L1 - Length & Time

objectives

Numbers and Units

• When you make a measurement, you might get a result like the one above: a distance of 10m. The complete measurement is called a physical quantity. It is made up of two parts: a number and a unit.
• 10m really means 10 X m (ten times metre), just as in algebra, 10x means 10 X x (ten times x). You can treat the m just like a symbol in an algebraic equation. This is important when combining units.

►In the diagram above, the girl cycles 10 metres in 2 s. So she travels 5 metres every second. Her speed is 5 metres per second. To work out the speed, you divide the distance travelled by the time taken, like this:

►As m and s can be treated as algebraic symbols:

Bigger or Smaller

►You can make a unit bigger or smaller by putting an extra symbol, called a prefix, in front. (Below, W stands for watt, a unit of power.)

Scientific notation

►An atlas says that the population of Iceland is this:

320 000

►There are two problems with giving the number in this form. Writing lots of zeros isn’t very convenient. Also, you don’t know which zeros are accurate. Most are only there to show you that it is a six-figure number. These problems are avoided if the number is written using powers of ten:

3.2 x 10⁵ (10⁵ = 10 x 10 x 10 x 10 x 10 = 100 000)

►‘3.2 X 10⁵’ tells you that the figures 3 and 2 are important. The number is being given to two significant figures. If the population were known more accurately, to three significant figures, it might be written like this:

3.20 X 10⁵

►Numbers written using powers of ten are in scientific notation or standard form. The examples below are to one significant figure.