It All Starts With a Number
Let's begin with a simple question. How tall are you?
You probably answered without thinking. Maybe "five foot eight", or "about 1.7 metres". Either way, you gave a number and a unit. That pairing is where physics begins.
Physics is really the craft of asking "how much?" and "how fast?" about the world. Before we can explain a kettle, a bike or a rainbow, we need a way to measure things that everyone agrees on. So that's our first stop.
Why the Unit Matters as Much as the Number
Imagine a friend texts you: "The shop is 5 away." Five what? Five minutes? Five miles? Five metres? The number on its own tells you almost nothing.
Here's a true story that shows how much this matters. In 1999 NASA lost a spacecraft called the Mars Climate Orbiter. One team's software reported thruster figures in imperial units (pound-force seconds). The navigation software expected metric units (newton-seconds). Nobody converted between them. The numbers looked fine, but they were out by a factor of about 4.45. The spacecraft came in far too low and was lost in the Martian atmosphere.
So here's our first habit: a measurement is always a number plus a unit. Drop the unit and the number becomes a guess.
Meet the SI Units
To avoid mix-ups like that, scientists around the world use one shared system, the International System of Units. It's called SI for short, from its French name.
The SI has seven base units. For now we only need three of them.
- Length is measured in metres (symbol m). A big adult stride is roughly a metre.
- Mass is measured in kilograms (symbol kg). A bag of sugar is about one kilogram.
- Time is measured in seconds (symbol s). Say "one-thousand-and-one" out loud and that's roughly a second.
You might wonder, who decides exactly how long a metre is? Today these units are tied to constants of nature, so anyone with the right lab can reproduce them. The second is set by a natural vibration of caesium atoms. The metre is the distance light travels in a vacuum in 1/299,792,458 of a second.
The kilogram was the last holdout. For over a century it was defined by a metal cylinder locked in a vault near Paris. Since 20 May 2019 it has been defined using a fixed constant of nature called the Planck constant. That means no single object anywhere "is" the kilogram any more.
One quick note. You'll meet plenty of everyday units that aren't SI base units, like the litre, the mile or the pound. They're handy, but when we do physics we turn them into SI units first.
Prefixes: Zooming In and Out
A metre is perfect for measuring a room. It's clumsy for measuring a grain of rice or the distance to the next town. So the SI uses prefixes, little words stuck on the front of a unit that scale it up or down.
Here are the three you'll use most:
- kilo- means a thousand. So 1 kilometre (km) = 1,000 metres.
- centi- means a hundredth. So 1 centimetre (cm) = 0.01 metres, and 100 cm make 1 m.
- milli- means a thousandth. So 1 millimetre (mm) = 0.001 metres, and 1,000 mm make 1 m.
The nice part is that they work on any unit. A kilogram is a thousand grams. A millisecond is a thousandth of a second.
Let's try a couple. Your walk to the shop is 2.5 km. How many metres is that? Kilo means a thousand, so 2.5 × 1,000 = 2,500 m.
Your friend is 180 cm tall. In metres? Centi means a hundredth, so we divide by 100. That gives 1.8 m.
Here's a handy tip. Going to a smaller unit, the number gets bigger. Going to a bigger unit, the number gets smaller. If your answer goes the wrong way, you've multiplied when you should have divided.
The Art of the Rough Estimate
Now for a physicist's favourite trick: the estimate. Before you measure something carefully, or work it out on a calculator, take a sensible guess first.
Why bother? Because a quick estimate catches silly mistakes. Remember the spacecraft? A good sense check is your early warning system.
Let's estimate the height of a stack of ten paperbacks. Here's how you'd think it through:
- Guess one item. A paperback is perhaps 2 to 3 cm thick. Call it 2.5 cm.
- Multiply up. Ten books × 2.5 cm = 25 cm.
- Ask if it's sensible. About 25 cm is roughly the length of a school ruler. Does that sound like a stack of ten books? Yes, it does.
- Check by measuring. Now grab a ruler and see how close you got.
If you got within a few centimetres, that's a great estimate. Physicists are happy when they get the right size of answer. If a calculation ever told you those ten books were 25 metres tall, as tall as a big building, you'd know straight away that something had gone wrong.
Kitchen-Table Experiment
Try this now. Find a ream or notebook of ordinary printer paper. Without measuring, guess how thick a single sheet is.
Then measure the thickness of a big stack, say 100 sheets, with a ruler. Divide by 100. A normal sheet usually comes out at around 0.1 mm. How close was your guess?
Notice the trick there. A single sheet is far too thin to measure with a ruler. A stack makes the job easy. That's real physics thinking!
Key Takeaways
- A measurement is always a number plus a unit. Without the unit, the number is meaningless.
- The SI base units for length, mass and time are the metre (m), kilogram (kg) and second (s).
- kilo- = × 1,000, centi- = ÷ 100, milli- = ÷ 1,000.
- A smaller unit means a bigger number, and a bigger unit means a smaller number.
- A quick estimate (guess one, multiply, sense-check, then measure) catches mistakes before they matter.