Metric Units

• Introduction
• Metric Units 
• Metric System Chart
• Metric Conversions
• The Metric System in Our Daily Life
• Comparison: Metric System Versus Imperial System
• Solved Examples
• Practice Problems
• Frequently Asked Questions

Introduction

The units of measurement used in a metric system are called metric units. The metric system is a universal system for measuring quantitative things, such as distance, volume and weight. Imagine you have a bottle of milk. You'd use liters to measure how much milk is inside and centimeters to measure its height. This system is used all over the world and is also called The International System of Units `(SI)`. It's not just for everyday stuff, though. From science labs to military operations, the metric system is everywhere. 

The metric system is introduced to provide a standard set of units for measuring these aspects. Essentially, it's a way of measuring things like length, distance, capacity, weight, volume, area, and temperature using a consistent system.

Metric Units 

In the world of measurement, we rely on a system called the metric system or SI unit system. It's based on seven base units: meter, kilogram, seconds, kelvin, ampere, mole, and candela. These units, like the kilogram, include subunits such as grams and milligrams, which serve specific purposes.

For instance, we measure length using units like millimeters, centimeters, meters, and kilometers, while weight is measured in grams and kilograms.

In the metric system, the units to measure length, weight (mass), and capacity (volume) are:

Metric System Chart

The metric system chart is like a cheat sheet for converting different metric units. It contains formulas that show how to change from one unit to another quickly.

Let’s take a look at the metric system chart provided below.

Metric Conversions

The metric system chart is like a roadmap for converting between different units of measurement. It organizes units from biggest to smallest, all based on one main unit.

Going to the right, each unit gets smaller by a factor of `10` and going to the left, each unit gets bigger by a factor of `10`. 

Weight Conversions

The kilogram serves as the standard unit for measuring weight, and we typically employ either a beam balance or a weighing scale as the standard tools for weight measurement. Some examples of weight measurements are: 

• A bag of apples weighing `2` kilograms.
• A sachet of medicine weighing `50` miligrams.
• A pack of chips weighing `50` grams.

Take a glance at the metric system chart that displays how to change metric weights.

Volume Conversions

Capacity refers to the volume or space taken up by an object, measured typically in liters. The measuring cup is the standard tool utilized for this purpose. It's used to gauge how much substance an object can contain. Some examples of volume measurements are:

• A liter of water
• `500` ml of juice
• `5` ml of olive oil

Take a glance at the metric system chart that displays how to change metric volume.

Length Conversions

Length can be measured in various units, however, millimeters, centimeters, meters, and kilometers are the main units in the metric system for measuring length. Length is widely used to measure the size or height of an object, and it's also useful for determining the distance between two objects. The basic unit of length in the metric system is the meter. Some examples of length measurements are:

• Length of pencil is `15` cm
• Road is `3` km long
• Height of the building is `50` meters

Take a glance at the metric system chart that displays how to change metric lengths.

The Metric System in Our Daily Life

• When cooking or baking, recipes often call for ingredients to be measured in metric units such as grams `(\text{g})` or milliliters `(\text{mL})`.
• Many people use metric units, such as kilograms `(\text{kg})`, to measure their body weight on scales at home or in gyms.
• Distances are typically measured in kilometers `(\text{km})`, whether it's for daily commutes, road trips, or estimating walking distances.
• At the grocery store, fruits, vegetables, and other items are often sold by weight, with the weight measured in grams `(\text{g})` or kilograms `(\text{kg})`.
• Beverages like milk, juice, and water are commonly sold in metric units such as liters `(\text{L})` or milliliters `(\text{mL})`, which are also used for measuring liquid quantities at home.

Comparison: Metric System Versus Imperial System

In math, we often use two main systems to measure things: the metric system and the imperial system. The metric system is simpler and used around the world, while the imperial system is more common in countries like the US, Myanmar, and Liberia. 

Let's take a look at how these systems compare in the table below:

Solved Examples

Example `1`: How many millimeters are there in `2.5` meters?

Solution:

Given that `1` meter is equivalent to `1000` millimeters, we can set up a proportion to find the number of millimeters in `2.5` meters:
`1 \text{ meter} = 1000 \text{ millimeters}`
`2.5 \text{ meters} = x \text{ millimeters}`

Cross-multiplying, we get:
`1 \times x = 2.5 \times 1000`
`x = 2500`

Therefore, there are `2500` millimeters in `2.5` meters.

Example `2`: Convert `3.75` kilograms to grams.

Solution:

Since `1` kilogram is equal to `1000` grams, to convert kilograms to grams, we simply multiply by `1000`
`3.75 \text{ kilograms} \times 1000 \text{ grams/kilogram} = 3750 \text{ grams}`

Therefore, `3.75` kilograms is equal to `3750` grams.

Example `3`: How many centimeters are there in `5.4` meters?

Solution:

Given that `1` meter is equivalent to `100` centimeters, to find the number of centimeters in `5.4` meters:
`1 \text{ meter} = 100 \text{ centimeters}`
`5.4 \text{ meters} = x \text{ centimeters}`

Using proportion, we have:
`1 \times x = 5.4 \times 100`
`x = 540`

Thus, there are `540` centimeters in `5.4` meters.

Example `4`. Convert `850` milliliters to liters.

Solution:

Since `1` liter is equal to `1000` milliliters, to convert milliliters to liters, we divide by `1000`
`850 \text{ milliliters} \div 1000 \text{ milliliters/liter} = 0.85 \text{ liters}`

Hence, `850` milliliters is equivalent to `0.85` liters.

Example `5`. If a bookshelf is `2.2` meters wide, how many millimeters wide is it?

Solution:

Given that `1` meter is equivalent to `1000` millimeters, to find the width of the bookshelf in millimeters:
`1 \text{ meter} = 1000 \text{ millimeters}`
`2.2 \text{ meters} = x \text{ millimeters}`

Setting up a proportion, we have:
`1 \times x = 2.2 \times 1000`
`x = 2200`

Therefore, the bookshelf is `2200` millimeters wide.

Practice Problems

Q`1`. What is `3.5` kilometers equivalent to in meters?

1. `350` `\text{m}`
2. `3500` `\text{m}`
3. `35` `\text{m}`
4. `0.35` `\text{m}`

Answer: b

Q`2`.  If a swimming pool contains `7500` liters of water, how many cubic meters (`m^3`) of water does it hold?

1. `7.5` `\text{m}^3`
2. `5` `\text{m}^3`
3. `0.75` `\text{m}^3`
4. `750` `\text{m}^3`

Answer: a

Q`3`. Convert `450` grams to kilograms.

1. `0.045` `\text{kg}`
2. `4.5` `\text{kg}`
3. `0.45` `\text{kg}`
4. `45` `\text{kg}`

Answer: c

Q`4`. How many milliliters are there in `3.25` liters of juice?

1. `32.5` `\text{mL}`
2. `3250` `\text{mL}`
3. `325` `\text{mL}`
4. `0.325` `\text{mL}`

Answer: b

Q`5`. If a rope is `2.8` meters long, how many centimeters long is it?

1. `280` `\text{cm}`
2. `2.8` `\text{cm}`
3. `28` `\text{cm}`
4. `0.28` `\text{cm}`

Answer: a

Frequently Asked Questions

Q`1`. What are metric units?

Answer: Metric units are a standardized system of measurement based on the metric system, using meters, grams, and liters as the fundamental units for length, mass, and volume, respectively.

Q`2`. How do I convert between different metric units?

Answer: To convert between different metric units, you can use conversion factors based on the relationships between units. For example, to convert meters to centimeters, you multiply by `100` because there are `100` centimeters in `1` meter.

Q`3`. Why are metric units preferred over imperial units?

Answer: Metric units are preferred in many fields due to their simplicity, consistency, and ease of conversion. They follow a decimal system, making calculations straightforward and providing a universal standard for measurements.

Q`4`. What are the most commonly used metric prefixes?

Answer: The most commonly used metric prefixes include `\text{kilo- (k)}`, `\text{hecto- (h)}`, `\text{deca- (da)}`, `\text{deci- (d)}`, `\text{centi- (c)}`, and `\text{milli- (m)}`. These prefixes denote powers of `10` and are used to scale measurements up or down.

Q`5`. Are metric units used globally?

Answer: Yes, metric units are widely used globally, with the exception of a few countries such as the United States, which primarily use the imperial system. However, even in countries using imperial units, metric units are commonly used in scientific, medical, and international contexts.