Question

How many meters are in one kilometer? In one decimeter?

Short answer

In conclusion, there are \(1,000\) meters in one kilometer and \(10\) decimeters in one meter.

Step-by-step solution

Understand the metric system and its prefixes

The metric system uses a base unit and prefixes that represent multiples or divisions of the base unit. In this case, our base unit is a meter (m). Some common prefixes are: - Kilo (k): Represents a multiple of 1,000 (10^3) - Deci (d): Represents a division by 10 (10^(-1))

Convert kilometers to meters

We are given one kilometer (1 km) and asked to convert it into meters. Using the kilo prefix, we know that 1 kilometer is equal to 1,000 meters. So, the conversion can be written as: 1 km = 1 * 10^3 m = 1,000 m

Convert meters to decimeters

We are also asked to convert meters into decimeters. Using the deci prefix, we know that 1 meter is equal to 10 decimeters. So, the conversion can be written as: 1 m = 1 * 10^1 dm = 10 dm In conclusion, there are 1,000 meters in one kilometer and 10 decimeters in one meter.

Key concepts

Meter to Kilometer Conversion

To convert meters to kilometers, you need to understand that a kilometer (km) is a larger unit than a meter (m) in the metric system. The word 'kilo' is derived from a Greek word meaning 'thousand.' Thus, the prefix 'kilo' in the metric system indicates a thousand, or \(10^3\). This means that one kilometer is exactly equivalent to 1,000 meters.

• If you have a distance in meters and you want to convert it to kilometers, you need to divide the number of meters by 1,000.
• This conversion is useful in scenarios where you need to express large distances, for instance, the distance between cities or the length of a marathon.

For example:

• To convert 5,000 meters to kilometers, divide 5,000 by 1,000, resulting in 5 kilometers.
• This can be written in terms of the formula: \( 5,000 \, \text{m} \div 1,000 = 5 \, \text{km} \).

Kilometer to Meter Conversion

The conversion from kilometers back to meters is essentially the reverse process. When you're moving from a larger unit to a smaller unit, you multiply. Since one kilometer equals 1,000 meters, you multiply the number of kilometers by 1,000 to get the equivalent number of meters.

• This conversion is especially important in detailed scientific calculations where precise measurements in smaller units, like meters, might be necessary.
• To convert kilometers to meters, use the following formula: \( \text{kilometers} \times 1,000 = \text{meters} \).

For example:

• If you have 3 kilometers and want to know how many meters this is, simply multiply 3 by 1,000 to get 3,000 meters.
• In mathematical terms, \( 3 \, \text{km} \times 1,000 = 3,000 \, \text{m} \).

Deci Prefix in Metric System

The 'deci' prefix is crucial when working with the metric system as it represents a factor of one-tenth, or \(10^{-1}\). This is smaller than the base unit. When you see 'deci,' it indicates that you are dividing by 10 to get the corresponding smaller unit. In terms of length, 1 meter equals 10 decimeters (dm).

• This conversion proves significant, particularly in measurements that require more precision, such as in design and construction disciplines.
• Understanding this prefix helps you determine smaller divisions of meters when exact measurements are needed.

For example:

• To know how many decimeters correspond to 2 meters, simply multiply by 10 to get 20 decimeters.
• This can be represented mathematically: \( 2 \, \text{m} \times 10 = 20 \, \text{dm} \).