The basic metric units are meter (for length), gram (for mass or weight), and liter (for volume).

One unit can be converted into another one. For example, one milliliter equals one cubic centimeter and one gram is the weight of one cc of water.

To convert various prefixes and thus variously-sized units, we move up and down this list of prefixes, moving the decimal point as we go. This is the process of converting one unit to another.

1 milliliter = 0.1 centiliters

    = 0.01 deciliters
    = 0.001 liters
    = 0.000 1 dekaliters
    = 0.000 01 hectoliters
    = 0.000 001 kiloliters

Unit conversion is defined as the process of converting one unit to another. There are a number of metric prefixes involved in unit conversions:

Metric prefixes: kilo-, hecto-, deca-, deci-, centi- and milli-

The following sentence is used to remember the prefixes in order :

"King Henry Doesn't (Usually) Drink Chocolate Milk"

kilo- hecto- deca- (Unit)- deci- centi- milli-

The first letters of the words stand for the prefixes. "Usually" stands for Unit being meters, grams or liters.

Each step is ten times or one-tenth as much as the step on either side. So, we have:

1 kilometer = 10 hectometers

= 100 decameters
= 1000 meters
= 10,000 decimeters
= 100,000 centimeters
= 1,000,000 millimeters

Metric Prefix Common Unit Exponent Symbol
Kilo 1000 $10^{3}$ K
Hecto 100 $10^{2}$ H
Deka 10 $10^{1}$ D or Da
Base Unit 1 $10^{0}$ Meters, Grams or Liters
Deci 0.1 $10^{-1}$ d
Centi 0.01 $10^{-2}$ c
Milli 0.001 $10^{-3}$ m

Even before the idea of measurements got standardized it was largely driven by who was doing the measuring. A yard was the distance from the tip of the nose to the end of an outstretched arm or foot. An inch was considered often as the length of the index finger’s second bone.

The units of measure for length most commonly used in the United States are inches, feet, yards and miles. Units of measurement are not case sensitive and so we could use either "CM" or "cm" to set a measure for a given rule when we are using centimeters.

Inches are standard measure of length in the imperial system of measurement.
The measure for converting mm to inch would be, 25.4 mm to an inch, 10 mm to cm and 2.54 cm to inch.

Pica’s and points are basic typesetting units of measure. There are 72 points for an inch, 12 points for 1 pica, and 6 pica’s equals to1 inch. The p-length and q-height refer to the length and height of the letters’ ‘p’ and ‘q’ respectively, while Pixels are the standard units of measure for gauging the height and width on computer screens.

Some equivalent measures are 12 inches = 1foot, 3 feet = 1 yard, 5280 feet = 1 mile.

Conversion of Lengths:

  • Feet to inches: number of inches = number of feet x 12
  • Inches to feet: number of feet = number of inches ÷ 12
  • Yards to feet: number of feet = number of yards x 3
  • Miles to feet: number of feet = number of miles x 5,280

This section would help us learn dimensional analysis and how this could this be used to solve various types of everyday problems.

If we need to complete a particular work which is not exactly matching with the available dimensions then we need to do a quick analysis and make necessary changes to match the required amount or length.

To do that, convert one unit of measurement into another and make use of the available sources into proper logical solutions.

How do we convert one measure into another?

Step 1: Find out the converting factor according to the definition.
Step 2: Ratio of the two measuring or the conversion factor is multiplied to change into the required unit.
Conversion factor: it is the ratio of the two parts of the statement that relates to the two units.
Unit 1 x conversion factor = Unit 2

Example of length conversion:

Suppose we need to buy one fabric of 3 feet and the store we intend to buy from is selling that in meters, then we need to think quickly and convert the required length of fabric from feet into meters.

Here, one meter is equivalent to 3.28 feet or 3 feet is equivalent to 0.3048 meters. So we have to buy 3 times this converting factor. So, fabric bought would be equivalent to = (3 x 0.3048) m = 0.9144 meters

The space occupied by a solid is called its Volume.

Standard Unit of Volume:

The standard unit of volume is 1 cubic centimeter, written as 1 cu cm or 1 $cm^{3}$. The smaller unit of volume is 1 cubic millimeter, written as 1 cu. mm or 1 $mm^{3}$. The larger unit of volume is 1 cubic meter, written as 1 cu. m or $m^{3}$.

The basic unit of capacity in metric system is liter.

Convert one milliliter to metric units.

S.No Metric Numerical Value
1 Cubic meter 1 x $10^{6}$
2 Cubic decimeter 0.001
3 Cubic centimeter 1
4 Cubic milliliter 1000
5 Hectoliter 1 x $10^{5}$
6 Decaliter 0.0001
7 Liter 0.001
8 Deciliter 0.01
9 Centiliter 0.1
10 Microliter 1000

Examples on Volume Conversion

Given below are some examples on volume conversion.

Example 1:

The capacity of a closed cylindrical vessel of height is 15.4 liters. What is the radius of the cylinder?

Solution:

Given, Volume = 15.5 liters = 15400 $cm^{3}$ and h = 1m = 100 cm.

1 liter = 1000 cm3, 1 m = 100 cm

$\pi$ x $r^{2}$ x h = 15400

$\frac{22}{7}$ x $r^{2}$ x 100 = 15400

$r^{2}$ = 49

r = 7 cm

Example 2:

The volume of the cistern is 3 m long, 2 m wide and 1 m deep. How many liters of water must be thrown out so as to keep the water level 50 cm?

Solution:

Length = 3 m, width = 2 m, Height = 1 m

Volume of water to be emptied in the cistern = 3 x 2 x $\frac{1}{2}$

= 3 $m^{3}$

Since 1 $m^{3}$ = 1000 liters, 3000 liters of water must be thrown out.

In an object, weight is defined as the amount of matter in it. It depends on the force of attraction for an object on the earth. The measure term is used for specific result and is obtained from the measurement process.

Standard Unit of Weight:

In metric system, the common units of weight are grams, kilograms and tons.

Conversion of Metric units to Imperial units:

S. No Metric Unit Imperial/U.S Units
1 Gram 0.035 ounces
2 Kilogram 2.21 pounds
3 Metric ton (1000 kg) 0.98 uk tons
4 Metric ton (1000 kg) 1.10 us tons

Convert 1 kilogram into metric units.

S. No Metric Symbol of Units Conversion
1 Kilotons - 0.000001
2 Tons - 0.001
3 Kilo Newtons kN 0.009807
4 Canter - 0.01
5 Kilo Gram (kg) 1
6 Newton N 9.807
7 Gram (g) 1000
8 Centigram (cg) 100,000
9 Milligram (mg) 1,000,000
10 Microgram mcg 1,000,000,000

Examples on Weight Conversion

Given below are some examples on weight conversion.

Example 1:

Convert 12 tons into kilogram?

Solution:

We know that, 1 ton = 1,000 kilogram

Therefore, 12 tons = 12 x 1000

= 12,000 kilograms

Example 2:

Convert 25 grams to kilograms?

Solution:

We know that, 1 kg = 1000 grams

Therefore, 25 grams = 25 x 0.001

= 0.025 grams

Example 3:

Convert 2 kg to pounds?

Solution:

We know that, 1 kg = 2.21 pounds

Therefore, 2 kg = 2 x 2.21

= 4.42 pounds

Given below is the chart used for unit conversions.

1 cubic meter 423.776 board feet
1 cubic yard 0.765 cubic meters
1 cubic yard 324.000 board feet
1 cubic yard 27 cubic feet
1 board foot 144 cubic inches
1 kilogram 2.204 pound
1 pound/sf 0.00694 psi
1 psi 144 pounds/sf
1 psi 6.895 kPa
1 pound/cubic foot 16.02 kg/cubic meter
1kg/cubic meter 0.06242 pounds/cubic meter

Given below are some examples on unit conversion.

Example 1:

Convert 14.25 kilometers to centimeters

Solution:

kilo- hecto- deca- (Unit) - deci- centi- milli-

To convert km to cm, we need to move 5 places towards the right. So, we move the decimal point 5 digits towards the right

14.25000 kilometers = 1,425,000 centimeters

Example 2:

Convert 256 mL to hL

Solution:

kilo- hecto- deca- (Unit)- deci- centi- milli-

To convert mL to hL, we need to move 5 places towards left. So, we move the decimal point 5 places towards the left.

256 mL would be 0.00256 hL

Example 3:

Mary made 1.25 L of juice. How many milliliters of juice does she have?

Solution:

We can write a proportion to change metric units of measurement.

Step1: Let us use the relationship of liter to milliliters to write a proportion:

$\frac{1\ L}{1,000ml}$ = $\frac{12.5\ L}{xml}$

Step 2: Find the cross product

x = 12.5 x 1000

Step 3: Solve for x

x = 12,500 ml

So, Mary has 12,500 ml of juice.