Physics is all about describing the world with numbers. But a number by itself, like 10, doesn't mean much. Is it 10 apples? 10 seconds? 10 meters? To make sense of our measurements, we need two things: a quantity and a unit.

A physical quantity is a property of a material or system that can be quantified by measurement. Length, mass, time, and temperature are all physical quantities. A unit is a standard amount of that quantity.

To avoid confusion, scientists around the world agreed on a single system of units: the International System of Units, or SI for short. It's built on seven base units, which form the foundation for all other measurements.

Every other unit can be derived from these seven. For example, the unit for speed is meters per second (m/s), which combines the base units for length and time. The unit for force, the newton (N), is defined as $kg \cdot m/s^2$.

You'll often need to convert measurements from one unit to another. Maybe a problem gives you a distance in kilometers, but the formula you need to use requires meters. The key is to multiply by a conversion factor, which is a fraction that equals 1.

For example, we know that 1000 meters = 1 kilometer. From this, we can build two conversion factors:

$\frac{1000 \text{ m}}{1 \text{ km}} = 1$ and $\frac{1 \text{ km}}{1000 \text{ m}} = 1$

To convert 3.5 kilometers to meters, you multiply by the conversion factor that has the unit you want (meters) on top and the unit you have (kilometers) on the bottom. This allows the original unit to cancel out.

This method works for more complex units, too. Let's convert a car's speed of 90 kilometers per hour (km/h) into meters per second (m/s). We'll need to convert kilometers to meters and hours to seconds.

Every measurement has a limit to its precision, determined by the tool used. If you measure a pencil with a basic ruler, you might say it's 18.7 cm long. You're confident about the 18, and you're pretty sure about the 0.7, but you can't say for sure if it's 18.72 cm or 18.73 cm. The digits you are reasonably sure of are called significant figures.

Significant figures, or "sig figs," tell us how precise a measurement is. The number 18.7 has three significant figures. A more precise instrument might give a measurement of 18.725 cm, which has five significant figures.

Here are the basic rules for counting them:

1. Non-zero digits are always significant. (e.g., 283 has 3 sig figs).
2. Zeros between non-zero digits are significant. (e.g., 203 has 3 sig figs).
3. Leading zeros are not significant. (e.g., 0.05 has 1 sig fig).
4. Trailing zeros are significant only if the number contains a decimal point. (e.g., 5.20 has 3 sig figs, but 520 has 2).

When you multiply or divide measurements, your answer should have the same number of significant figures as the measurement with the fewest significant figures. If you add or subtract, the answer's precision is limited by the measurement with the fewest decimal places.

Sometimes, you don't need a precise answer. You just need a rough idea. This is where estimation comes in. A good physicist can look at a problem and make a reasonable estimate before doing any detailed calculations. This helps you check if your final answer is sensible.

One powerful form of estimation is an order-of-magnitude calculation. The goal is to get within a factor of 10 of the actual answer. You do this by rounding every number in your calculation to the nearest power of 10.

Let's estimate the number of breaths you take in a lifetime. We don't need exact numbers, just ballpark figures.

1. Breaths per minute: You take about 10 to 20 breaths per minute. Let's round that to 10 for simplicity. So, $10^1$ breaths/minute.
2. Minutes per hour: 60. That's close to $100$, or $10^2$. (This is a rough estimate, remember!)
3. Hours per day: 24. That's close to 20, which is $2 \times 10^1$.
4. Days per year: 365. Let's round that to 400, or $4 \times 10^2$.
5. Years per lifetime: Let's say 80 years, or $8 \times 10^1$.

Now, let's multiply them all together.

So, a human takes roughly a billion breaths in their lifetime. This type of calculation, named a "Fermi problem" after physicist Enrico Fermi, is a great way to practice thinking like a scientist. It forces you to break down a complex problem into simpler parts and make reasonable assumptions.

Mastering measurement and estimation provides the foundation for everything else you'll do in physics. It's the difference between blindly plugging numbers into a formula and truly understanding the physical world you're describing.