Scientific Notation and Standard Form
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Scientific Notation and Standard Form — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionMultiplying and Dividing Numbers in Scientific NotationConcept Practice
2 marks~3 minCriterion A
A satellite imaging system captures two circular coverage zones. The large zone has a radius of 9×1049 \times 10^4 km and the small zone has a radius of 3×1023 \times 10^2 km.

Using A=πr2A = \pi r^2, calculate the ratio of the area of the large zone to the area of the small zone. Express your answer in scientific notation. [1]

A minimum coverage ratio of 1×1041 \times 10^4 is required for the large zone to be classified as a primary zone. Justify whether the large zone meets this classification. [1]
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Solutions

2QuestionConverting Between FormsAssessment Practice
8 marks~12 minCriterion D
A biologist models the population of a bacterial colony using the formula

P=5.0×106×(1.02)tP = 5.0 \times 10^6 \times (1.02)^t

where tt is time in hours. Actual population counts are recorded below.

Time (hours)0510
Actual population5.0×1065.0 \times 10^65.8×1065.8 \times 10^66.5×1066.5 \times 10^6
a
Calculate the predicted population at t=5t = 5 and t=10t = 10. Give each answer in standard form to two significant figures. [2]
b
Convert the predicted populations from part (a) and the actual populations at t=5t = 5 and t=10t = 10 into ordinary numbers. [2]
c
Calculate the absolute difference between the predicted and actual populations at t=5t = 5 and t=10t = 10. Express each difference in standard form to two significant figures. [2]
d
Advise the biologist whether this model should be used to predict the size of the colony beyond t=10t = 10 hours. Use your results from parts (a) to (c) and give one biological reason to support your advice. [2]
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Solutions

3QuestionConverting Between FormsAssessment Practice
8 marks~12 minCriterion C
The Andromeda Galaxy is approximately 2.5 million light-years from Earth. One light-year is equivalent to 9.46×10129.46 \times 10^{12} km. A student claims the distance to Andromeda is 2.365×10192.365 \times 10^{19} km.
a
Write 2.5 million light-years and 9.46×10129.46 \times 10^{12} km each as an ordinary number. [2]
b
Show that the distance to Andromeda in kilometres is 2.365×10192.365 \times 10^{19} km, and deduce whether the student's claim is accurate. [2]
c
A science communicator must present the distance 2.365×10192.365 \times 10^{19} km to a general audience. Advise the communicator which format — scientific notation or ordinary number form — to use, justifying your recommendation and acknowledging the limitations of your chosen format. [4]
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Solutions

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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