Scientific Notation and Standard Form
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Scientific Notation and Standard Form — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionMultiplying and Dividing Numbers in Scientific NotationConcept Practice
2 marks~3 minCriterion C
The mass of Earth is approximately 5.97×10245.97 \times 10^{24} kg and the mass of Mars is approximately 6.39×10236.39 \times 10^{23} kg.
a
Calculate the ratio of Earth's mass to Mars' mass, expressing your answer in scientific notation. [1]
b
A spacecraft mission planner states: "Because Earth is roughly 9 times more massive than Mars, the fuel required to escape Earth's gravity will be significantly greater than that required to escape Mars." Assess whether this statement is mathematically reasonable, using your result from part (a). [1]
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2QuestionConverting Between FormsAssessment Practice
2 marks~3 minCriterion D
A team of demographers is comparing global population data across multiple decades. The world population in 2024 is 8,100,000,000.

Justify why expressing this population as 8.1×1098.1 \times 10^9 is preferable to using the full integer form when presenting findings in a published research report. Your response must reference a specific practical advantage relevant to this context. [2]
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3QuestionApplications in Science and Engineering ContextsConcept Practice
2 marks~3 minCriterion A
Proxima Centauri, the nearest star to our solar system, is approximately 4.2464.246 light-years from Earth. Given that 11 light-year ≈9.461×1012\approx 9.461 \times 10^{12} km, calculate the distance to Proxima Centauri in kilometres, expressing your answer in standard form. [1]

Explain why scientists use scientific notation when working with astronomical distances such as this. Give two distinct reasons. [1]
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4QuestionAdding and Subtracting with Powers of 10Assessment Practice
2 marks~3 minCriterion B
Three sums involving scientific notation are shown below.

(2×101)+(3×102)=320(2 \times 10^1) + (3 \times 10^2) = 320

(5×103)+(4×101)=5040(5 \times 10^3) + (4 \times 10^1) = 5040

(1×104)+(7×102)=10700(1 \times 10^4) + (7 \times 10^2) = 10700

Analyse the three calculations and explain the pattern connecting the exponent of each term to the position of its coefficient digit in the final sum. [2]

Solutions

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