Chapter 1 — Physical Quantities and Measurement

A physical quantity is anything that can be measured and expressed using a number and a unit. Examples include length, mass, time, temperature, and speed. Quantities allow us to compare objects and describe natural phenomena. When you say the length of a pencil is 15 cm, '15' is the number and 'cm' is the unit; together they form the measured quantity.

Physical quantities are often classified as base quantities and derived quantities. Base quantities are defined independently, and derived quantities are formed from base quantities by mathematical relations. For example, area is derived from length (area = length × width). Organising quantities in this way helps scientists use standard methods and communicate results clearly.

Quantities also have dimensions. The dimension of a physical quantity shows how it depends on base quantities. For instance, speed has dimensions of length divided by time (L T−1). Understanding dimensions helps check equations and convert units correctly.

When measuring, always give both a number and a unit. Write the unit using the standard symbol (for example, m for metre, s for second). Avoid adding units in words inside calculations; convert to the correct units first, then perform operations.

Finally, measured values are not exact; every measurement has some uncertainty. Recording the estimated digit and writing the result to the correct number of significant figures tell the reader how precise the measurement is. Good measurement practice, standard units and clear notation make physics useful and reliable.

The International System of Units, abbreviated SI, is the standard system of measurement used worldwide in science and most countries. SI ensures that measurements are uniform and can be compared anywhere. It is built on seven base units from which other units are derived.

The seven SI base quantities and their units are length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol) and luminous intensity (candela, cd). In Class 7 we focus on length, mass, time and temperature.

SI units have standard symbols that must be used exactly. Units are written after the number with a space: 5 m, not 5m or 5 metre(s). Prefixes allow us to express very large or very small quantities. For example kilo- means 1000, so 1 km = 1000 m; centi- means 1/100, so 1 cm = 0.01 m. Using prefixes keeps numbers manageable and makes comparisons easier.

Derived SI units come from combining base units by multiplication or division. For instance, the unit of area is square metre (m2) and volume is cubic metre (m3). Some derived units have special names like newton (N) for force or joule (J) for energy, but at this level we mainly use simple combinations.

Using SI units and the correct prefixes is a habit that will help you in all science subjects. It avoids confusion and ensures that numerical answers are meaningful and comparable.

Base quantities are the fundamental measurable properties chosen by the SI system. They are defined independently and serve as building blocks for other quantities. The SI selects seven base quantities, but for Class 7 we concentrate on the most common ones: length (metre, m), mass (kilogram, kg) and time (second, s). Each base quantity has a symbol for its dimension: length is L, mass is M and time is T. These symbols help when we write dimensions of other quantities.

Derived quantities are formed by combining base quantities through multiplication or division and by using algebraic relations. For example, speed comes from the relation speed = distance / time, so its dimensions are length divided by time (L T−1) and its unit is metres per second (m/s). Area is derived by multiplying two lengths (length × breadth) giving square metre (m2). Volume multiplies three lengths (length × breadth × height) giving cubic metre (m3). These are simple examples of derived quantities made directly from base quantities.

Some derived quantities are common in experiments and daily life. Density equals mass divided by volume, so its dimensions are M L−3 and a convenient unit is g/cm3 in the laboratory. Acceleration equals change of velocity per unit time; its dimensions are L T−2 and its SI unit is m/s2. Pressure is force per unit area and has derived dimensions M L−1 T−2 with unit pascal (Pa) in higher classes, though you will encounter simpler forms now.

Understanding how derived quantities are formed helps in checking calculations and converting units. For area and volume conversions remember to square or cube the conversion factor respectively: since 1 m = 100 cm, 1 m2 = (100 cm)2 = 10 000 cm2 and 1 m3 = (100 cm)3 = 1 000 000 cm3. Dimensional notation (like L, M, T) is also a quick way to test whether an equation is plausible: both sides must have the same dimensions. This practice prevents simple mistakes and builds a foundation for solving more complex problems later.

Length is the measure of how long or far something is. To measure length we use instruments such as the metre rule, measuring tape, and metre scale. Choose an instrument whose range and precision suit the object: use a ruler for a pencil, a tape for a room's length.

The metre rule is marked in centimetres and millimetres. When measuring, place the object along the scale so one end lines up with zero, avoid parallax by keeping your eye directly above the mark, and read the last full division then estimate the next digit if needed. For example, if the last clear mark is 12 cm and the next mark is one-tenth between centimetres, you might read 12.3 cm. The estimated digit increases precision.

There are two ways to take readings: direct reading for small objects and indirect using difference for long measurements. For long distances, measure in parts and add, or use a tape measure. Record length with the correct unit and the estimated digit shown, for example 24.7 cm. If you convert to metres, 24.7 cm = 0.247 m.

Always note instrument precision: a standard ruler marked in mm is precise to ±0.5 mm for the estimated digit. Good technique, straight placement and steady observation reduce random error. Write measurements with proper significant figures and the unit symbol. Practise measuring many objects to gain steady hand and consistent readings.

Mass tells us how much matter an object contains. Common instruments to measure mass are the beam balance, electronic balance and spring balance (for weight). In class practicals, beam and electronic balances are usually used to find mass in grams or kilograms. Choosing the right balance depends on the mass range and required precision.

A beam balance works by comparing the unknown mass with standard masses. Place the object on one pan and add standard masses to the other pan until the pointer aligns with the central mark. If the pointer is not exactly at the centre, use rider adjustments or smaller masses until balanced. The total of the known masses equals the mass of the object. This mechanical method is reliable if the balance is level and zeroed before use.

An electronic balance gives a direct digital readout when an object is placed on its pan. Before using, press the zero or tare button, and ensure the balance is on a steady surface free from drafts and vibrations. Electronic balances can measure small masses to decimal places, for example 0.01 g or 0.001 g, depending on the model. When recording mass, write the displayed value and include the correct unit and uncertainty implied by the instrument's last digit.

Spring balances measure weight (a force) rather than mass, and should be used only when you must compare weights, not when mass is required in grams or kilograms. Also remember mass is constant irrespective of location, while weight depends on gravity and changes with altitude or planet. In school we report mass in kg or g and convert between them when needed (1 kg = 1000 g). Proper handling—placing objects centrally, avoiding touching with dirty hands, and noting the least count—reduces measurement errors and gives more reliable results.

Time measurement is essential in experiments to find rates, speeds and durations. The SI unit of time is the second (s). Instruments used in the laboratory for timing include digital stopwatches, mechanical stopwatches, clocks and electronic timers. In Class 7 you will mainly use handheld stopwatches and wall clocks.

Using a stopwatch correctly requires clear observation and practice. To measure a short event, press the start button the moment the event begins and stop it the moment it ends. For example, when timing how long a marble takes to roll down a track, start as the marble passes the starting line and stop when it crosses the finish line. Record the time shown, including decimal places if shown on the display. If you repeat the measurement several times, calculate the average to reduce the effect of random errors.

Human reaction time affects manual timing: it takes about 0.2–0.3 s to respond, which adds uncertainty to short measurements. To reduce this, practice your timing, use two observers (one to start, one to stop) and take more trials. For very short events or high accuracy, teachers use electronic gates or sensors that start and stop timers automatically; these remove reaction time error but are not required at this stage.

Convert hours and minutes to seconds when required by formulae: 1 minute = 60 seconds and 1 hour = 3600 seconds. When adding or averaging time values, convert all times to the same unit first. Record time results with the correct unit and an appropriate number of significant figures based on the stopwatch precision. Good technique—clear signal, steady operation, and repeated trials—improves the reliability of time measurements used in experiments.

Temperature measures how hot or cold a body is; it reflects the average energy of the particles in a substance. For laboratory work we commonly use the Celsius scale (°C). Another scale, Kelvin (K), is used in higher studies and is related to Celsius by adding 273.15. In Class 7 you will use mercury or alcohol thermometers and digital thermometers to measure temperature in °C.

Liquid-in-glass thermometers contain a liquid (mercury or coloured alcohol) that expands when heated and contracts when cooled. The bulb of the thermometer is dipped into the substance whose temperature is to be measured; wait until the liquid column stabilises. Read the temperature at the top of the liquid column. Always hold your eye level with the marked scale to avoid parallax and read the number including the estimated digit between the smallest divisions. Different thermometers have different ranges and least counts; choose one appropriate to the expected temperature.

Digital thermometers use electronic sensors such as thermistors to measure temperature and display a numerical value quickly. They are useful for fast readings and for clinical or cooking use. Clinical thermometers are designed for measuring body temperature and usually have a limited range around human body temperatures. Never use a thermometer beyond its safe temperature range and avoid sudden shocks that can break glass thermometers containing mercury. If mercury breaks, inform the teacher immediately as it is hazardous.

Know two important reference points for the Celsius scale: freezing point of water at standard pressure is 0 °C and boiling point is 100 °C. For practical conversions, use K = °C + 273.15 when Kelvin is required. Record temperatures with the unit and the estimated precision, for example 36.8 °C, and follow safety rules for handling thermometers carefully to prevent accidents.

Volume measures the space occupied by a substance. For solids, liquids and gases the measurement methods differ. Common instruments in school are measuring cylinders, beakers, and for regular solids a ruler (using formula). The SI unit of volume is cubic metre (m3), but litres (L) and cubic centimetres (cm3) are commonly used in the laboratory.

To find the volume of a regular solid like a rectangular block, multiply length × breadth × height and give the result in cubic units (for example cm3). For irregular solids, use the displacement method: place a measured volume of water in a graduated cylinder, note the level, immerse the object fully and record the new level. The rise in water level equals the volume of the object. This method is useful for stones or small toys.

When measuring liquids, use a measuring cylinder placed on a flat table, read the meniscus at eye level and record the volume to the estimated digit. A meniscus is the curved surface of a liquid; read from the lowest point for water and clear liquids. Be careful with units: 1 L = 1000 mL and 1 cm3 = 1 mL; therefore 1 L = 1000 cm3.

Record volumes with appropriate units and significant figures. When converting between units, change all values to the same unit before adding or subtracting. Practise measuring different liquids and solids to become comfortable using the instruments and the displacement method.

Density measures how much mass is packed into a unit volume of a substance. It is a useful property to compare materials and decide whether an object will float or sink in a fluid. The basic relation is density = mass / volume. The SI unit is kilogram per cubic metre (kg/m3), but grams per cubic centimetre (g/cm3) and grams per millilitre (g/mL) are commonly used in school labs.

To find density experimentally, first measure the mass of the object using a balance. Then measure the volume: use geometric formulae for regular shapes (for example a cuboid or cylinder) and the displacement method for irregular objects. For a cuboid, volume = length × breadth × height measured in cm, and mass may be in grams, so density in g/cm3 follows directly. For very small objects or liquids, use pipettes and micropipettes where available or measure mass of a known volume, such as 10 mL of liquid.

Example procedure: to measure the density of a small stone, weigh it on a balance to get mass in grams. Fill a graduated cylinder with water to a known level, record it, immerse the stone fully and read the new level. The difference gives the volume in mL (which equals cm3). Divide the mass by this volume to get density in g/cm3. Note that trapped air bubbles reduce apparent volume; ensure the object is fully submerged and gently tapped if needed to remove bubbles.

Density values help identify substances: water at 4 °C has density ≈ 1 g/cm3; many metals have densities much greater than 1 g/cm3. When converting units remember that 1 g/cm3 = 1000 kg/m3. Always state density with appropriate significant figures and units, and consider sources of error such as balance calibration or imprecise volume reading when reporting the result.

Measurements have two important qualities: accuracy and precision. Accuracy tells how close a measurement is to the true or accepted value. Precision shows how closely repeated measurements agree with one another. A set of measurements can be precise but not accurate if they are consistent yet far from the true value. Both concepts are important when evaluating experimental results.

Significant figures (sig figs) express the precision of a measured or calculated number. Significant figures include all certain digits plus one uncertain digit that is estimated. For example, if a ruler marked in millimetres is used to read 12.34 cm, the digits 1, 2 and 3 are certain and 4 is the estimated digit, so there are four significant figures. When recording results, the number of sig figs indicates the reliability of the measurement.

Rules for recognizing significant figures: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros before the first non-zero digit are not significant; trailing zeros after the decimal point are significant. For example, 0.00520 has three significant figures (5, 2, 0) while 5200 without a decimal point has only two significant figures (5, 2) unless otherwise indicated.

When performing calculations, follow the rules for significant figures: for multiplication and division, the final answer should have the same number of significant figures as the factor with the fewest sig figs. For addition and subtraction, align decimal places and round the result to the least precise decimal place among the quantities. These rules keep the precision of results consistent with the precision of the input data. Always show units and round sensibly rather than over-reporting digits that the instruments could not support.

No measurement is perfectly exact. Errors are the differences between measured values and the true value. Recognising error types and their causes helps improve experiments and estimate how reliable results are. At school level we separate errors into systematic and random types and learn how to reduce them.

Systematic errors shift all measurements in the same direction and arise from causes that affect each reading similarly. Examples include an uncalibrated balance that reads 2 g too high, or a stopwatch that runs slow. Systematic errors produce bias and cannot be reduced by repeating measurements; instead they should be found and corrected by calibration, zeroing the instrument, or using a different method or instrument.

Random errors vary unpredictably between readings because of small, uncontrollable effects such as hand tremor, slight changes in environmental conditions or variable reaction time. Random errors affect the scatter of measurements and can be reduced by taking a number of readings and averaging them; the mean value is usually closer to the true value than a single reading. Reporting the spread (range) or a simple estimate of uncertainty alongside the average gives more informative results.

Uncertainty can be quoted as absolute (for example ±0.2 cm) or relative/percentage (for example 0.4%). Percentage uncertainty = (absolute uncertainty / measured value) × 100%. When combining measurements in calculations, propagate uncertainties approximately: for multiplication/division the percentage uncertainties add; for addition/subtraction the absolute uncertainties add. In Class 7 a simple awareness—identifying likely sources of error, repeating readings, and stating an uncertainty—is sufficient and shows good scientific practice.

Converting units is a crucial skill in physics. Always write the starting number with units, then multiply by conversion factors that equal one, so the unwanted units cancel and the desired units remain. For example, to convert 5 km to metres: 5 km × (1000 m / 1 km) = 5000 m. Use powers of ten and prefixes to simplify conversions.

Dimensional analysis checks that an equation is consistent by comparing dimensions on both sides. Replace each quantity with its base dimensions (for example length = L, mass = M, time = T). If dimensions match on both sides, the equation is potentially correct; if not, it is definitely wrong. Dimensional analysis does not give numerical constants but it is a useful error-checking tool.

Practice converting between units for area and volume: to convert cm2 to m2 divide by 10,000 because (1 m = 100 cm) so 1 m2 = (100 cm)2 = 10,000 cm2. For volume, to convert cm3 to m3 divide by 1,000,000 because 1 m3 = (100 cm)3 = 1,000,000 cm3. Remember to square or cube the conversion factor for area and volume respectively.

Using scientific notation makes conversion of very large or small numbers easier. Write numbers as a × 10n and move powers of ten according to prefixes. Dimensional analysis and unit conversion together help avoid mistakes and keep calculations consistent in experiments and numerical problems.

Scientific notation and SI prefixes help us write very large or very small numbers neatly and perform calculations without many zeros. Scientific notation expresses a number as a × 10n where 1 ≤ |a| < 10 and n is an integer. For example, 4,500,000 becomes 4.5 × 106 and 0.00032 becomes 3.2 × 10−4. This form is useful in multiplication and division because powers of ten combine simply.

SI prefixes denote common powers of ten and are used with units to keep numbers readable. Some common prefixes are kilo- (k) = 103, centi- (c) = 10−2, milli- (m) = 10−3 and micro- (µ) = 10−6. Using prefixes you can write 0.001 m as 1 mm or 1000 m as 1 km. When converting units with prefixes, change the prefix to the base unit by moving the decimal point or adjusting the power of ten accordingly.

When multiplying numbers in scientific notation, multiply the coefficients (a values) and add the exponents: (a × 10m) × (b × 10n) = (a × b) × 10(m+n). For division, divide the coefficients and subtract exponents. After calculation, make sure the coefficient is between 1 and 10 by shifting the decimal point and adjusting the exponent. This keeps the result in proper scientific form.

Practise converting between ordinary decimal form, scientific notation and prefixed units. For school problems, being fluent with scientific notation makes unit conversions and comparisons of magnitudes quick and reduces copying errors. Always include units when using prefixes so the meaning is clear, for example 3.2 × 10−3 m = 3.2 mm is incorrect: 3.2 × 10−3 m = 3.2 mm would mean 3.2 × 10−3 m = 3.2 × 10−3 × 1000 mm = 3.2 mm; check transformations carefully each time.

Good laboratory technique reduces errors and keeps experiments safe. Before measuring, check instruments for damage and cleanliness. Make sure balances are level and zeroed, thermometers are clean, and measuring cylinders have clear markings. A stable, flat working surface helps reduce mistakes when reading scales.

Place measuring cylinders on a flat table and read the meniscus at eye level to avoid parallax. For balances, calm air currents and vibrations reduce fluctuations — close windows or use shields if available. When using stopwatches practise starting and stopping to reduce reaction time errors. Label samples clearly to avoid mixing and write readings immediately in a notebook so values are not forgotten.

Use suitable containers and supports. Clamp long thermometers or burettes so they do not tip. For liquid transfers, use funnels and pouring techniques to avoid spills. When weighing powders, use weighing paper to keep the balance pan clean and tare the balance to zero first. For small masses, place the object in a small container then subtract the container mass (tare) from the total.

Observe safety rules: wear goggles when heating or handling chemicals, do not taste substances, and report broken glassware to the teacher. Handle mercury thermometers with care or avoid them if possible; if spillage occurs follow teacher instructions. Keep flammable items away from Bunsen burners and switch off electrical equipment after use. These simple practical habits improve measurement quality and protect everyone in the lab.