All units of length in the metric system are defined in terms of the metre. A prefix is added to indicate the decimal place value position of the measurements.

**Conversions
within the Metric System:**

All units of length in the metric system are defined
in terms of the metre. A prefix is added to indicate the decimal place value position
of the measurements. Similarly the units of weight and volume are defined in terms
of gram and litre respectively. Let us observe the conversion chart.

* when we move from higher unit to lower unit, multiply
the given measure by the powers of 10's.

* when we move from lower unit to higher unit, divide the given measure by the powers of 10's.

Remember the following Conversion table:

Before we study Conversion of metric units, we should
learn about decimal point position when multiplying / dividing of a decimal number
by the powers of ten.

__Example 1: __

The official distance of Marathon race
is 42.195** ***km.*** **Express this distance in metre.

**Solution : **The official distance of Marathon race is 42.195** ***km.*

= 42.195 X 1000
*m*

= 42195 *m*

1 *km* = 1000 *m*

__Example 2:__** **The average rainfall of Tamilnadu is
998** ***mm*. convert it into** ***cm*.

**Solution :**The average rainfall = 998** ***mm*** **

= 99.8* cm*

__Example 3:__

** **A flag pole is 5** ***m*** **35** ***cm*** **long. What is the length of the flag
pole in** ***cm?*

**Solution: **The length of a flag pole = 5** ***m*** **35** ***cm*** **long

1 *m* = 100 *cm*

= (5 × 100)
*cm* + 35 *cm*

= 500 *cm* + 35 *cm*

= 535 *cm*

The flag pole is 535 *cm* long.

__Example 4:__

Janaki bought 650** ***mg*** **of a tablet. What is its weight in gram?

**Solution : **weight of a tablet = 650** ***mg*

__Example 5: __

Murali has a bag that weighs 3** ***kg*** **and 450** ***g*.What is its weight in gram?

**Solution: **weight of Murali’s bag = 3** ***kg*** **and 450** ***g*** **,

1 *kg* = 1000 *g*

= (3 × 1000
*g*) + 450 *g*

= 3000 *g* + 450 *g*

= 3450 *g*

__Example 6: __

A calf drinks 5.750** ***l*** **of water ,convert** **into** ***ml*

**Solution: **Quantity of water drunk by the calf = 5.750** ***l*

= 5750 *ml*

__Example 7__**: **Convert 526** ***ml*** **into** ***l*

**Solution :** 526 *ml* = 526.0 × (1/1000) *l*

** **

**Try these**

Convert the following

i) 23 *km* into *m*

23 *km* = 23 × 1000 *m *= 23000 *m*

ii) 1.78 *m* into *cm*

1.78 *m* = 1.78 × 100
c*m* = 178 *cm *

iii) 7814 *m* into *km*

7814 *m* = 7814 ÷ 1000
*km* = 7.814 *km *

iv) 8.67* mm *into* cm*

8.67 *mm* = 8.67 ÷ 10 *cm
*= 0.867 *cm *

v) 16 *l* into *ml*

16 *l* = 16 × 1000 *ml*
= 16000 *ml*

vi) 1500 *ml* into *l*

1500 *ml* = 1500 ÷
1000 *l* = 1.500 *l*

vii) 2360 *l* into *kl*

2360*l* = 2360 ÷ 1000*
kl* = 2.360 *kl *

viii) 873 *l* into *ml*

873 *l* = 873 × 1000 *ml* = 873000 *ml *

ix) 40* mg* into *g*

40 *mg* = 40 ÷ 1000 *g*
= 0.040* g*

x) 1550*g* into *kg*

1550 *g* = 1550 ÷ 1000*
kg* = 1.550 *kg*

xi) 6.5 *kg* into g

6.5 *kg* = 6.5 × 1000 *g*
= 6500 *g*

xii) 723g into* mg*

723 *g* = 723 × 1000 *mg*
= 723000 *mg*

** **

**Think**

Which of these is heavier in weight?
5 *kg* of cotton; 5000 g of Iron

Some measures that are not part of metric system.

1* inch *= 2.54* cm*

1* m *= 3.281 *ft*

1* m *= 39.37 *inches *

1 ft = 0.305* m *= 30.48* cm *

1* mile *= 1.609 *km*

1 tonne = 1000 *kg*;

1 quintal = 100 *kg*;

1 tonne = 10 quintal

1 soverign = 8 g

TMC: (Thousand Million Cubic
feet), 1 TMC =28,316,846,592 litres

1 kg = 1000 g

¼ kg = 250 g

½ kg = 500 g

¾ kg = 750 g

The following Tamil puzzle is taken from the famous
Mathematics problems collection book in Tamil called **“Kanakkathikaram” **in
which is a good example of conversion of units of distance :

முப்பத்தி ரணடு முழம்உளமுட் பனையை

தப்பாமல் ஒந்தி தவழ்ந்தேறிச் − செப்பமுடச்

சாணேறி நான்குவிரற்கிழியும் என்பரே

நாணா தொரு நாள் நகர்ந்து

**Meaning of this puzzle:**

On a palm tree of height 32 cubit , a chameleon
tried to reach the top of the tree. If it climbed one hand span on it but slipped
four fingers on one day, in how many days will it reach the top of the tree?

**Solution:**

1 hand span = 12 fingers;

1 cubit = 2 hand spans = 24 fingers.

Height of the palm tree = 32 cubit = 32 × 24 fingers
= 768 fingers.

Distance climbed in 1 day = 1 hand span = 12 fingers.

Distance slipped in 1 day = 4 fingers.

Actual distance climbed in 1 day = 12 − 4 = 8 fingers.

Number of days required to climb the top of the
tree = 768/ 8 = 96 days

Tags : Measurements | Term 2 Chapter 2 | 6th Maths , 6th Maths : Term 2 Unit 2 : Measurements

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6th Maths : Term 2 Unit 2 : Measurements : Conversions within the Metric System | Measurements | Term 2 Chapter 2 | 6th Maths

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