Measurement / Mensuration - Length, mass, capacity metric measures - conversion of units, addition, subtraction, and word problems
Introduction
Measurement involves quantifying physical properties like Length, Mass, and Capacity. The Metric system is a decimal system, meaning it is based on powers of 10.
Explanation Step by Step
The standard units are Meter (length), Gram (mass), and Liter (capacity). To convert between them, we use prefixes like Kilo, Hecto, Deca, Deci, Centi, and Milli.
| Category | Kilo (x1000) | Hecto (x100) | Deca (x10) | Base Unit (x1) | Deci (/10) | Centi (/100) | Milli (/1000) |
|---|---|---|---|---|---|---|---|
| Length | Kilometer (km) | Hectometer (hm) | Decameter (dam) | Meter (m) | Decimeter (dm) | Centimeter (cm) | Millimeter (mm) |
| Mass | Kilogram (kg) | Hectogram (hg) | Decagram (dag) | Gram (g) | Decigram (dg) | Centigram (cg) | Milligram (mg) |
| Capacity | Kiloliter (kl) | Hectoliter (hl) | Decaliter (dal) | Liter (l) | Deciliter (dl) | Centiliter (cl) | Milliliter (ml) |
Sub-topics
Metric Conversions and Units
Key conversions for daily use:
- 1 km = 1000 m | 1 m = 100 cm
- 1 kg = 1000 g | 1 Quintal = 100 kg
- 1 L = 1000 ml
Examples
Example 1
Convert 2.5 kg into grams.
2.5 x 1000 = 2500 grams.
Tricks and Shortcuts
Use the phrase "King Henry Died Unusually Drinking Chocolate Milk" to remember the order: Kilo, Hecto, Deca, Unit, Deci, Centi, Milli.
Common Mistakes
Forgetting that 1.5 kg is 1500 g, not 1050 g. Always multiply decimal values carefully by 1000.
Practice Questions
Easy Questions
- How many meters are in 3 kilometers?
- Convert 5000 ml into liters.
- Which unit is used to measure the weight of a gold ring?
Medium Questions
- What is the sum of 4.5 m and 250 cm in meters?
- A bag of flour weighs 2.75 kg. Convert this into grams.
- How many ml are there in three-quarters of a liter?
Hard Questions
- A truck carries 5 metric tons of sand. If 1200 kg is used, how many quintals are left?
- A wire 10 m long is cut into 8 equal pieces. What is the length of each piece in cm?
- Add 5 L 250 ml, 2 L 500 ml, and 1 L 750 ml. Express the total in Liters.
Revision Summary
The metric system is simple because it uses base 10. Remember 1000 units = 1 Kilo and 1000 Milli = 1 Unit.
Length of a room is 5.25 m, width is 3.75 m. How many meters length + width?
A
9 m
B
9.25 m
C
9.5 m
D
9.75 m
4.25 kg oranges + 3.75 kg apples in a fruit bag = ? Kilo
A
8 kg
B
8.1 kg
C
8.05 kg
D
7.95 kg