The Maths Student: Standard Form

Well, after a week off, largely because what we did last week wasn't really meaty enough to warrant a full blog, we're back with a bang, and the first thing we're going to talk about is standard form.

Standard form (sometimes called scientific notation) is, broadly speaking, a way of writing numbers. See, this is the kind of analysis that makes me the hard-hitting investigative blogger that I am. More specifically speaking, standard form is a way of writing numbers that can't be conveniently represented by normal means. Even more specifically, the type of standard form we will be looking at, called normalized standard form, demands that the coefficient being used in standard form is at least 1, but not greater than 10. It's very commonly used in science, for example the age of the universe.

A number written using scientific notation looks like this

where the coefficient (represented by a) can be any number that is at least one but less than ten, and the exponent "b" is any integer.

So, if we look at the age of the universe for example, which is approximately 13.798 billion years old, or 13,798,000,000, we could write that number using normalized standard form, and it would look like this:

1.3798 x 10^10 (Times 10 to the 10th power)

In simple terms, the exponent, 9 in this case, is the number of places we are moving the decimal point by. If it's 9, we move the point 9 places to the right. Standard form can also be used to represent very small numbers. If we wanted to write 0.0000001, we could write that using standard form as 1 x 10^-7. A - sign in this case means we move the point to the left, not the right. Standard form is a simple, beautifully elegant way of writing large numbers, and it's very much worth remembering.

This is a new format I'm trying out, a bite-size approach, rather than one blog for the whole class, so expect another one later in the week, until then, I've been the maths student, signing off.