For the conversion of standard unit of length the relation between the three units are given below:
1 kilometer = 1000 meters
1 meter = 100 centimeters
Thus,
(i) To convert centimeters (cm) into meters (m), the number of cm is divided by 100.
(ii) To convert kilometer (km) into meters (m), the number of km is multiplied by 1000.
There are other units also for measuring length. A very small length is measured in millimeters (mm). It is the 10^{th} part of a centimeter, i.e., 10 mm = 1cm or 1 cm = 10 mm.In between centimeter and meter there is a unit of measuring length named decimeter (dm). It is 10 times of a centimeter.
1 decimeter = 10 centimeters (1 dm = 10 cm)
and, 10 decimeters = 1 meter (10 dm = 1 m)
Now, 10 mm = 1 cm (1 cm = 10 mm)
10 cm = 1 dm (1 dm = 10 cm = 100 mm)
10 dm = 1 m (1 m = 10 dm = 100 cm = 1000 mm)
1 km = 1000 m = 100000 cm
On the basis of these facts, one type of unit is converted into another.
Workedout problems on conversion of standard unit of length:
1. Convert the following into centimeters:
(i) 4 m
Solution:
4 m
To convert ‘m’ into ‘cm’, the number of meters is multiplied by 100. The product followed by ‘cm’ is the result.
= (4 × 100) cm
= 400 cm
(ii) 10 m
Solution:
10 m
To convert ‘m’ into ‘cm’, double zeroes (00) are added after the number of meters and unit ‘cm’ is added to it instead of ‘m’.
= (10 × 100) cm
= 1000 cm
(iii) 15 m
Solution:
15 m
To convert ‘m’ into ‘cm’, the number of meters is multiplied by 100. The product followed by ‘cm’ is the result.
= (15 × 100) cm
= 1500 cm
2. Convert the following into centimeters:
(i) 3 m 55 cm
Solution:
3 m 55 cm
First ‘3 m’ is converted into ‘cm’ and then given ‘cm’ is added to it.
= (3 × 100) cm + 55 cm
= 300 cm + 55 cm
= 355 cm
(ii) 17 m 8 cm
Solution:
17 m 8 cm
First ’17 m’ is converted into ‘cm’ and then given ‘cm’ is added to it.
= (17 × 100) cm + 8 cm
= 1700 cm + 8 cm
= 1708 cm
(iii) 6 m 67 cm
Solution:
6 m 67 cm
First ‘6 m’ is converted into ‘cm’ and then given ‘cm’ is added to it.
= (6 × 100) cm + 67 cm
= 600 cm + 67 cm
= 667 cm
3. Convert the following into metre and centimeters:
(i) 736 cm
Solution:
736 cm
To convert ‘cm’ into ‘m’ and cm, the first two digits from the right are taken as ‘cm’ and the rest is written as ‘m’.
= 7 m 36 cm
(ii) 1875 cm
= 18 m 75 cm
(iii) 305 cm
= 3 m 05 cm or 3 m 5 cm
4. Convert the following into meters:
(i) 8 km
Solution:
8 km
As, 1 km = 1000 meters so to convert kilometers into meters, the number of km is multiplied by 1000 or three zeroes are placed after the number of km and meter is written in place of km.
= (8 × 1000) m
= 8000 m
(ii) 3 km
= (3 × 1000) m
= 3000 m
(iii) 6 km
= (6 × 1000) m
= 6000 m
5. Convert the following as required:
(i) 5 km 325 m into meters
Solution:
5 km 352 m
= (5 × 1000) m + 325 m
= 5000 m + 325 m
= 5325 m
(ii) 15 dm 7 cm into centimeters
Solution:
15 dm 7 cm
= (15 × 10) cm + 7 cm
= 150 cm + 7 cm
= 157 cm
[Since, 1 dm = 10 cm]
6. Convert the following:
(i) 3 km 315 m into meters
Solution:
3 km 315 m
= (3 × 1000) m + 315 m
= 3000 m + 315 m
= 3315 m
(ii) 5006 m into kilometre
Solution:
5006 m
= (5006 ÷ 1000) km
= 5 km 006 m
= 5 km 6 m
(Since, first three digits number is taken for metre and the rest for km)
(iii) 375 cm into decimeters
Solution:
375 cm
= (375 ÷ 10) dm
= 37 dm 5 cm
(Since, 10 cm = 1 dm, so the first one digit from right is for ‘cm’ and therest for ‘dm’)
(iv) 2 m 5 dm into decimeters
Solution:
We know, 1 meter = 10 decimeters
2 m 5 dm
= (2 × 10) dm + 5 dm
= 20 dm + 5 dm
= 25 dm
We know the relation between the units of length on that basis we will solve more problems as required for the conversion of standard unit of length.
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