Year 9 Maths • AC9M9M02 • Authored homework
Scientific notation and measurement accuracy
Solve problems involving very large and very small measurements using scientific notation, significant figures and appropriate accuracy. Interpret rounded values carefully. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
Write 4 500 000 in scientific notation.
Write 0.00072 in scientific notation.
Convert 3.2 × 10^5 to ordinary notation.
Round 56.738 to 3 significant figures.
State whether 0.00480 has 2, 3 or 4 significant figures and explain.
Explain why scientific notation is useful for very large or very small measurements.
Estimate 6.1 × 10^4 + 2.8 × 10^4.
Write 750 nanometres in metres using scientific notation.
Correct this error: 45 × 10^3 is in standard scientific notation.
Give one example from science or technology where small measurements matter.
Part B
Long-answer questions
A virus has diameter about 1.2 × 10^-7 m. Write this in ordinary notation and compare it with 0.000001 m.
The distance from Earth to the Sun is about 1.496 × 10^8 km. Round it to 3 significant figures and explain the effect of rounding.
Calculate (3.0 × 10^6) × (2.0 × 10^-4), giving the answer in scientific notation.
Compare 4.5 × 10^-3 and 6.2 × 10^-4. Which is larger and by what factor approximately?
A measurement is reported as 2.40 m. Explain what the trailing zero communicates about accuracy.
Solve a problem involving bytes, kilometres, nanometres or cells using scientific notation and unit conversion.
Explain how rounding too early can affect a multi-step calculation. Give an example.
Create a table comparing ordinary notation, scientific notation and SI prefix form for three measurements.
Evaluate whether a calculator answer should be reported with all digits or rounded suitably in context.
Write a full response solving a very large or very small measurement problem, including units, significant figures and interpretation.
Part C
Research and understanding task
Research one real very large or very small measurement, such as a planet distance, cell size, atom radius, data storage size or wavelength. Write it in ordinary notation, scientific notation and a suitable SI-prefix form where possible.