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Long and Short - Standard Units of Length

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Introduction to Standard Units: To measure length accurately and consistently, we use standard units like centimeters (cmcm), meters (mm), and kilometers (kmkm). Unlike handspans or footsteps, standard units provide the same measurement for everyone.

Centimeter (cmcm): This unit is used for measuring small objects like a pencil, an eraser, or a mobile phone. On a standard 15 cm15\ cm plastic ruler, you can see small markings numbered 00 to 1515. The distance between two consecutive numbers, such as 22 and 33, is exactly 1 cm1\ cm. Small lines between these numbers represent even smaller units.

Meter (mm): The meter is the standard unit of length used for measuring longer things like the length of a room, the height of a wall, or a piece of cloth. Visually, 1 meter1\ meter is roughly the width of a single door or the length of a long stride of an adult. It is made up of 100 cm100\ cm.

Kilometer (kmkm): We use kilometers to measure very long distances, such as the distance between two cities or the length of a highway. On a road, you will often see milestones—small stone pillars with a curved top—that show the distance to a place in kmkm. One kilometer is equal to 1000 meters1000\ meters.

Measuring with a Ruler: To measure correctly, align one end of the object exactly with the 00 mark on the ruler (not the edge of the ruler itself). The number that aligns with the other end of the object is its length. For example, if a toothpick starts at 00 and ends at the 55 mark, its length is 5 cm5\ cm.

Estimation of Lengths: It is important to choose the right unit for the right object. For instance, the length of a fingernail is measured in cmcm, the length of a playground is measured in mm, and the distance from Delhi to Mumbai is measured in kmkm.

Conversion Basics: To change a larger unit to a smaller unit, we multiply. For example, to change mm to cmcm, we multiply by 100100. To change kmkm to mm, we multiply by 10001000.

📐Formulae

1 m=100 cm1\ m = 100\ cm

1 km=1000 m1\ km = 1000\ m

Length in cm=Length in m×100\text{Length in } cm = \text{Length in } m \times 100

Length in m=Length in km×1000\text{Length in } m = \text{Length in } km \times 1000

💡Examples

Problem 1:

Rohan has a piece of rope that is 6 m6\ m and 45 cm45\ cm long. What is the total length of the rope in centimeters?

Solution:

Step 1: Convert the meters into centimeters using the formula 1 m=100 cm1\ m = 100\ cm. \ 6 m=6×100=600 cm6\ m = 6 \times 100 = 600\ cm. \ Step 2: Add the extra centimeters to the result. \ 600 cm+45 cm=645 cm600\ cm + 45\ cm = 645\ cm. \ Final Answer: The rope is 645 cm645\ cm long.

Explanation:

Since we need the answer in centimeters, we first change the 6 m6\ m part into cmcm by multiplying by 100100 and then add the remaining 45 cm45\ cm.

Problem 2:

A bus traveled a distance of 5 km5\ km from the station to a school. How many meters did the bus travel?

Solution:

Step 1: We know that 1 km=1000 m1\ km = 1000\ m. \ Step 2: To find the distance in meters, multiply the distance in kilometers by 10001000. \ 5×1000=5000 m5 \times 1000 = 5000\ m. \ Final Answer: The bus traveled 5000 meters5000\ meters.

Explanation:

To convert kilometers into meters, we use the standard conversion factor of 10001000 because there are 10001000 meters in every kilometer.