IB Maths AI 1.1 Notes

This page contains our IB Maths AI notes for 1.1. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Scientific notation'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Introduction To Exponents & Logs 1.6: Handling Numbers 1.7: Use Of Technology (HL)1.8: Advanced exponents & logs (HL)1.9: Introduction to complex numbers (HL)1.10: Advanced complex numbers (HL)1.11: Introduction to matrices (HL)1.12: Advanced matrices

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Chapters

1. Scientific notation & significant figures

2. Usefulness of scientific notation

3. Conversions

4. Operations

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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:

Number	Significant figures	Explanation
7	1	Only one non-zero digit.
0.00450	3	Start at first non-zero digit (4). Thus, 4, 5, and 0 are significant.
0.203	3	Start at first non-zero digit (2). Thus, 2, 0, and 3 are significant.
3080	Ambiguous	Trailing zero may be significant.
3.080	4	Decimal point shows trailing zero is significant too.
1.000	4	All zeros after the decimal point are significant.
2.50	3	Decimal point shows trailing zero is significant too.

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