Tools & Skills for Quantitative Thinking and Scientific Notation

by Jared Rovny

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    00:00 As I said we’re gonna start with some tools and skills for quantitative thinking because this will be very useful for you as we move ahead just to have a sort of a quantitative toolbox for you as we go. This will help you to solve problems. It will be very key skill to have, especially in exam setting, in which it will help you to move much more quickly through the material.

    00:18 The three things that I would like to make sure to cover are, first, scientific notation and how we write numbers and can use it in problems. Second, unit analysis, how we can just look at the units of key variables we’ll introduce, an example of which is here which you do not need to memorize yet. And how we’ll be able to use unit analysis in problems and sometimes be able to solve entire difficult looking problems just by analyzing the units in front of us.

    00:42 And then finally, I would like to introduce and help practice a key mindset, which is the mindset of proportionalities, understanding how one quantity can depend on another in a particular way can help you to solve seemingly difficult problems very very efficiently and quickly.

    00:58 So let’s see what these three skills are. First in sciences and certainly in physics, and also will be the case in medicine, we deal with very very big numbers. Sometimes these numbers have many digits as this number right here does before the decimal point and sometimes they’ll even be very very small numbers. Because we don't want to write huge numbers all the time over and over again, we introduce a notation, a particular way of writing numbers.

    01:23 This way of writing numbers that we’re gonna use is called scientific notation, it comes form the basic fact that in our system which it’s a based ten system. When you multiply a number by ten, it just gets a zero added to it. We can use this fact to rewrite a number as big as this one just by moving the decimal point from one end all the way back so instead of writing two, three, four and then a lot of zeros, we can just write 2.340 and tell you how many tens you need to multiply by to get back to the original big number. Practically, in order to do this, you just take your decimal point, move it over as many places as you need to, counting as you go and however many places you need to move that decimal point, that’s how many power of ten you’re gonna need.

    02:04 In this case we have to move the decimal point 12 places over and so the actual number written in scientific notation is 2.340 times 10 to the power of 12. In scientific notation we have a convention which is that you always put the decimal point right after the first non zero digit.

    02:21 And in this number, the first digit that is not zero is a 2, and so we’ll move the decimal point over until we reach the 2, then we stop the decimal place after the 2. Once we’ve done that, we can write many many big numbers in scientific notation. This will be very useful as we go forward.

    02:36 We get to see the usefulness of scientific notation immediately right now because we’re dealing with so many big numbers and so many small numbers that we introduce some notation and some names for powers of 10 that we see very often. An example you might be familiar with is kilo, this 10 to the third on the first column you see on your left. This kilo is something you might have heard of with kilograms. We don’t like measuring masses that, that small as grams or maybe kilometers here, or maybe a meter is too small when you’re talking about something like driving long distances and so we introduce a prefix, kilo, which tells us that we’re talking about, not meters but thousands of meters or kilometers. As we go forward, in fact, the right column here, the one with the lower case prefixes like deci, and centi, and milli, et cetera. are actually gonna be more useful as we go forward in terms of how commonly they come up. Especially, I’d like to draw your attention to milli, micro and nano. These are ones that are probably the least familiar initially for people but also come up the most often. And so you wanna really practice using those. In terms of writing numbers using this notation, what you wanna do is take your numbers, say it a very small number of seconds, like a millisecond and instead of writing 0.001 seconds, you can say that it’s one millisecond. And the way you write that unit you can see, in the far right column, with m.

    03:57 The letter m you just put it in front of the letter s and that will tell people that it’s milliseconds.

    04:02 And you’ll be able to see and use all these notations as we go forward.

    About the Lecture

    The lecture Tools & Skills for Quantitative Thinking and Scientific Notation by Jared Rovny is from the course Methods and Common Calculations. It contains the following chapters:

    • Tools and Skills for Quantitative Thinking
    • Scientific Notation

    Included Quiz Questions

    1. 1.23 x 10^8
    2. 1.23 x 10^6
    3. 123 x 10^6
    4. 1.23 x 10^-8
    5. 123 x 10^-8
    1. 1.23×10^6 J
    2. 1.23×10^6 MJ
    3. 1.23×10^-6 J
    4. 1.23×10^-6 MJ
    5. 1.23×10^6 kJ
    1. 6.5 m
    2. 0.0000065 m
    3. 65,000 μm
    4. 65 m
    5. 65,000,000 m
    1. 116,000,000.
    2. 116,00,000.
    3. 116,000,000,000.
    4. 1.16,00,000,000.
    5. 1.1600000000.
    1. 1/1,000,000,000.
    2. 1e+9.
    3. 1e+8.
    4. 1000000000.00.
    5. 1/-1,000,000,000.
    1. 45miles/hour.
    2. 50miles/hour.
    3. 55 mile/hour.
    4. 66 miles/hour.
    5. 65 miles/hour.

    Author of lecture Tools & Skills for Quantitative Thinking and Scientific Notation

     Jared Rovny

    Jared Rovny

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