CONVERSION OF UNITS OF LENGTH

Convert the following lengths.

Example 1 :

480 cm to m

Solution :

1 cm = 1/100 m

480 cm = (480)/100 m

= 4.8 m

Example 2 :

54 mm to cm

Solution :

1 mm = 1/10 cm

54 mm = (54)/10 cm

= 5.4 cm

Example 3 :

5280 m to km

Solution :

1 m = 1/1000 km

5280 m = (5280)/1000 km

= 5.28 km

Example 4 :

2000 mm to m

Solution :

1 mm = 1/1000 m

2000 mm = (2000)/1000 m

= 2 m

Example 5 :

580000 cm to km

Solution :

1 cm = 1/100000 km

580000 cm = (580000)/100000 km

= 5.8 km

Example 6 :

7000000 mm to km

Solution :

1 mm = 1/1000000 km

7000000 mm = (7000000)/1000000 km

= 7 km

Example 7 :

Mike ran 8.5 km while mal walked 3200 m. How much farther did Mike run than Mal walk ?

Solution :

Mike runs = 8.5 km

Mal walks = 3200 m

We need to know mike runs (in meters).

8.5 km to m

1 km = 1000 m

8.5 km = (8.5 × 1000) m

= 8500 m

Difference between mile run and mal walk = (8500 - 3200)m

= 5300 m

Converting m to km,

1 m = 1/1000 km

5300 m = (5300)/1000 km

= 5.3 km

So, 5.3 km Mike ran than Mal walked.

Example 8 :

I have 45 coils of fencing wire and each coil is 275 m long. How many kilometres of wire do I have ? 

Solution :

Total length of coil wire = Number of coil wire × Each length of wire

= 45 × 275

= 12375 m

Converting m to km,

1 m = 1/1000 km

12375 m = (12375)/1000 km

= 12.375 km

I have 12.375 km of wire.

Example 9 :

Liesel swims eighty 25 m laps in 1 hour. If she continues to swim at that speed, how many kilometres will she swims in 3 hours ?

Solution :

Liesel swims in 1 hour = 80(25) m

= 2000 m

she swims in 3 hours  =  2000 × 3

= 6000 m

Converting m to km,

1 m = 1/1000 km

6000 m = (6000)/1000 km

= 6 km

she will swim 6 km in 3 hours.

Example 10 :

John has 3.85 km of copper wire and needs to cut it into 1.5 cm lengths to be used in electric toasters. How many lengths can he make ?

Solution :

John has 3.85 km of copper wire.

Converting km to m,

1 km = 100000 cm

3.85 km = (3.85 × 100000) cm

= 385000 cm

He needs to cut it into 1.5 cm lengths.

Required lengths = (385000)/1.5

= 256666

He can make 256666 lengths.

Example 11 :

A donor gives blood at a rate of 0.125 pint per minute. What is the rate in milliliters per second?

Solution :

1 pint = 473.176 millimeters

0.125 pint = 473.176 x 0.125

= 59.147 millimeters

Example 12 :

What is the speed of the snail in kilometers per hour?

Solution :

1 meter per second = 3.6 kilometer per hour

0.013 meter per second = 0.013 x 3.6

= 0.0468 kilometer per hour

Example 13 :

An oil tanker is leaking oil at a rate of 300 gallons per minute. Convert this rate to gallons per second

Solution :

1 minute = 60 seconds

300 gallons per minute = 300/60

= 5 gallons per second

Example 14 :

A tennis ball travels at a speed of 120 miles per hour. Convert this rate to feet per second

Solution :

Speed = 120 miles per hour

1 mile = 5280 feet

1 hour = 3600 seconds

120 miles per hour = 120 x (5280/3600)

= 176 feet per second

Example 15 :

A kite boarder travels at a speed of 10 meters per second. Convert this rate to kilometers per minute.

Solution :

1 kilometer = 1000 meters

1 minute = 60 seconds

10 meters = 10/1000 km

= 1/100 km per second

= (1/100) x 60

= 60/100

= 6/10

= 0.6 km per minute

Example 16 :

The painting Fracture by Benedict Gibson has an area of 2880 square inches. What is the area of the painting in square feet?

Solution :

1 ft = 12 inches

Converting square inches to square feet, we have to multiply by 1/12.

= 2880 x (1/12)²

= 2880 x (1/144)

= 20 square ft

The area of the painting is 20 square feet.

Example 17 :

What is the volume of the cylinder in cubic centimeters?

Solution :

1 meter = 100 cm

80 m3 = 80(100)³

= 80000000 cm³

The volume is 80,000,000 cubic centimeters.

Example 18 :

The painting Busy Market by Haitian painter Frantz Petion has an area of 6 square feet. What is the area of the painting in square inches?

Solution :

Area = 6 square feet

1 feet = 12 inches

6 square feet = 6 x 12²

= 6 x 144

= 864 square inches