Measurement, Units & Experimental Evidence — Practice · Grade 11 Science

Chapter: Investigating Matter

What this practice covers

By the end of Measurement, Units & Experimental Evidence you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: density, systematic error, significant figures.

Problem 1

A 42.0 g sample occupies 15.0 mL. Find density.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

2.8 g/mL

42.0/15.0 = 2.80.

Problem 2

Three readings are 2.01, 2.02, 2.01 g/mL but the reference is 2.50. Interpret them.
Answer and explanation

Precise, but inaccurate relative to the reference; investigate calibration or consistent method bias.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

A 18.0 g sample occupies 6.00 mL. Find density.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

3 g/mL

18.0/6.00=3.00.

Problem 4

Design a repeatable density measurement for a small waterproof object.
Answer and explanation

Measure mass on a calibrated balance; record initial and final water volumes, subtract for displaced volume, repeat, and note trapped-air or scale-reading uncertainty.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

Convert 0.0350 kg to grams and preserve significant figures. Show the reasoning, not just the conclusion.
Hints

Unit conversion and significant figures are different checks.

Answer and explanation

35.0 g; the exact conversion factor 1000 g/kg does not reduce the three significant figures.

Problem 6

Repeated volumes are 9.8, 9.9 and 9.8 mL, but a reference is 10.5 mL. Explain precision versus accuracy.
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

The readings agree closely, indicating precision; their offset from the reference suggests lower accuracy or systematic error.

Problem 7

Reported digits should reflect the measuring processReported digits should reflect the measuring process2.03.0Read between marksInclude one estimate2.40 cm × 1.2 cm = 2.88 cm² → 2.9 cm²The limiting measured input has two significant figures.
Original schematic ruler and independent area calculation. The marker illustrates interpolation rather than supplying the dimensions for that area problem.
Interpret the supplied visual. Why is the area reported as 2.9 cm² rather than 2.8800 cm²?
Answer and explanation

The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.

An instrument’s resolution is the smallest change it can distinguish or display; an analog scale usually supports an estimated digit beyond its marked intervals. That does not make every last digit exact. In classroom significant-figure rules, a multiplication result follows the least precise measured factor in significant figures. Addition and subtraction instead follow decimal-place precision. Keep guard digits while calculating and round once at the end; extra calculator digits cannot improve the original measurement.

The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the chemistry relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

An unknown has mass 37.5 g at volume 15.0 mL. Three repeat densities cluster near 2.50 g/mL, but the independently certified reference is 2.80 g/mL. Calculate density and explain the evidence limits.
Answer and explanation

Density is 37.5/15.0 = 2.50 g/mL. Repetition supports precision, but the difference from 2.80 suggests a method/reference comparison issue; check calibration, conditions and uncertainties rather than claim identity from one property.

Density is 37.5/15.0 = 2.50 g/mL. Repetition supports precision, but the difference from 2.80 suggests a method/reference comparison issue; check calibration, conditions and uncertainties rather than claim identity from one property.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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