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Chapter 2: Problem 62

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

Short Answer

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

Step by step solution

01

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))
02

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
03

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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: \( 2 \, \text{m} \times 10 = 20 \, \text{dm} \).

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Most popular questions from this chapter

Describe how adding the prefix mega- to a unit affects the quantity being described

Challenge Express each quantity in regular notation along with its appropriate unit. \(\begin{array}{llllll}{\text { a. } 3.60 \times 10^{5} \mathrm{s}} & {\text { b. } 5.4 \times 10^{-5} \mathrm{g} / \mathrm{cm}^{3}} & {\text { c. } 5.060 \times 10^{3} \mathrm{km}} & {\text { d. } 8.9 \times 10^{10} \mathrm{Hz}}\end{array}\)

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Write two conversion factors for each of the following. a. a 16\(\%\) (by mass) salt solution b. a density of 1.25 \(\mathrm{g} / \mathrm{mL}\) c. a speed of 25 \(\mathrm{m} / \mathrm{s}\)
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