IB Maths AA SL 1.1 Scientific Notation Questions

Practise IB Maths AA SL 1.1 by converting scientific notation, rounding quantities and interpreting scale in applied problems.

Exam points

Convert a quantity or a calculated result to the normalized form a × 10^k, with 1 ≤ a < 10 and integer k.
Use a geometric or applied calculation to obtain a very large or small value, then report the result in normalized scientific notation.

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Study SL 1.1—Scientific notation conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 4]

The diameter of a spherical planet is $6 \times 10^{4} \mathrm{~km}$ .

(a)

Write down the radius of the planet.

The volume of the planet can be expressed in the form $\pi\left(a \times 10^{k}\right) \mathrm{km}^{3}$ where $1 \leq a<10$ and $k \in \mathbb{Z}$ .

[ 1 ]

$3\times10^4$
or $30000\,\mathrm{km}$ . Accept $3\bullet10^4$ .

(b)

Find the value of a and the value of k.

[ 3 ]

Use the volume of a sphere with radius $3\times10^4$ :
$\frac43\pi(3\times10^4)^3=36\pi\times10^{12}=\pi(3.6\times10^{13}).$ $a=3.6,\qquad k=13$

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IB Maths AA SL 1.1 Scientific Notation Questions question 1

Question (a)

Question (b)