##### Units of measurements

### What is a unit of measurement?

A unit of measurement is a definite magnitude of a quantity that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of the measurement.

To measure a unit means to compare it with another unit of the same kind of unit measurement.

The International System of Units (SI)

SI is a system of measurement that is known in almost every country in the world. It is made from a coherent system of unit measurements with seven base units that are:

### Unit of Lengths

Length describes how long a thing is from one end to another. The meter is the base unit of length in the International System of Units (SI). The SI unit symbol is m.

### Multiples and Submultiples of Meter

### Multiples

**Kilometer (km)**

**1 km = 1000 m**

**Hectometer (hm)**

**1 hm = 100 m**

**Decameter (dam)**

**1 dam = 10 m**

Submultiples

**Decimeter (dm)**

**1 dm = 0.1 m**

** Centimeter (cm)**

** 1 cm = 0.01 m**

** Millimeter (mm)**

** 1 mm = 0.001 m**

### Example 1: Convert the units into meter.

Based on the figure above we convert our units.

a) 153 km

Kilometer is a multiple of meter so:

153 km = 153 x 10 x 10 x 10

= 153 x 1000 = 153’000

b) 52 hm

Hectometer is a multiple of meter so:

52 hm = 52 x 10 x 10

= 52 x 100 = 5’200

c) 12 cm

Centimeter is a submultiple of meter so:

12 cm = 12 ÷ 10 ÷ 10

= 12 ÷ 100 = 0.12 m

d) 2 mm

Millimeter is a submultiple of meter so:

2 mm = 2 ÷ 10 ÷ 10 ÷ 10

= 2 ÷ 1000 = 0.0002 m

Example 2: Simplify by applying the basic operations.

Firstly we need to convert all the terms on the same unit.

a) 11 cm + 5 mm + 20 m

We see that the lowest unit is mm and the highest. You can convert each whatever unit you want, all it matters is they are all converted as the same unit.

We are going to converts to the lowest unit mm:

11 cm = 11 x 10 = 110 mm

20 m = 20 x 10 x 10 x 10

= 20 x 1000 = 20’000 mm

Now we add all the terms:

11 cm + 5 mm + 20 m

= 110 mm + 5 mm + 20‘000 mm

= 20’115 mm

b) 62 km – 500 m – 3 km

In this case is more appropriated to convert meter to kilometer since the other two terms are in kilometers.

500 m = 500 ÷ 10 ÷ 10 ÷ 10

= 500 ÷ 1000 = 0.5 km

Now we subtract all the terms:

62 km – 500 m – 3 km

= 62 km – 0.5 km – 3 km

= 58.5 km

c) 5 hm + 1200 dm + 1 dam

Let’s convert the terms into decameter:

5 hm = 5 x 10 = 50 dam

1200 dm = 1200 ÷10 ÷ 10 = 1200 ÷ 100 = 12 dam

Now we add all the terms:

5 hm + 1200 dm + 1 dam = 50 dam + 12 dam + 1 dam = 63 dam

### Units of Area

Area is the space occupied by a flat shape. The square meter is unit of area derived from the International System of Units (SI). The symbol is m2. It is defined as the area of a square with sides of exactly 1 m.

Multiples and Submultiples of Square Meter

### Multiples

**1 km2 = 1’000’000 m2**

**1 hm2 = 10’000 m2**

**1 dam2 = 100 m2**

Submultiples**1 dm2 = 0.1 m2**

**1 cm2 = 0.01 m2**

**1 mm2 = 0.001 m2**

Example 4: Find the area of a rectangle on cm2 where the length is 5dm and the width is 3dm.

The area of a rectangle is: A= length x width = 5dm x 3 dm = 15 dm2

Converting into cm2

15 dm2 = 15 x 100 = 1’500 cm2

### Units of Volume

Volume is the quantity of three dimensional space enclosed by a closed surface. Its labeled V and it´s quantified numerically using the SI derived unit the cubic meter.

Multiples and Submultiples of Square Meter

Multiples

1 km3 = 1’000’000’000 m3

1 hm3 = 1’000’000 m3

1 dam3 = 1000 m3

Submultiples

1 dm3 = 0.001 m3

1 cm3 = 0.000001 m3

1 mm3= 0.000000001 m3

Example 5: Compare the units.

a) 5 cm3 and 3 dm3

b) 0,5 km 3 and 100 dam3

c) 1 mm3 and 5-10m3

Firstly we have to convert them in the same unit and then compare which one is smaller or larger.

a) 3 dm3 = 3 x 1000 = 3’000 cm3

5 cm3 < 3’000 cm3

so 5 cm3 < 3 dm3

b) 0,5 km 3 = 0,5 x 1000 x 1000 = 500’000 dam3

500’000 dam3 > 100 dam3

so 0,5 km 3 > 100 dam3

c) 5-10 m3 = 0,0000000005 m3 =0,0000000005 m3 x 1000 x 1000 x 1000= 5 mm3

1 mm3 < 5 mm3

so 1 mm3 < 5-10 m3

### Units of Capacity

To measure the volume of fluids we use other units that are called the unit of Capacity. Capacity is how much a container can hold. The basic unit of the volume of fluids is liter and is labelled with l or L.

Multiples

**Kiloliter**

**1 kl = 1000 l**

**Hectoliter**

**1 hl = 100 l**

**Decaliter**

**1 dal = 10 l**

**Submultiples **

**Deciliter**

**1 dl = 0.1 l**

**Centiliter**

**1 cl = 0.01 l**

**Milliliter**

**1 ml = 0.001 l**

The liter is a metric unit of volume. It is equal to 1 cubic decimeter.

1 l = 1 dm3

The SI unit of volume is the cubic meter (m3)

### Unit of Mass

Mass is the amount of matter a thing consists of. Kilogram is the base unit of mass in the International System of Units (SI). The SI unit symbol is kg.

Multiples of Kilogram

Ton

1 ton = 1000 kg

Quintal

1 = 100 kg

**Submultiples of Kilogram**

**Hectogram**

**1 hg = 0.1 kg**

**Decagram**

**1 dag = 0.01 kg**

**Gram**

**1 g = 0.001 kg**

**Decigram**

**1 dg = 0.0001 kg**

**Centigram**

**1 cg = 0.00001 kg**

**Milligram**

**1 mg = 0.000001 kg**

### Units of Time

Time is the ongoing sequence of events in life. Second is the base unit of time in the International System of Units (SI). The SI unit symbol is s.

The units of time

1 minute = 60 seconds (1min = 6s)

1 hour = 60 minute (1h = 60min)

1 day = 24 hours

1 week = 7 days

1 month = 30 or 31 days

1 year = 12 months

Example 6: Convert the units.

a) 5 hours into minutes

Since 1h = 60min

then 5h = 5 x 60 = 360min

b) 360 seconds into hours

Since 1h = 60min and 1min = 60s

then 1h = 60min = 60 x 60 = 3600s

Now divide the seconds with 3600

360 ÷ 3600 = 0.1h

so 360s = 0.1h

c) 2 days into minutes

Since 1 day = 24 hour and 24 hour = 24 x 60 = 1440 minutes

then 2 days = 2 x 24h

= 48h and 48h x 60

= 2880 minutes.