**Converting within measurement systems :**

The two most common systems of measurement are the customary system and the metric system.

If we do conversion within customary system or metric system, it is called converting units within measurement systems.

That is, we are not doing conversion of units from customary to metric or metric to customary.

The table given below is much useful to do conversion of units within customary and metric systems.

**Question : **

Use a model to do the following conversion.

Convert 12 feet into yards

Convert 18 yards into feet

**Solution : **

Let us write ratios of feet to yards from the above model.

3/1, 6/2, 9/3, 12/4

From the above equivalent ratios, it is clear that for an increase of every yard, there is an increment of 3 feet.

So, the ratio of feet to yards in any measurement from the above model is

3 feet / 1 yard

To convert 12 feet into yards, we have to change the first quantity in the above ratio as 12 using multiplication.

3 / 1 = (3x4) / (1x4) = 12 feet / 4 yards

Therefore, 12 feet = 4 yards.

To convert 12 feet into yards, we have to change the second quantity of the ratio 3/1 as 18 using multiplication.

3 / 1 = (3x18) / (1x18) = 54 feet / 18 yards

Therefore, 18 yards = 54 feet.

**Example 1 :**

Convert 3.5 yards into inches.

**Solution : **

**Here, we convert bigger unit into smaller unit. So we have to multiply.**

3.5 yards = 3.5 x 36 inches

3.5 yards = 126 inches

Hence, 3.5 yards is equal to 126 inches

**Example 2 :**

Convert 3.5 tons into pounds .

**Solution : **

**Here, we convert bigger unit into smaller unit. So we have to multiply.**

3.5 tons = 3.5 x 2000 pounds

3.5 tons = 7000 pounds

Hence, 3.5 tons is equal to 7000 pounds.

**Example 3 :**

Convert 24 quarts into gallons

**Solution : **

**Here, we convert smaller unit into bigger unit. So we have to divide.**

24 quarts = 24 / 4 gallons

24 quarts = 6 gallons

Hence, 24 quarts is equal to 6 gallons.

**Example 4 :**

Convert 3.5 decimeters into centimeters.

**Solution : **

**Here, we convert bigger unit into smaller unit. So we have to multiply.**

3.5 dm = 3.5 x 10 cm

3.5 dm = 35 cm

Hence, 3.5 decimeters is equal to 35 centimeters.

**Example 5 :**

Convert 48 milligrams into centigrams.

**Solution : **

**Here, we convert smaller unit into bigger unit. So we have to divide.**

48 milligrams = 48 / 10 centigrams

48 milligrams = 4.8 centigrams

Hence, 48 milligrams is equal to 4.8 centigrams.

**Example 6 :**

Convert 3.5 deciliters into centiliters.

**Solution : **

**Here, we convert bigger unit into smaller unit. So we have to multiply.**

3.5 deciliters = 3.5 x 10 centiliters

3.5 deciliters = 35 centiliters

Hence, 3.5 deciliters is equal to 35 centiliters.

**Example 7 :**

David travels 60 miles in two hours. How many yards of distance will he cover in one minute ?

**Solution : **

Distance covered in 2 hours = 60 miles

Distance covered in 1 hour = 30 miles

We know that 1 hour = 60 minutes and 1 mile = 1760 yards

1 hour ---> 30 miles ===> 60 minutes -----> 30 x 1760 yards

60 minutes -----> 52800 yards

So, distance covered in 60 minutes = 52800 yards

Distance covered in one minute = 52800 / 60 yards

= 880 yards

Hence 880 yards of distance covered in 1 minute.

**Example 8 : **

Mark jogged 15840 feet in 45 minutes. Find the speed of Mark in feet per minute.

**Solution : **

Speed = Distance / Time

Speed = 15840 / 45

Speed = 352 feet per minute

Hence the speed of Mark is 352 feet per minute.

**Example 9 : **

Use a fraction to find the length in meters of a tile that is 9 centimeters long.

**Solution : **

**Here, we convert smaller unit (centimeters) into bigger unit (meters). So we have to divide.**

Since we divide, we have to use the fraction 1/100.

Because, 1 meter = 100 centimeters

9 centimeters = 9 x 1/100 meters

9 centimeters = 9/100 meters

Hence 9 centimeters is equal to 9/100 meters.

**Example 10 : **

Kevin has a pole that is 24 meters tall. If Kevin sets the pole on a 300 centimeters stand, how far from the floor will the top of the pole be (in meters) ?

**Solution : **

**Height of the pole = 24 meters**

**Height of the stand = 300 centimeters = 300/100 = 3 m**

**Distance from the floor to the top of the pole is **

**= Height of the stand + Height of the pole**

**= 30 + 3 **

**= 33 meters**

Hence the top of the pole is 33 meters far from the floor.

After having gone through the stuff given above, we hope that the students would have understood "Converting within measurement systems".

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