# Converting Metrics

Suppose you are walking to school from home. And you reached the school after walking for 1 kilometre. So here you talked about a specific measurement that is a kilometre. But instead of saying 1 kilometre, you could also say that you walked 1000 meters. Both 1 kilometre and 1000 meters measure equal distance but the unit changes.

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So in this section, we will learn how to convert metric units and see how to calculate them.

## Converting metrics meaning

The metric system is the standard and most widely used method of measurement. The most basic metric system consists of measuring units of length, weight, and volume.

Like in the above example one cannot just say I travelled 1 from home to school. It does not make any sense. We have to include some measuring units to make them more understandable and specific. As we are talking about distance, we say it in the form of kilometres.

When comparing any object or quantity we need similar unit measures. And the way to make it happen is by converting the metric into the same unit measures.

John bought 1 kilogram of apples. And Anne bought 1500 grams of apples. So to know who bought more apples, we cannot just tell by looking at the values. We need to either convert kilogram to gram or vice versa.

## Metric conversion calculation

We need to calculate the metric conversion to compare the given values of measurements. First, let's take a look at the base units and prefixes which are common for the basic units of measurement.

### Metric prefixes for conversion

The metric system is a base 10 system of units built on a collection of base units. This translates to a system where each unit is a combination of a base unit and a prefix, and each succeeding unit is 10 times larger than the previous one. And all the values are in the reference to the base unit.

Here in the table, the prefix with its value is mentioned to make it easier to understand.

 Prefix Symbol Value Exponent kilo k $1000$ ${10}^{3}$ hecto h $100$ ${10}^{2}$ deca da $10$ ${10}^{1}$ Base unit $1$ ${10}^{0}$ deci d $\frac{1}{10}$ ${10}^{-1}$ centi c $\frac{1}{100}$ ${10}^{-2}$ milli m $\frac{1}{1000}$ ${10}^{-3}$

Metrics prefix, StudySmarter Originals

### Metric conversion for individual measuring units

Here we will see the individual conversion of metric units from the above-mentioned table for the following three types of measuring units:

• Length

• Mass

• Volume

 Measuring quantity Base unit Symbol Length metre m Mass/weight gram g Volume litre l

#### Length

Length is used to measure any type of distance or size. The base unit for length is always taken as a metre. And based on it other conversions are defined. For example the size of the book in terms of thickness and length, or distance between two places.

 Unit Symbol Value kilometre km $1000$ hectometre hm $100$ decametre dam $10$ metre (base) m $1$ decimetre dm $\frac{1}{10}$ centimetre cm $\frac{1}{100}$ millimetre mm $\frac{1}{1000}$

#### Mass

Mass is the unit measure for finding the weight of any object. The base unit for weight is considered a gram. Example - the weight of our body, the quantity of vegetables in weight.

 Unit Symbol Value kilogram kg $1000$ hectogram hg $100$ decagram dag $10$ gram (base) g $1$ decigram dg $\frac{1}{10}$ centigram cg $\frac{1}{100}$ milligram mg $\frac{1}{1000}$

#### Volume

The capacity of any object that can hold the amount of any liquid is measured in volume. Litre is considered the base unit for volume. Examples of volume can be juice in a bottle, or water in a jug.

 Unit Symbol Value kilolitre kl $1000$ hectolitre hl $100$ decalitre dal $10$ litre (base) l $1$ decilitre dl $\frac{1}{10}$ centilitre cl $\frac{1}{100}$ millilitre ml $\frac{1}{1000}$

## Converting metric methods

We can use the following methods for converting metrics between the same units:

1. Through multiplication or division

2. Through decimal movement

### Through multiplication or division

We can either multiply or divide the correct conversion factor with the given value to convert the metric units. The following steps are applied to the given unit for converting it into the other metric units:

1. Identify if the conversion unit has a small or larger prefix than the given measure unit.

2. If the conversion unit is smaller then multiply it with the appropriate power of 10. Or if the conversion unit is larger then divide it with the appropriate power of 10.

Metric conversion by multiplication and division, StudySmarter Originals

Convert 7 km into cm.

Solution:

We will follow the above-given steps to make the conversion.

Step 1: Given unit is kilo and the conversion unit is centi. So a centi is smaller than a kilo.

Step 2: As the conversion unit is smaller we will perform multiplication. So from kilo to centi, we will multiply by:

$10×10×10×10×10={10}^{5}$

So conversion of 7 km to cm is

$7km=7×{10}^{5}=700000cm$

### Through decimal movement

The other method to convert metric units is through decimal movement. Here we shift the decimal point based on the prefix of the conversion units. We will follow the given steps to convert the metric units:

1. Identify the prefix of the conversion unit, and check if it is smaller or larger than the given unit.

2. If the prefix is smaller then shift the decimal point to the right side for each power of 10. And if the prefix is larger, then shift the decimal point to the left side for each power of 10.

Note: If the number doesn’t contain a decimal point and is a whole number, then convert and write it in the decimal form and then apply the above steps for unit conversion.

Converting metrics by decimal point, StudySmarter Originals

Convert 2 dg to dag

Solution:

To convert decigram to decagram we will use the above-mentioned steps.

Step 1: Here decagram(dag) is larger than the decigram(dg).

Step 2: As the conversion unit dag is larger than the given unit dg, the decimal point will shift to the left side. The decimal point will shift by:

decigram to gram = 1 shift

gram to decagram = 1 shift

So the decimal point will shift to 2 points on the left side.

Then dag of 2 dg

$2dg=2.0dg=0.02dag$

## Imperial to Metric conversion

One of the other systems of measurement is the imperial system. Though mostly the metric system has replaced the imperial system, it is still used for measurement. The units included in the imperial system are pounds, ounces, miles, feet, inches, yard, pint, and gallon.

We can also make conversions from imperial to metric systems. For that, empirical units have a particular calculated conversion unit in the metric system. These conversion units are shown in the table below.To learn more detailed information on imperial units and their conversion you can refer to the other article on Metric and imperial units.

 Imperial units Metric units 1 inch 2.5 cm 1 foot 30 cm 1 yard 91.4 cm 1 mile 1.6 km 1 ounce 28 g 1 pound 453 g 1 stone 6.4 kg 1 pint 473 ml 1 gallon 3.785 l

## Converting metrics examples

Here some solved examples of converting metrics are shown for a better understanding.

How much 500 mg is in a hectogram?

Solution:

Here we are given the quantity in milligram (mg), and we need to convert it into hectogram (hg).

Step 1: We need to check if the prefix of hg is larger or smaller than mg. From the metric prefix chart, we know that hg is larger than mg.

Step 2: As hg is larger we will perform division on the value of mg to convert it into hg.

$500mg=500÷{10}^{5}\phantom{\rule{0ex}{0ex}}=\frac{500}{{10}^{5}}\phantom{\rule{0ex}{0ex}}=\frac{5×\overline{)10}×\overline{)10}}{10×10×10×\overline{)10}×\overline{)10}}\phantom{\rule{0ex}{0ex}}=\frac{5}{10×10×10}\phantom{\rule{0ex}{0ex}}=0.005hg$

So 500 mg is 0.005 hg.

Alice has 2.5 kl of orange juice. How much will it be in the terms of litres?

Solution:

Here we will convert kl into litres using the decimal movement method. (We can also use the multiplication or division method to convert the metric.)

Step 1: Using the metric prefix chart we can say that l is smaller than kl.

Step 2: So we will shift the decimal point on the right side. From kl to l there will be 3 shifts, so we get that

$2.5kl=2.5000kl=2500.0l$

Hence, Alice has 2500 litres of orange juice.

John has travelled 13 miles to visit his friend's place. How much distance did he cover in kilometres? (1 mile = 1.6 km)

Solution:

Here the distance is given in miles which is an imperial system. We need to convert it into a metric system.

Using the table for conversion of imperial to metric from the above topics (it is also given in the question), we get that

$1mile=1.6km\phantom{\rule{0ex}{0ex}}⇒13mile=1.6×13\phantom{\rule{0ex}{0ex}}=20.8km$

John travelled 20.8 km to reach his friend's place.

## Converting Metrics - Key takeaways

• The basic metric system consists of measuring units of length, weight, and volume.
• The metric system is a base 10 system of units built on a collection of base units.
• The methods to convert metrics between the same units are: Through multiplication or division, Through decimal movement.
• The units included in the imperial system are pounds, ounces, miles, feet, inches, yard, pint, and gallon.

#### Flashcards in Converting Metrics 14

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What are metric conversions?

Comparing and converting values in the same metric units are considered as metric conversion.

How do you calculate conversion metrics?

Metrics can be converted using either multiplication or division of power of 10 or by shifting decimal points in the proper direction.

What are some examples of metrics conversion?

Examples of metric conversion can be the calculating distance from km to m, or converting fruit weight from g to kg.

What are the steps in metrics conversion?

At first for the metric conversion is to identify the place of the prefix and the next step is to perform the proper operation based on that prefix.

How do you convert metrics to standard?

Metric can be converted to standard by multiplying or dividing the appropriate metric value.

## Test your knowledge with multiple choice flashcards

1 mm is equal to how many km?

How much is 1 ml in litres?

Is decilitre a measuring unit for metric system?

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