Units and Measurement
Class 11 · Physics
4 ideas in Class 11 Physics, explained in plain words, with games and quizzes to practise.
SI Units and Systems of Measurement
Part of: Standard Units and Precise Numbers
Every measurement is a number plus a unit. Scientists once used different unit systems in different countries. Today the world uses the SI system with seven base units: metre, kilogram, second, ampere, kelvin, mole and candela. Every other unit, such as speed or force, is built from these seven.
Why it matters. Without shared units, a measurement made in one country would confuse another. Standard units let engineers, doctors and traders trust each other's numbers, and they make converting between sizes simple.
Formulas
- Angle in radian = arc length / radius
Key words
- Measurement
- : Expressing a quantity as a number combined with a unit.
- SI system
- : The worldwide standard system built on seven base units.
- Base unit
- : A unit defined on its own, such as the metre or the second.
- Derived unit
- : A unit built from base units, such as the newton for force.
- Radian
- : The angle formed when the arc length equals the radius.
Try it in two minutes
- Ask the child to read the unit printed on three packets or tools at home.
- Sort those units into basic ones and ones built from others.
- Convert a height in centimetres into metres and back again.
Try at home. List the units on five kitchen packets and mark which ones measure mass, volume or length.
Significant Figures
Part of: Standard Units and Precise Numbers
No instrument is perfect, so the last digit of any reading is always a little uncertain. Significant figures are the digits we trust: all the certain digits plus the first doubtful one. Rules tell us which zeros count and which are only holding a place.
Why it matters. Writing extra digits pretends a measurement is more precise than it really is. Correct figures keep scientists, engineers and doctors honest about what they actually know.
Formulas
- Leading zeros are never significant.
- Zeros between nonzero digits are always significant.
- Trailing zeros count only when a decimal point is shown.
Key words
- Significant figures
- : The digits in a reading that carry real meaning about precision.
- Certain digit
- : A digit the instrument reads clearly and surely.
- Doubtful digit
- : The last kept digit, which is estimated and uncertain.
- Exact number
- : A counted or defined number with unlimited significant figures.
- Place-holding zero
- : A zero that only sets the decimal place and is not counted.
Try it in two minutes
- Measure a book with a ruler and decide which digits are certain.
- Circle the significant figures in three printed readings at home.
- Rewrite one reading in different units and check the count stays the same.
Try at home. Find three measurements at home and count their significant figures together.
Arithmetic with Significant Figures
Part of: Calculating and Checking in Physics
A calculated answer can never be more precise than the roughest measurement in it. In multiplication we keep as many figures as the weakest input; in addition we keep the fewest decimal places. Extra digits are rounded off with standard rules.
Why it matters. A calculator shows many digits, but most of them are meaningless. Rounding correctly keeps results honest and lets others compare them fairly.
Formulas
- In multiply and divide, keep as many figures as the weakest input.
- In add and subtract, keep the fewest decimal places of the inputs.
Key words
- Rounding
- : Dropping extra digits so the answer matches the precision of the inputs.
- Least precise input
- : The measurement that limits how precise the final answer may be.
- Decimal places
- : The digits written after the decimal point in a value.
- Even-odd rule
- : When the dropped part is exactly five, the last kept digit is made even.
Try it in two minutes
- Multiply two values from labels and round to the weaker one.
- Add two measurements and cut to the fewest decimal places.
- Practise the even-odd rule on numbers ending exactly in five.
Try at home. Take any bill, add two amounts on it and round the total the correct way.
Dimensions and Dimensional Analysis
Part of: Calculating and Checking in Physics
Each quantity has dimensions: the powers of mass, length and time hidden inside it. Force works out to mass times length over time squared. Checking that every term of an equation carries the same dimensions catches wrong formulas, and matching dimensions can even reveal new relations.
Why it matters. A dimension check takes seconds and exposes impossible equations before any experiment. It is a standard safety step in physics and engineering.
Formulas
- Dimensional formula of force = [M^1 L^1 T^-2]
- Dimensional formula of energy = [M^1 L^2 T^-2]
- Only terms with matching dimensions may be added or equated.
Key words
- Dimension
- : The powers of mass, length and time hidden inside a quantity.
- Dimensional formula
- : The expression showing the powers of M, L and T for a quantity.
- Homogeneity
- : The rule that every term of an equation must share one dimension.
- Dimensionless quantity
- : A pure ratio, such as an angle, carrying no dimensions.
Try it in two minutes
- Write the dimensions of speed, force and energy together.
- Test a familiar relation term by term.
- Spot exactly why a wrong formula fails the test.
Try at home. Pick any formula from the chapter and check its dimensions term by term.
What your child will practise
- Arithmetic with Significant Figures: Candy Quick Fire (Quick Fire)
- Dimensions and Dimensional Analysis: Desert Puzzle (Clue Puzzle)
- Dimensions and Dimensional Analysis: Desert Quick Fire (Quick Fire)
- SI Units and Systems of Measurement: Space Quick Fire (Quick Fire)
- Significant Figures: Ocean Puzzle (Clue Puzzle)
- Quiz: Arithmetic with Significant Figures (8 questions)
- Quiz: Dimensions and Dimensional Analysis (8 questions)
- Quiz: SI Units and Systems of Measurement (8 questions)
- Quiz: Significant Figures (8 questions)