Metric Units of Length: 동영상 및 연습문제
Metric Units of Length are based on the metric system, a decimal system built from the basic unit, the meter (m). Common metric length units include kilometer (km), hectometer (hm), decameter (dam), meter (m), decimeter (dm), centimeter (cm), and millimeter (mm). These units scale by powers of ten, so moving to larger units means dividing by 10 each step, while moving to smaller units means multiplying by 10 each step.
Key relationships include \(1\text{ km}=1000\text{ m}\) , \(1\text{ cm}=0.01\text{ m}\) , and \(1\text{ mm}=0.001\text{ m}\) . Converting between metric units can be done with unit fractions or a prefix line by moving the decimal point left for smaller-to-larger units and right for larger-to-smaller units.
When working with measurements, addition and subtraction require like units first, so values must be converted to the same unit before combining. Multiplication or division by a number keeps the same unit. Estimating reasonable units is also important, since small objects are often measured in millimeters or centimeters, while longer distances are commonly measured in meters or kilometers.
Intro to the Metric System
Intro to the Metric System Example 1
Select the most reasonable metric unit for the given object.
A pencil is about 18 ___ long.
mm
cm
m
km
Select the most reasonable metric unit for the given object.
A soccer field is about 100 ___ long.
mm
cm
m
km
Select the most reasonable metric unit for the given object.
A grain of rice is about 7 ___ long.
mm
cm
m
km
Conversions: Metric Length
Fill in the blank to convert as indicated.
4500 mm = _____ m
Fill in the blank to convert as indicated.
650 m = ______ dam
Fill in the blank to convert as indicated.
7300 cm = ________ mm
Fill in the blank to convert as indicated.
65 hm = _________ dm
Conversions: Metric Length Example 2
Conversions: Metric Length Example 3
Operations: Metric Length
Perform the indicated operation.
Perform the indicated operation.
Perform the indicated operation.
Perform the indicated operation.
Operations: Metric Length Example 4
학생들이 이 주제에 대해 묻는 질문은 다음과 같습니다:
The basic unit of length in the metric system is the meter (m). Other units are derived from the meter using 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 are based on multiplying or dividing by 10, making conversions straightforward. The metric system’s decimal nature allows easy scaling up or down by moving the decimal point, which is why it is widely used in science and everyday measurements worldwide.
To convert between metric units of length, you can use the prefix line method or unit fractions. The prefix line orders units from largest to smallest: kilometer (km), hectometer (hm), decameter (dam), meter (m), decimeter (dm), centimeter (cm), and millimeter (mm). Since the metric system is base 10, converting involves moving the decimal point. Moving from a smaller unit to a larger unit (e.g., centimeters to meters) means moving the decimal point to the left. Moving from a larger unit to a smaller unit (e.g., kilometers to meters) means moving the decimal point to the right. The number of places you move corresponds to the difference in prefixes. For example, converting 250 meters to kilometers involves moving the decimal three places left, resulting in 0.25 km.
The 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, H for hecto, D for deka, U for the base unit (meter), D for deci, C for centi, and M for milli. This helps you recall the sequence from largest to smallest units, which is essential for converting between units by moving the decimal point the correct number of places. For example, kilo is 1000 times the base unit, while milli is 1/1000 of the base unit.
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 kilometers to meters by moving the decimal three places to the right, resulting in 2500 meters. Then subtract 560 meters to get 1940 meters. Similarly, to add 1.6 meters and 12 centimeters, convert 12 centimeters to meters by moving the decimal two places left, resulting in 0.12 meters. Then add 1.6 meters and 0.12 meters to get 1.72 meters. Always convert to like units before performing operations.
The metric system is preferred in science because it is decimal-based and standardized worldwide, which reduces confusion. Its units are based on powers of ten, making conversions simple by moving the decimal point rather than complex calculations. This consistency allows scientists to easily compare and communicate measurements globally. Additionally, the metric system’s use of a single base unit (the meter) with prefixes for larger or smaller units streamlines calculations and reduces errors, making it ideal for precise scientific work.
