# Converting Units

## Converting Units

Converting units means being able to change a value of a measurement or calculation from one unit to another. This can only be done with certain units, the units must represent the same quantities for this to be possible.

Let us look at an everyday example before we look at some examples from physics.

Image you are going on holiday after your exams, to sunny Spain. You need to take some money to spend and you have £300. This has to be converted to a different unit of currency, the Euro (€). The £ and the € are both units of currency, so we can convert between them. All we need to know is the value a £1 compared to €1,(exchange rate).

£1 = € 1.12 so £300 x 1.12 = € 335.61

To convert between units you need:

**●** Two units that both measure the same quantity, you can not change newtons into meters for example

**●** An exchange rate or conversion factor

Example 1: Temperatures

Most thermometers have a scale set in Celcius (^{o }C) where 0 ^{o }C is the freezing point of water.

However, in many calculations using temperatures, the value has to be in the SI unit of the kelvin (^{o }K).

They both measure temperature, so we can convert them.

Conversion factor: add 273 to a Celsius reading to find the kelvin reading.

Therefore 25.1 ^{o }C =273 + 25.1 = 298.1 K

Example 2: Time

When you use a stopwatch to measure time in an experiment, the time on the display will be in;

Hours : Minutes : Seconds : Fractions of a second

However, any calculations we perform with time values must be in the SI unit of the second.

We can converts between hours, minutes and seconds because they are all units of time.

**Conversion factors**

1 hour = 60 minutes

1 minute = 60 seconds

Therefore 1 hour = 60 minutes x 60 seconds = 3600 s

E.g. Convert 2 hours 34 minutes to seconds.

2 hours x 3600 s = 7200 s

34 minutes x 60 s = 2040 s

Total = 9240 s

## Signficant Figures

The number of significant figures in a number, refers to the number of digits you record. In an exam question you may be told how many significant figures to use in your answer.Check this when you carefully read your questions.

If you have to decide for yourself then here are some rules to help you.

**●** All non-zero digits are significant (1 -9).

**●** Zeros are significant if they are after a decimal point.

**●** Rounding

**▪** Values of 4 or less round down

**▪** Values of 5 or more round up

The value 0.0081 has 5 significant figures. The value 81000 has only 2 significant figures, (the 8 and the 1).

Example: Speed=distance ÷ time. A car travels 10.0 m in 5.5 s

If you type this into a calculator the display will read 1.818181818, but you would not write this as your answer. Unless the question says otherwise, the rule is to round to the same number of significant figures as the least accurate value used in the calculation.

In this example the time is to 2 significant figures (sf) and distance to 3 sf, so we round to 2 significant figures ie1.8 m/s

Example: Speed= distance ÷ time distance = 18.99mtime = 3.444 s

The calculator display :5.513937282

Both measurements are to 4 sf, therefore we give the answer as 5.514 m/s. The 3 was rounded up to a 4 because the next digit was a 9.

## Standard Form

Measurements that are very large or very small can be presented using the multiples or submultiples of SI units.

i.e. 1,000,000 Pa can be written as 1 MPa ( one mega pascal).

This has its limits, however. Image measuring the width of our galaxy, the Milky Way.

Its around 950,000,000,000,000,000,000 m across or 950,000,000,000 Gm. Which is not really much help, plus you can not put that into a calculator or spreadsheet to do any calculations.

Standard form, sometime called scientific notation, is a way of presenting numbers in powers of 10. It uses a set format as follows.

a x 10^{n}

a is any number from 1 to 9, it can be a decimal, but should not contain any zeros as the last digit.

n is any positive or negative whole number. It represents the number of places the decimal point has to move to create the value ‘a’.

Width of the Milky Way a = 9.5, we have removed all the zeros. n= 20.

Therefore the Milky Way is 9.5 x 10^{20 }m wide.

(Tip: before the exams make sure you know how to enter these into your calculator, look for a button with 10^{x }or EXP or EE : Try it 2,000,000can be entered as 2 EXP 6, press the = to see the result).

When n is positive it refers to a large value 1 x 10^{6} is 1 million. If the value of n is negative it refers to values less than 1. 1 x 10^{-6 }is 1 millionth or 0.000001

i.e 0.00000045 m is 4.5 x 10^{-7}m

- A car travels 100.1 m in 35.5 s. (Speed = distance ÷ time) What is the speed of the car in m/s to 3 significant figures?
- Your answer should include: 2.82 / 2.82m/s