Writing Standard Form

Alison asked the following:

"What does 3.84E+4 mean when written down?"

Thank you for this, Alison! This is a common problem, as some calculators or computer programs (e.g. Excel) display standard form in this way.

The E+4 (also sometimes displayed E+04) means ×10⁴, so in this case:

3.84E+4 = 3.84×10⁴
or 38,400

Standard Form

In science lessons, you have no doubt used scientific notation, or standard form, to write numerical answers to questions that are either very large or very small.

There are many confusions that arise when using this technique, so let's sort them out by beginning with the number 420.

In standard form we re-write it in terms of powers of ten:
420 = 4.2 × 10²

One important rule is that the number we are multiplying by ten must itself lie between 1 and 10:

NumberCorrect Standard FormIncorrect 5432 5·432 × 10³ 54·32 × 10² 14,500 1·45 × 10⁴ 14·5 × 10³ N.B. Values are however numerically correct!

Standard Form

What about numbers that are very small? How can they benefit from being written in standard form? Let's try 0·092.

We need to move the 9 and the 2 two places to the left (so we have a number more than 1 but less than 10). We indicate that the number needs to be divided by 10 twice using a negative power:

9·2 × 10²

Now try the example 0·00000864.

The numbers 8, 6 and 4 (we always ignore 0's) need moving 6 places to the left:

8·64 × 10⁶