IB Maths AA 1.1 Notes

Scientific notation & significant figures

Scientific notation is used to write very large or very small numbers in the form

$a\times10^k$

where $1\le a\lt 10$ and $k\in\mathbb{Z}$.

Before using scientific notation, it is helpful to review significant figures. Significant figures describe the precision of a value. As a general rule, when giving a final answer, the number of significant figures should match the least precise value used in the question.

To count significant figures, start at the first non-zero digit. Every digit after that is significant.

• Zeros between non-zero digits are significant.
• Zeros after a decimal point can be significant.
• Trailing zeros in a whole number without a decimal point can be ambiguous, which is one reason scientific notation is so useful.

For example, $0.00450$ has $3$ significant figures because the significant digits are $4$, $5$ and the final $0$.

The number $3080$ is ambiguous unless extra context is given, because the final zero may or may not be intended as significant. Writing the number in scientific notation removes this uncertainty.

Look at a summary of examples in the table below: