000 m), resulting in 0.25 km. To convert 23.6 hectometers to centimeters, you move the decimal four places right (since 1 hm = 100 m and 1 cm = 0.01 m), giving 236,000 cm. A helpful mnemonic to remember the order of prefixes is "King Henry Doesn't Usually Drink Chocolate Milk," representing kilo, hecto, deca, unit (meter), deci, centi, and milli.

Yes, addition and subtraction with metric units of length are possible but require the units to be the same. Unlike the US system, metric units are not written as mixed units, simplifying operations. To add or subtract, first convert all measurements to the same unit. For example, to subtract 560 meters from 2.5 kilometers, convert 2.5 km to meters by moving the decimal three places 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, resulting in 0.12 m. Then add: 1.6 m + 0.12 m = 1.72 m. This method ensures accuracy and consistency in calculations.

A popular mnemonic to remember the order of metric prefixes is "King Henry Doesn't Usually Drink Chocolate Milk." Each word's first letter corresponds to a prefix: K for kilo (1000), H for hecto (100), D for deca (10), U for the base unit (meter), D for deci (0.1), C for centi (0.01), and M for milli (0.001). This helps students quickly recall the sequence and relative sizes of metric units, making conversions and understanding easier.

When multiplying or dividing metric units of length by a number, the unit remains the same. For example, dividing 12.6 meters by 3 results in 4.2 meters. The operation affects only the numerical value, not the unit. This is simpler than addition or subtraction because you do not need to convert units before performing the operation. Just perform the arithmetic on the number and keep the unit unchanged.