IB Maths AA SL 1.1 Scientific notation Question Bank

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

Exam points

Convert a quantity between ordinary notation and scientific notation with the required significant figures.
Use scientific notation to multiply, divide or compare quantities that differ greatly in scale.
Interpret the coefficient and power of ten in a scientific-notation answer within its context.

[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 $3\times10^4$ :
$\frac43\pi(3\times10^4)^3=36\pi\times10^{12}=\pi(3.6\times10^{13}).$ $a=3.6,\qquad k=13$
A1, A1, A1

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SL 1.1—Scientific notation question 1

Question (a)

Question (b)