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Class 9 Measurement – Foundation of Science (Advanced): cheat sheet
CBSE Science. Measuring means comparing with a standard unit: the CGS, FPS, MKS and SI systems, changing units without changing the quantity, and judging the error in an estimate.
Key ideas
- A quantity is its number times its unit; changing the unit changes the number, never the quantity.
- The bigger the unit, the smaller the number: a floor is fewer lengths of a long stick than of a short one.
- An area unit is a length unit squared, so a stick twice as long makes the area number four times smaller.
- CGS uses centimetre, gram, second; FPS uses foot, pound, second; MKS (metre, kilogram, second) grew into SI.
- SI has seven base units, including the kelvin, ampere, candela and mole, and works in powers of ten.
- A common system lets trade and science share measurements without confusion.
Remember
| Same quantity, two units | Q = n₁u₁ = n₂u₂, so n₂ = n₁ × u₁ ÷ u₂ |
| Force and density | 1 N = 10⁵ dyne; 1 g/cm³ = 1 kg/L = 1,000 kg/m³ |
| Speed | km/h × 5/18 = m/s; m/s × 18/5 = km/h |
| Other units | 1 kg = 2.2 pounds; 1 inch = 2.54 cm |
| Percentage error | |estimate − measured| ÷ measured × 100 |
Watch out
- Multiplying by the ratio of units the wrong way round: a larger unit must give a smaller number.
- Scaling an area by the length ratio instead of its square.
- Dividing the error by the estimate instead of by the measured value.
Worked example
In an estimation game: the blackboard: estimated 256 cm, measured 260 cm; a bench: estimated 196 cm, measured 180 cm; a cupboard: estimated 92 cm, measured 120 cm. Find the percentage error for (a) the blackboard, (b) a bench and (c) a cupboard. (d) Which estimate was the most accurate? Name the object. (Give the answer to 2 decimal places where needed.)
Working: percentage error = |estimate − measured| ÷ measured × 100; the smallest error is the most accurate
Answer: (a) 1.54%; (b) 8.89%; (c) 23.33%; (d) blackboard
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