1.1 Scientific notation
Large and small numbers are best expressed by using scientific notation. The convention of scientific notation is that a quantity is presented as a number, equal to or greater than 1 but less than 10, multiplied by a power of ten.
For example, 3500 000, or 3.5 million, is written as 3.5 × 106. Here, the number part is 3.5, which is clearly greater than 1 but less than 10, and the power of ten is 6. Similarly, 0.0095 is written as 9.5 × 10−3 in scientific notation. Table 1 shows some examples of powers of ten and their meanings.
| Thousands | Hundreds | Tens | Units | Tenths | Hundredths | Thousandths | |
|---|---|---|---|---|---|---|---|
| Value | 1000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 |
| Power of 10 | 103 | 102 | 101 | 100 | 10−1 | 10−2 | 10−3 |
You might already be familiar with these concepts. Have a go at the following questions to test your knowledge.
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Write 365 000 000 in scientific notation.
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365 000 000 is written in scientific notation as 3.65 × 108.
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Write 0.0465 in scientific notation.
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0.0465 in scientific notation is written as 4.65 ×10−2.
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