Class 8 · English Version · Mathematics
2026 Class 8 Mathematics · English Version · Chapter 3 · Chapter companion part
Choose units, convert lengths and masses, use measuring tools and explain exact factors and measurement limits.
Class 8 English Version: part A of the Measurement companion. Eight sections, 30 written tasks and a notebook challenge. Selected companion coverage, not complete textbook coverage. Use all four parts for the mapped chapter methods; these fresh tasks do not reproduce every printed question. Drawings and explanations need guardian or teacher review.
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Measurement compares a quantity with a chosen unit. A length of 2 m is twice one metre; an area of 2 m² covers two unit squares; a volume of 2 m³ fills two unit cubes. Those three quantities cannot be added. Counts such as 12 books are distinct from measurements such as 12 kg. State both the value and the unit in every written answer.
For length, km, hm, dam, m, dm, cm, mm follow factors of ten. Kilo means 1000, hecto 100, deca 10, deci one tenth, centi one hundredth and milli one thousandth of the named unit. A smaller unit requires more units for the same quantity: 2.35 m = 235 cm. Do not count columns blindly when the units are squared or cubed.
For 2 km 35 m 6 cm, convert to metres: 2000 + 35 + 0.06 = 2035.06 m. Keep absent places as zero rather than joining the digits. A runner completing 18 laps of a 250 m track travels 4500 m = 4.5 km. A wheel with circumference 2.5 m makes 600 full turns over 1500 m if there is no slipping.
The international inch is exactly 2.54 cm; the foot is 12 inches = 0.3048 m; the yard is 3 feet = 0.9144 m. A statute mile is 1760 yards = 1609.344 m and a furlong is 220 yards. The modern international nautical mile is 1852 m. Keep the kind of mile explicit. A rounded reciprocal, such as 39.37 inches per metre, is approximate even when the underlying definition is exact.
SI means International System of Units. The length base unit is metre and the mass base unit is kilogram. Grams and kilograms measure mass; weight is a force measured in newtons. School problems often say weight when they give mass in kg: interpret the quantity and label it carefully. One tonne is 1000 kg and a quintal in this chapter is 100 kg. One litre (L), accepted for use with SI, is one cubic decimetre; 1000 mL = 1 L.
Align the ruler zero, not a damaged edge, with the start. If an object runs from 2.0 cm to 7.6 cm, length is 7.6 − 2.0 = 5.6 cm. A ruler divided in millimetres cannot justify many extra decimal places. Read a pointer or liquid scale at eye level to reduce parallax, an apparent shift caused by viewing from an angle. Zero or tare a balance before using it, and state the instrument unit.
Estimate a box capacity, then measure its internal dimensions or use a graduated vessel. If your estimate is 480 mL and the measured value is 525 mL, the estimate is 45 mL low; the absolute difference is 45 mL. The measured value is a reference reading with limited precision, not automatically an exact truth. Divide a stated 2.4-tonne store equally among 80 bags: 2400/80 = 30 kg per bag. Measure books or classroom objects without uploading anyone’s body data.
Printed page 31 says 1 yard = 0.9144 cm. Its unit is a typo: use 0.9144 m = 91.44 cm. The nearby claim that British–metric relations cannot be exact is not true for the international inch and yard. Its 6080-foot nautical mile is not the modern definition of 1852 m. Page 30 describes historical metre standards; today the metre uses the fixed speed of light in vacuum. Keep a source’s stated rounded factor when a question explicitly asks for it, label that approximation and distinguish it from the modern exact factor.
To convert 5 feet 6 inches, first count inches: 5 × 12 + 6 = 66. Then 66 × 2.54 = 167.64 cm. This is an exact conversion of the stated length, although an actual tape reading has its own measurement limits.
A factor must refer to the named quantity. For area and volume, square or cube the length factor; those rules are taught in the next parts.
International factors and the modern metre were checked against NIST’s SI Units – Length and Guide to the SI, chapters 5 and appendix B.8, on 22 October 2026. No third-party artwork is copied.
These factors apply to the named unit before any square or cube is taken.
| Prefix | Symbol | Factor | Length example |
|---|---|---|---|
| kilo | k | 1000 | 1 km = 1000 m |
| hecto | h | 100 | 1 hm = 100 m |
| deca | da | 10 | 1 dam = 10 m |
| no prefix | — | 1 | 1 m |
| deci | d | 0.1 | 1 dm = 0.1 m |
| centi | c | 0.01 | 1 cm = 0.01 m |
| milli | m | 0.001 | 1 mm = 0.001 m |
For 2.35 m, divide by 0.01 m per cm to get 235 cm. The letter m is metre as a whole unit, but milli when used as a prefix in mm.
International length definitions; reciprocal decimal approximations must be labelled.
| Unit relation | Value | Status |
|---|---|---|
| 1 foot | 12 inches = 0.3048 m | Exact |
| 1 yard | 3 feet = 36 inches = 0.9144 m | Exact |
| 1 furlong | 220 yards = 201.168 m | Exact |
| 1 statute mile | 1760 yards = 8 furlongs = 1609.344 m | Exact |
| 1 nautical mile | 1852 m | Modern international definition |
| 1 metre | about 39.37 inches | Rounded reciprocal |
Three yards are 3 × 0.9144 = 2.7432 m. Do not use the source’s 0.9144 cm typo or confuse statute and nautical miles.
Use the same six prefix meanings, while keeping mass and volume separate.
| Kind | Larger to smaller | Numerical factor |
|---|---|---|
| Mass | kg → hg → dag → g → dg → cg → mg | ×10 at every adjacent step |
| Mass | 1 quintal → kg | 100 |
| Mass | 1 tonne → kg | 1000 |
| Liquid capacity | kL → hL → daL → L → dL → cL → mL | ×10 at every adjacent step |
| Capacity bridge | 1 L → cm³ | 1000 |
For 3 kg 45 g, write 3000 + 45 = 3045 g. For 2 L 75 mL, write 2000 + 75 = 2075 mL. Adding grams to litres is not a unit conversion.
A ratio expressing the same length has value one; it changes the unit without changing the physical length.
Length in cm = length in inches × 2.54 Mixed length = converted component 1 + component 2 + ... Absolute difference = |estimate − reference|
An exact unit factor does not make a ruler reading infinitely precise. Give only the precision justified by the measurement or task.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original conversion schematic. Box positions are not proportional distances. The prefix m in mm means milli; the final m means metre.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original schematic, not a calibrated on-screen measuring tool. Never measure a real object against the phone picture; zoom changes its physical size.
Show your working on paper. Check your answer, then choose Next.
235
2.35 × 100 = 235 cm.
0.48
480/1000 = 0.48 m.
2035.06
2000 + 35 + 0.06 = 2035.06 m.
4.5
18 × 250 = 4500 m = 4.5 km.
600
1500/2.5 = 600 turns.
15.24
6 × 2.54 = 15.24 cm.
2.7432
3 × 0.9144 = 2.7432 m.
3218.688
2 × 1609.344 = 3218.688 m.
3704
2 × 1852 = 3704 m.
2400
2.4 × 1000 = 2400 kg.
30
2400/80 = 30 kg per bag.
300
3 × 100 = 300 kg.
5.6
Subtract the starting reading: 7.6 − 2.0 = 5.6 cm.
45
525 − 480 = 45 mL; the estimate is low.
2075
2000 + 75 = 2075 mL.
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Metres measure length while square metres measure area. A unit square has two length dimensions; the equal numeral 3 does not make the quantities interchangeable.
Name the quantities and show a line and a unit square.
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km → hm → dam → m → dm → cm → mm. Each move towards the smaller unit multiplies the numerical value by 10; reverse moves divide by 10.
Use correct symbols and explain that the physical length does not change.
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4007.009 m and 4007009 mm. Convert components separately: 4000 + 7 + 0.009 m.
Check the empty centimetre place and do not concatenate mixed-unit numerals.
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25 × 320 = 8000 m = 8 km. This uses track length per lap, not its diameter or enclosed area.
Show the multiplication and both units.
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One yard is 36 inches; 36 × 2.54 cm = 91.44 cm = 0.9144 m. The printed centimetre label is wrong.
Identify the source typo explicitly rather than silently changing the number.
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100/2.54 = 5000/127 inches, an exact rational value with a non-terminating decimal. Rounding it gives 39.37. Exact definitions and rounded displayed reciprocals can coexist.
Distinguish the exact ratio from its decimal approximation.
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An international statute mile is 1609.344 m, a nautical mile is 1852 m, and a furlong is 220 yards = 201.168 m. Eight furlongs make a statute mile.
State the mile type and avoid the source’s obsolete 6080-foot value as a modern definition.
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Kilogram is a unit of mass. Weight is gravitational force measured in newtons; its value depends on gravitational acceleration. A classroom word problem may use weight informally, but the unit identifies its mass calculation.
Do not numerically convert to newtons without a specified gravitational model.
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Check zero and divisions, align the tape straight along the chosen edge, read at eye level, record unit and instrument resolution, and repeat. Compare the readings and discuss any disagreement rather than inventing precision.
A real observation is needed; a model sentence is not a fabricated measurement.
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Tare the empty pan or container. Weigh the five books together, record kg or g and scale divisions, and compare with the sum of individual readings if available. Small differences may arise from rounding.
Use actual classroom readings, identify tare and avoid invented observed data.
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The estimate is 0.12 m = 12 cm low. The reference comes from a measuring tool and has limited precision; the difference is not proof that the tool is exact.
Explain direction, unit and the role of the reference reading.
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3000 + 45 = 3045 g = 3.045 kg. Three kilograms and forty-five grams is not 3.45 kg.
Show the conversion and a reverse check.
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The current metre is linked to the fixed speed of light in vacuum and the second; a platinum-iridium bar was an earlier physical standard. The book’s historical account should not be presented as today’s definition.
A plain explanation is sufficient; no need to memorise a long constant for this exercise.
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U.S. liquid and Imperial gallons/fluid ounces have different sizes. A unit name without the system does not determine one universal litre conversion. Ask for the convention or use the task’s explicit factor.
Do not confuse fluid ounces of volume with ounces of mass.
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Columns should include container, estimated capacity in mL, measured reference in mL, absolute difference and whether the estimate was high or low. Fill it from real measurements and name the tool.
Review the arithmetic and reading precision; no made-up measurement is required.
Make a unit ladder and a table of three estimated and measured classroom objects.
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This original Kidemy practice follows the topic order of 2026 Class 8 Mathematics · English Version, chapter 3, printed pages 29–47. It does not replace the complete chapter or its practical teaching.
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