How do you convert between different units?

In one line

The rule

Conversions between units involve changing a measurement from one unit to another while maintaining its value. (NCERT Class 9)

The formula is: Value in new unit = Value in old unit × Conversion factor

Let's understand it simply

Imagine you have ₹100 and want to know how many 10-rupee notes that is. You divide 100 by 10 and get 10 notes. Unit conversion works the same way. You change from one type of "note" (unit) to another, but the total value stays the same.

Think of buying rice in the market. If the shopkeeper says you bought 2 kilograms, but your mother wants to know how many grams that is, you need to convert kilograms to grams. You use the fact that 1 kilogram = 1000 grams.

How it works

1. Find the conversion factor. (Example: 1 km = 1000 m)
2. Decide if you need to multiply or divide.

• To go from bigger to smaller units (km to m), multiply.
• To go from smaller to bigger units (m to km), divide.

1. Do the calculation.

• Example: 5 km to m: 5 × 1000 = 5000 m.
• Example: 5000 m to km: 5000 ÷ 1000 = 5 km.

1. Write the answer with the correct unit.

The story behind it

Long ago, people used different units in every region—like handspans or footsteps. This caused confusion in trade and science. To solve this, scientists agreed on standard units (like meter, kilogram, second). Now, everyone uses the same system, but sometimes we need to switch between units for convenience.

Where you see it in real life

• Cricket pitch length: 22 yards. To know it in meters, convert yards to meters.
• Milk in the kitchen: Milk is sold in liters, but a recipe may ask for milliliters.
• Buying vegetables: You buy 1.5 kg potatoes, but the shopkeeper uses grams on the scale.
• Speed of a scooter: Speedometers show km/h, but sometimes you need m/s for science problems.
• Water in a pressure cooker: The cooker may hold 2 liters, but a recipe says 500 mL.

Why it matters

• Science and exams: Questions often ask you to convert units before solving problems.
• Daily life: Buying, cooking, travelling—all need unit conversions.
• Jobs: Engineers, doctors, and shopkeepers use conversions every day.
• Understanding: It helps you compare things easily, like petrol prices per liter or per milliliter.

Worked example

Given: 3.5 kg, convert to grams
Step 1: Write the rule        1 kg = 1000 g
Step 2: Multiply              3.5 × 1000
Step 3: Answer                3500 g

Common mistakes

• Forgetting to multiply or divide: Always check if you are going from big to small (multiply) or small to big (divide).
• Using the wrong conversion factor: Double-check the numbers (e.g., 1 m = 100 cm, not 10).
• Forgetting units in the answer: Always write the correct unit after the number.

Remember it

Big to small: Multiply. Small to big: Divide. Always use the right conversion factor!