RBSE Solutions Class 5 Maths Chapter 13 Measurement of Length Exercise 13.1

Question 1. Convert the unit in following questions:
(i) 12 kilometer = ......... meter
(ii) \( 10 \frac {1}{2 } \) kilometer = ......... meter
(iii) \( 25 \frac {1}{4} \) meter = ......... centimeter
(iv) \( 15 \frac {3}{4} \) meter = ......... centimeter
(v) \( 4 \frac {1}{5} \) cm. = ......... millimeter
(vi) \( 1 \frac {4}{5} \) cm. = ......... millimeter
Answer:
(i) To convert kilometers to meters, we multiply by 1000. So, \( 12 \text{ km} = 12 \times 1000 \text{ meters} = 12000 \text{ meters} \). This is because 1 kilometer equals 1000 meters.
(ii) To convert \( 10 \frac {1}{2 } \) kilometers to meters: First, change the mixed number to an improper fraction or a decimal: \( 10 \frac{1}{2} = 10.5 \). Now, multiply by 1000. \( 10.5 \text{ km} = 10.5 \times 1000 \text{ meters} = 10500 \text{ meters} \). Remember that a mixed fraction combines a whole number and a fraction.
(iii) To convert \( 25 \frac {1}{4} \) meters to centimeters, we multiply by 100. First, \( 25 \frac{1}{4} = 25.25 \). So, \( 25.25 \text{ meters} = 25.25 \times 100 \text{ cm} = 2525 \text{ cm} \). One meter is equal to 100 centimeters.
(iv) To convert \( 15 \frac {3}{4} \) meters to centimeters, we multiply by 100. First, \( 15 \frac{3}{4} = 15.75 \). So, \( 15.75 \text{ meters} = 15.75 \times 100 \text{ cm} = 1575 \text{ cm} \). This calculation helps to understand the smaller units of measurement.
(v) To convert \( 4 \frac {1}{5} \) centimeters to millimeters, we multiply by 10. First, \( 4 \frac{1}{5} = 4.2 \). So, \( 4.2 \text{ cm} = 4.2 \times 10 \text{ mm} = 42 \text{ mm} \). There are 10 millimeters in every centimeter.
(vi) To convert \( 1 \frac {4}{5} \) centimeters to millimeters, we multiply by 10. First, \( 1 \frac{4}{5} = 1.8 \). So, \( 1.8 \text{ cm} = 1.8 \times 10 \text{ mm} = 18 \text{ mm} \). Converting to a decimal first can make the multiplication easier.
In simple words: To change a larger unit to a smaller unit, you usually multiply. To change a smaller unit to a larger one, you usually divide. Make sure to use the correct conversion factor like 1000 for km to m, or 100 for m to cm, or 10 for cm to mm.

🎯 Exam Tip: Always remember the basic conversion factors (e.g., 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm) and handle mixed fractions carefully by converting them to decimals or improper fractions before multiplying.

Question 2. Convert the units in following questions:
(i) 120 centimeter = ......... meter
(ii) 2250 meter = ......... kilometer
(iii) 50 millimeter = ......... kilometer
(iv) 9500 meter = ......... kilometer
(v) 150 centimeter = ......... meter
(vi) 175 millimeter = ......... centimeter
Answer:
(i) To convert centimeters to meters, we divide by 100. So, \( 120 \text{ cm} = \frac{120}{100} \text{ meters} = 1.2 \text{ meters} \). This is the opposite of converting meters to centimeters.
(ii) To convert meters to kilometers, we divide by 1000. So, \( 2250 \text{ meters} = \frac{2250}{1000} \text{ kilometers} = 2.25 \text{ kilometers} \). This can also be written as \( 2 \frac{1}{4} \text{ kilometers} \).
(iii) To convert millimeters to kilometers: First, convert millimeters to centimeters by dividing by 10, then centimeters to meters by dividing by 100, and finally meters to kilometers by dividing by 1000. So, \( 50 \text{ mm} = \frac{50}{10} \text{ cm} = 5 \text{ cm} \). Then, \( 5 \text{ cm} = \frac{5}{100} \text{ meters} = 0.05 \text{ meters} \). Finally, \( 0.05 \text{ meters} = \frac{0.05}{1000} \text{ kilometers} = 0.00005 \text{ kilometers} \). This shows how many steps are needed for larger conversions.
(iv) To convert meters to kilometers, we divide by 1000. So, \( 9500 \text{ meters} = \frac{9500}{1000} \text{ kilometers} = 9.5 \text{ kilometers} \). This can also be written as \( 9 \frac{1}{2} \text{ kilometers} \).
(v) To convert centimeters to meters, we divide by 100. So, \( 150 \text{ cm} = \frac{150}{100} \text{ meters} = 1.5 \text{ meters} \). This is a common conversion used in everyday measurements.
(vi) To convert millimeters to centimeters, we divide by 10. So, \( 175 \text{ mm} = \frac{175}{10} \text{ centimeters} = 17.5 \text{ centimeters} \). It is important to know which unit you are converting to and from.
In simple words: When changing a smaller unit to a bigger one, you divide. Always remember the right number to divide by for each unit change. For example, 1000 for meters to kilometers, or 10 for millimeters to centimeters.

🎯 Exam Tip: When converting from a smaller unit to a larger unit, always divide. Keep track of the number of steps and the correct division factor for each step to avoid errors.

Question 3. Kavita's house is, at a distance of 7 kilometer 300 meter from her school. How much distance Kavita has to travel, while she goes to school and returning back home?
Answer:
Distance from Kavita's house to school = 7 km 300 meters
Distance from school to Kavita's house (returning) = 7 km 300 meters
Total distance travelled = (7 km 300 meters) + (7 km 300 meters)
Add kilometers and meters separately:
7 km + 7 km = 14 km
300 meters + 300 meters = 600 meters
So, the total distance Kavita travels is 14 km 600 meters. The journey involves going to school and coming back, so the distance is doubled.
In simple words: Kavita travels the distance to school and back home. So, you need to add the distance from her house to school twice to find the total distance she covers.

🎯 Exam Tip: For problems involving travel "to and fro" or "round trip," remember to calculate the distance for one way and then double it. Make sure to add kilometers and meters separately.

Question 4. Manju had to travel 46 kilometers. Her bus broke down after covering 32 kilometers and 600 meters. How much distance does she still need to cover?
Answer:
Total distance Manju had to travel = 46 km 000 meters
Distance covered by bus before breaking down = 32 km 600 meters
To find the remaining distance, subtract the covered distance from the total distance:
Remaining distance = (46 km 000 meters) - (32 km 600 meters)
We need to borrow from kilometers because 000 meters is less than 600 meters. One kilometer is 1000 meters.
So, 46 km 000 meters becomes 45 km 1000 meters.
Now, subtract:
1000 meters - 600 meters = 400 meters
45 km - 32 km = 13 km
Therefore, Manju still needs to cover 13 km 400 meters. This is a practical example of subtracting mixed units of length.
In simple words: To find how much distance is left, subtract the distance already traveled from the total distance. If you need to subtract more meters than you have, borrow 1 kilometer and convert it to 1000 meters.

🎯 Exam Tip: When subtracting distances with mixed units (kilometers and meters), always align the units. If the meters in the second value are larger than the first, borrow 1 km (1000 m) from the kilometer part before subtracting.