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.
Table 1 Translating values into powers of ten
| 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.
-
Write 365 000 000 in scientific notation.
-
365 000 000 is written in scientific notation as 3.65 × 108.
-
Write 0.0465 in scientific notation.
-
0.0465 in scientific notation is written as 4.65 ×10−2.
How confident did you feel completing those questions?
- If you were able to answer the questions correctly then move straight to the next section.
- If you found some of the questions challenging then look at the additional maths resources that are available from the link below.
If you need any guidance on the maths content, take a look at the badged open course, Mathematics for science and technology.
OpenLearn - Scales in space and time
Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.