[MUSIC] In the last question in the quiz, we needed to work out the number of seconds in a year, and do it formally. I'll write one year equals 365.24 days. Then I can multiply both sides of that equation by 1, without changing it. The 1 that I use is 24 hours divided by 1 day, which will cancel the days. Then 3600 seconds over an hour, to cancel the hours. Then the calculator tells me, the number of seconds in an average year, leap seconds not included. So now I can convert 14 billion years. Again, multiplying by 1. Here's something important. My calculator gave me lots of digits, but I didn't write them all down. We started with the value 14 billion years. I know that this value is not exact, because it only has two digits. We say that 14 has two significant figures. So here I take 14 to mean somewhere between 13.5 and 14.5. In other words, there is an implied error of up to 0.5 over 14 or a few percent. So, when I give my answer, I also give that to two significant figures, 4.4 times 10 to the 17 seconds. Note, the number of significant figures is not the number of decimal places. It's the total number of digits in scientific notation. If a cosmologist said, 13.8 billion years, then I'd have three significant figures and an implied error of a fraction of a percent. My calculator gives me a new long number, but I keep only the first three. Round up I get, 4.35 by 10 to the 17 seconds. The difference is important, because that last digit is significant. It gives me an idea of the precision of the value. We'll do more examples of significant figures as we go, and we'll expect you to be careful with them when doing problems. By the way, you might want to remember that a year is roughly 30 million seconds [NOISE] 30 million of these. Don't waste them. So, we've introduced the standard unit of time, and also how we measure it. We measure ratios. A year is about 30 million times longer than these ticks. Scientists use the Units of the Systeme International, for length, we use the meter. This long, and again, we measure it by ratios in counting. When I said that this bench is 9, 0.93 meters high, I'm giving you a ratio,. Now, I'm more likely to say 930 millimeters, which introduces one of the standard prefixes, milli, meaning one thousandth. While we're measuring lengths, here's an example that might give you some ideas for your first experimental investigation. What's the acceleration of this train [SOUND]. I've previously measured the width of the door as 1.22 meters. So, in the first frame of my little video, I can relate the lengths on the side of the train, to pixels in the image, provided that the distance from the camera is fixed. Now I compare two successive frames of the video. Count how far the train door has moved in pixels, which I can now convert to millimeters. This little camera take 30 frames per second. So now I can work out the average speed of the train between these two video frames. Provided I don't move the camera, I can use other parts of the train to measure distance per frame, and so ultimately we can plot speed as function of time, as the train accelerates. But how accurately could I measure the distance? No matter how good my camera, ruler, or whatever. There is always some uncertainty in any measurement, and that's why we draw graphs with error bars. These lines mean that for this measurement, the speed was probably in this range, and the time was probably in this range. Making good scientific graphs and dealing with uncertainty. Requires special skills. So we'll provide resources for those and we'll have special resources for your investigation. Well, you've now met the units for speed in the Systeme International meters per second. The meter per second is a nice human scale unit. You can walk at a couple of meters per second. But you probably know another unit for speed, kilometers per hour. New units call kilo as a prefix for a 1,000, so a kilometers is a 1,000 meters. And an hour is 3,600 seconds. Well, easy to convert, multiplying by 1 again. 1 meter per second equals 3.6 kilometres per hour. Exactly. We'll use real world examples in this course and here's a preview of one of them. The world record for a car powered by the sun alone, no batteries, is 88.7 kilometers per hour, set by this car, built and raced by UNSW students. Americans use miles, so let's convert. A land mile is defined as 1.60934 kilometers, which I'll rearrange to get 1. Again, why didn't I write down all the figures on my calculator. Yes, significant figures. This answer would be misleading. It implies a precision that the original value doesn't have. [LAUGH] And this one is just wrong. A speed cannot equal a number. But note that meters per second, or miles per hour, or kilometers per hour, all have what we call the dimensions of distance over time. Dimensions and units are important. You can't measure distance in kilograms or force in seconds. So, you'll have to be careful with units and with significant figures because we'll be checking. There's a complication with significant figures when we do subtraction. Let's suppose I have a metal bar that is 300.0 millimeters long. I heat it over a flame, and it expands. Suppose its new length is 300.3 millimeters. By how much has it expanded? Well, our original data were accurate to about 0.1 millimeter, and our result cannot be more accurate than this. It's also accurate to about 0.1 millimeter. So in this subtraction, we've actually lost significant figures. We started with 4, and ended up with just 1. The increase in proportional error produced by subtraction, is often a problem in experimental data and in calculations. You'll probably run into it in your first experimental investigation. [LAUGH] You've thought of that already, have you? Well then, you're ready for another quiz. But remember, you can come back to look at this video again if you need it.