Scientific Notation and Units

Science deals with the very large and the very small, so we write numbers in a form that keeps them readable.

$$3450000=3.45\times 10^{6}0.000072=7.2\times 10^{-5}$$

How to use this page

Every answer is hidden until you click it. Work the question first — reading a worked answer feels like learning, and mostly is not. The feeling of recognising an answer is not the same as being able to produce one.

Write in scientific notation

1. $149600000\mathrm{km}$ — the distance from Earth to the Sun.

Answer

$1.496\times 10^8\mathrm{km}$

2. $0.0000000001\mathrm{m}$ — roughly the width of an atom.

Answer

$1\times 10^{-10}\mathrm{m}$

3. $8640\mathrm{s}$

Answer

$8.64\times 10^3\mathrm{s}$

Write as ordinary numbers

4. $6.02\times 10^{23}$

Answer

$602000000000000000000000$ — six hundred and two sextillion. This one has a name: Avogadro’s number.

5. $1.6\times 10^{-19}$

Answer

$0.00000000000000000016$ — the charge on a single electron, in coulombs.

Convert

6. $2.5\mathrm{km}$ to metres.

Answer

$2500\mathrm{m}$

7. $450\mathrm{mL}$ to litres.

Answer

$0.450\mathrm{L}$

8. $3\mathrm{h}$ to seconds.

Answer

$10800\mathrm{s}$ — $3\times 60\times 60$.

9. $1500\mathrm{W}$ to kilowatts.

Answer

$1.5\mathrm{kW}$

Significant digits, briefly

Your answer cannot be more precise than your least precise measurement. If you measured $12.4\mathrm{cm}$ and $3\mathrm{cm}$, do not report $37.2\mathrm{c}{\mathrm{m}}^2$ — report $40\mathrm{c}{\mathrm{m}}^2$.