UNITS and Sig Figs

The working physicist’s guide to the bits you usually forget in an exam.

What do these people have in common?

Newton

Ohm Volta

1. They’re all blokes.

2. They’re all famous scientists.

3. They all have UNITS named after them.

Hey – what about me?

So sorry – you should have been born a bloke!

Units come in 3 types:

BASICMass kg M

Length m L

Time s T

Lower case

Capitals

DERIVEDSpeed ms-1

LT-1

Acceleration ms-2

LT-2

Density kgm-3 ML-3And SCIENTISTS: N, J, V, A, Pa, etc

The examiners expect you to be able to explain what the SCIENTIST-UNITS are in BASIC UNITS.

Even worse, you’re expected to use the kg/m/s AND M/L/T ways of writing them!

Don’t worry – they’re easy if you just follow some simple rules.

Rule 1: all derived units can be written as kg/m/s or M/L/T using the formula for the quantity.

e.g. Speed = distance/time ms-1 LT-1

Momentum = mass x velocitykgms-1

MLT-1

Rule 2: JOULES and NEWTONS are the only important scientist-units you’ll need.

NEWTONSNEWTONSRemember your GCSE formulas?

F = m x a

so, Newtons must be kg x ms-2

or M x LT-2

If you can’t work it out, remember it! N are kgms-2

JOULESJOULES

Energy change in J = Force x distance

Work done in J = F x dso…

Joules are kgms-2 x m

which is………..kgm2s-2

or ML2T-2

Try one yourself.

What are Pascals in kg/m/s and M/L/T?

Formula?

Pressure in Pascals = Force/Area

Units?

Pascals will be N/m2

or kgms-2

m2

or kgm-1s-2 or ML-1 T-2

Here’s a tricky one….

Young’s Modulus is STRESS/STRAIN.

Stress is Force/area.

Strain is extension/original length.

What’s the unit of Young’s Modulus?

Hint: units can cancel, just like in formulas.

Try it out and then check your answer with your teacher.

SIGNIFICANT FIGURES(or sig figs)

A sig fig tells you how accurate your measurements are.

For example: how accurately could you measure volume with this?

To 1 ml? 0.5 ml? 0.1 ml? 0.01 ml?Probably to ~ 0.2 ml.

Maybe an older teacher couldn’t do as well as this!

That means “to + or – 0.2 ml”.

And that means “+ or – 2/10 ml”.But what if we wrote ~ 0.20 ml?

What would that mean?

It means “+ or – 2/100 ml.

You couldn’t do that with this measuring cylinder – it isn’t accurate enough.

What sort of equipment would you need?Probably a piece of apparatus your school

does not have!

How do you work out the sig figs?How do you work out the sig figs?Rule 1.

If it’s in standard form, count the numbers in the front number.

e.g. 2.37 x 106 3 sig figs

1.5 x 10-4 2 sig figs

2 x 10-23 1 sig fig.

Rule 2. If it’s an ordinary number, count the numbers AFTER ANY ZEROS.

0.00456 3 sig figs

0.02 1 sig fig

0.020 2 sig figs

This counts!

Using standard form makes sig figs much easier.

GOLDEN RULE for exams.GOLDEN RULE for exams.

NEVER QUOTE AN ANSWER TO MORE SIG FIGS THAN IN THE QUESTION.

E.g. 8.31 x 12.3 = ?

Answer: 102 (to 3 sig figs only!)

GENERAL RULE OF THUMB

2 sig figs common

3 sig figs maximum