Shortcut Methods and Tricks to Solve Numericals

1. Conversion between different units:

• For length: Multiply the given value by 1000 to convert kilometers to meters, and divide the given value by 1000 to convert meters to kilometers.
• For mass: Multiply the given value by 1000 to convert grams to kilograms, and divide the given value by 1000 to convert kilograms to grams.
• For volume: Multiply the given value by 1000 to convert liters to cubic centimeters, and divide the given value by 1000 to convert cubic centimeters to liters.

2. Dimensional analysis:

• Check validity: Compare the units on both sides of the equation to see if they match. If they match, the equation is dimensionally consistent.
• Derive SI units: Follow these steps:

1. Identify the physical quantity being measured.
2. Write the formula involving the physical quantity and its base units.
3. Simplify the formula by substituting base units for each term.
4. The result is the SI unit for the physical quantity.

3. SI unit conversions:

• For power: To convert megawatts to kilowatts, divide the given megawatt value by 1000.
• For length: To convert micrometers to millimeters, divide the given micrometer value by 1000.
• For velocity: To convert centimeters per second to kilometers per hour, multiply the given centimeters per second value by 3600 and then divide by 100,000.

4. Fundamental units and derived units:

• Fundamental units: запомнить “MKSA-CDI”

• Meter (M) for length

• Kilogram (K) for mass

• Second (S) for time

• Ampere (A) for electric current

• Kelvin (K) for thermodynamic temperature

• Candela (CD) for luminous intensity

• Mole (mol) for amount of substance

• Derived units: Numerous derived units are defined based on fundamental units. Here are a few examples:

• Force: Newton (N) = kg m/s^2

• Energy: Joule (J) = N m

• Power: Watt (W) = J/s

5. Calculations involving units:

• Average speed:

1. Convert the given distance from kilometers to meters if necessary (120 kilometers = 120000 meters)
2. Convert the given time from hours to seconds (2 hours = 7200 seconds)
3. Divide the distance in meters by the time in seconds to obtain the average speed in meters per second.

• Area of a rectangle:

1. Multiply the given length and width to obtain the area in square meters (10 meters x 5 meters = 50 square meters)

• Volume of a water tank:

1. Convert the given volume from liters to cubic centimeters (20 liters = 20000 cubic centimeters)