In mathematics, we come across with physical quantities, such as - length, weight, temperature etc. These quantities are associated with some magnitude and a unit. Magnitude is a constant number, while the unit is a standard according to which the magnitude has been expressed. Each physical has its predefined unit of measurement. There are metric units of measurement in mathematics. **Metric units** are one of the most important and useful topics.

The metric system is defined as an international decimal system of measuring physical quantities. Metric units or metric measurement units are used for the purpose of calculating units of other quantities. Metric units are the most common system for measuring different types units in all over the world. It is widely utilized scientifically, commercially and personally. Metric units are the base units that are used to formulated other larger and smaller units from the standard set of prefix in powers of ten. Metric system of units is also termed as **SI system**. It defines the 7 basic units which are length, mass, time, temperature, luminous intensity, electric current and amount of substance. The units of all other quantities are derived from these 7 basic units.

Let us see some metric measurement units.

In Metric System,

**The unit of Length is meter (m)**

**The unit of Mass is kilogram (g)**

**The unit of Time is second (s)**

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Metric units is a system for measuring different type of units. This system is

used for the purpose of calculating an international decimalised system of measurement. In the metric system other units of measurement are obtained by multiplying and dividing by powers of 10. The metric system has

**m**the**meter**for length**Kg**the**kilogram**for mass**S**the**second**for time**A**the**ampere**for electric current^{}**K**the**kelvin**for Temperature**cd**the**candela**for luminous intensity**mol**the**mole**for Amount of substance

1 kilometer = 1000 meters

1 hectometer = 100 meters

1 decameter = 10 meters

A meter is the basic unit of length

1 decimeter = $\frac{1}{10}$ meter

1 centimeter = $\frac{1}{100}$ meter

1 millimeter = $\frac{1}{1000}$ meter

In the metric system the standard unit of mass is given as "gram". Some more units of mass and their equivalent units are given below:

1milligram = 0.001 gram

1centigram = 0.01 gram

1decigram = 0.1 gram

1kilogram = 1000 grams

- The symbolic form of this masses are given as follow:

1milligram = 1 mg

1centigram = 1 cg

1decigram = 1 dg

1gram = 1 g

1kilogram = 1 kg

1 gram mass is about the mass of a paper clip.

one kilogram mass is about the mass of one liter of water.

Metric units of volume are:

1 Milliliter = 0.001liter

1 Centiliter = 0.01liter

1 Deciliter = 0.1liter

1 Kiloliter = 1000liters

- The symbolic form of the above measurements are given below:

1 Milliliter = 1 ml

1 centiliter = 1 cl

1 deciliter = 1 dl

1 liter = 1 l

1 kiloliter = 1 kl

**Here are some useful conversions are given for the time.**

1 minute = 60 seconds

1 hour = 60 minutes = 3600 seconds

1 day = 24 hours

1 week = 7 days

1 year = 365 $\frac{1}{4}$ days

1 centiliter = 10 milliliters

1 deciliter = 10 centiliters

1liter = 10 deciliters

1cubic meter = 1000 liters

Metric units and measurements of length, mass, volume and temperature:

1 meter (m) = 10 decimeters (dm) = 100 centimeter (cm)

1 centimeter (cm) = 10 millimeters (mm) = 0.01 meter

1 decimeter (dm) = 10 centimeters(cm) = 0.1 meter

1 dekameter (dam) = 10 meters

1 kilometer (km) = hectometers = 1,000 meters

1 hectometer (hm) = 10 dekameters = 100 meters

1 gram = 1000 milligram

1 gram = 100 centigram

10 decigrams = 1 gram (g) = 1,000 milligrams

1 kilogram = 1000 grams

10 dekagrams = 1 hectogram (hg) = 100 grams

10 hectograms = 1 kilogram (kg) = 1,000 grams

10 milligrams (mg) = 1 centigram (cg)

10 centigrams = 1 decigram (dg) = 100 milligrams

1 kiloliter = 1000 liters

1 liter = 1000 milliliter

1 liter = 100 centiliter

1 liter = 10 deciliter

1 centiliter (cl) = 10 milliliter (ml)

10 centiliters = 1 deciliter (dl) = 100 milliliters

10 deciliters = 1 liter (l) = 1,000 milliliters

Celsius Fahrenheit Kelvin

100 212 373 (Boiling point of water)

30 86 303 (a hot day)

20 68 293 (Average room temperature)

0 32 273 (Freezing point)

- 40 - 40 233 (Celsius and Fahrenheit are same)

Metric units system convert larger units to smallest unit or smallest unit to larger units.

1 km = 1000 m

1 m = 100 cm

1 cm = 10 mm

From here we can say that, a kilometre is a larger unit than a metre, a metre is a larger unit than a centimetre and a cm is a larger unit than millimeter.

Let see

(1) To convert length from a large unit into a small unit, multiply by the relevant power of 10.

(2) To convert length from a small unit into a large unit, divide by the relevant power of 10.

Step 1:

= 5000000 mm

1 km = 1000 m

5 km = 5 x 1000 m

= 5000 m

Step 2:

1 m = 100 cm

5000 m = 5000 x 100 cm

= 500000 cm

Step 3:

1cm = 10 mm

500000 cm = 500000 x 10 mm

= 5000000 mm

1 m = 10^{-3} km

10 m = 10 x 10^{-3} km

= $\frac{10}{1000}$ km

= $\frac{1}{100}$ km

= 10 ^{-2} km

Here we have to convert acres to Hectares.

1 acres = 0.404685642 hectares

Therefore,

1000 acres = 0.404685642 hectares [xx] 1000 acres

= 404.685642

The answers for 1000 acres are equal to 404.685642 Hectares.

Here we have to convert Hectares to Square feet.

1 hectare = 107 639.104 square feet

Therefore,

700 Hectares = 107 639.104 square feet [xx] 700 Hectares

= 75347372.8 sq.ft

The answers for 700 Hectares are equal to 75347372.8 Square feet.

Here we have to convert Kilometers (km) to Miles.

1 kilometer (km) = 0.621371192 miles

Therefore,

100 km = 0.621371192 miles [xx] 100 km

= 62.1371192 miles

The answers for 100 Kilometers (km) are equal to 62.1371192 miles.

Here we have to convert millimeters (mm) to inches

1 millimeter (mm) = 0.0393701 inches

Therefore,

300 mm = 0.0393701 inches [xx] 300 mm<

= 11.81103 inches

The answers for 300 millimeters (mm) are equal to 11.81103 inches.

Here we have to convert centimeters (cm) to meters.

1 centimeter (cm) = 0.01 meters

Therefore,

600 cm = 0.01 meters [xx] 600 cm

= 6 meters

The answers for 600 centimeters (cm) are equal to 6 meters.

1000 grams = 1 kilogram

1000 kilograms = 1 ton

10 milliliters = 1 centiliter

10 centiliters = 1 deciliter

10 deciliters = 1 liter

1000 liters = 1 cubic meter

10 millimeters = 1 centimeter

10 centimeters = 1 decimeter

10 decimeters = 1 meter

10 meters = 1 decameter

10 decameters = 1 hectometer

10 hectometers = 1 kilometer

100 square mm = 1 square centimeter

10 centimeters = 1 decimeter

10000 square cm = 1 square meter

100 square m = 1 acre

100 acres = 1 hectare

100 hectares = 1 square kilometer

1 centimeter = 1 cm

1 meter = 1 m

1 decimeter = 1 dm

1 kilometer = 1 km

Mass

1 milligram = 1 mg

1 centigram = 1 cg

1 decigram = 1 dg

1 gram = 1 g

1 kilogram = 1 kg

degree kelvin = k

degree Celsius =

Fahrenheit = F

For Volume

1 milliliter = 1 ml

1 centiliter = 1 cl

1 deciliter = 1 dl

1 liter = 1 l

1 kiloliter = 1 kl

Below are the examples on converting metric units -

4 km = 40 hm (4 × 10) = 4 × 10

= 400 dam (4 × 100) = 4 × 10

= 4000 m (4 × 1000) = 4 × 10

=40000 dm (4 × 10000) = 4 × 10

= 400000 cm (4 × 100000) = 4 × 10

= 4000000 mm (4 × 1000000) = 4 × 10

12675477 mm = 126754.7cm[1267547/10] =1267547 x 10

=12675.47dm[1267547/100] =1267547 x 10

= 1267.547m[1267547/1000] =1267547 x 10

=126.7547dam[12.6754]/10000 = 1267547 x 10

=12.67547hm[1267547/100000] =1267547 x 10

=1.267547km[1267547/1000000] =1267547 x 10

We know that ,

1m =1000mm

Therefore ,7m = 7*1000mm

=7000mm

We know that,

1kg =1000g

1dag =10g

Therefore, 10kg5dag = 10 *1000g +5 *10g

=10000g +50g

=10050g

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