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Section 1.4 Lecture Video (Sig Figs, Sci Notation and Units)

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hello AP Physics this is mrs. Comstock and today we're going to talk about significant figures scientific notation and units this information can be found textbook chapter 1 section 4 all measurements taken require some sort of measuring instrument this device can only do so with a Precision which is determined by the instrument itself for example look at the caliper shown the digital display reads 15.57 mm calipers Precision is determined by how many digits the display will show in our example to caliper only gives values to the point 0 1 mm therefore the Precision of this instrument and its readings will be plus or minus .01 mm we will talk more about Precision in the next weeks but for now you need to realize the device used determines the Precision of the measurement and we will stay at our knowledge of the measurement through the use significant figures  an easy way to determine the number of significant digits in a number is shown on the screen let's say I want to determine the number of significant figures in the number 3.07 notice I put the number in between the words P or in between the words present and absent and easy way to try to remember side the word present shows up shows up on and which side apps and shows up on in relation to your number is think of the number United States of America  the Pacific Ocean is found on the west coast in the Atlantic Ocean is found on the East Coast the p in Pacific will help you remember the word present shows up on the left side of the number and the word absent shows up on the right side of the number now to determine which way you're going to count digits what are you going to count digits from right to left or left to right that's determined by whether or not number you're looking at has a decimal place is your decimal place present or is it absent in our example there is a decimal point present so we're going to start counting on the left and we're going to count digits to the right until we get across the number now that only will you have to remember now is that you're not allowed to start counting with a zero but once you start counting you count all zeros until you get to the their side so when are example 3.070 we're going to start on the left side of the number we're going to start counting with the three and count every digit until we get to the right which will give us for significant digits  in this number a couple more examples how many significant figures are in the number 175,000 remember in your Pacific and Atlantic you'll put the p on the left side of the number the A on the right side of the number ask yourself the question is there a decimal point present or is my decimal is a disappoint in this example the disappoint is absent so we're going to count from the right towards the left you're not allowed to counting with a zero to the first digit that the that is significant will be the 5 and you start counting and finish to the other side so the five is significant the seven Vatican and the one is significant and this number has three significant figures  the bottom number we can take a look at also using your Pacific and your Atlantic or present and absent you can see this number has a decimal point present so we're going to start on the the number and count digits to the right the first non-zero digit will count is 6 in every other number will be significant sew in example there will be six significant figures  the what happens if your number is in scientific notation if it's in rotation you can ignore the * 10 and only concentrate on the base and treat the base number just like the other please. There's a decimal point present so we're going to count from left to right starting with the four  and turned towards the right this will have significant figures  the what happens when we start to do calculations we need to make sure around or answer to the number that is the least precise value that we started with but there's a couple rules here you're multiplying or dividing numbers you need to count the number of significant figures in each number you are provided with and round your answer to the lowest significant figures so what are example we have 3.73 which has three significant figures and 1 * 5.7 which only has two significant figures so we want our answer to only have two significant figures know what happens if you're multiply what happens if you're going to add or subtract numbers in this kind of situation you're going to take a look at decimal places in the example shown there are two decimal places and 18.54 but there's only one in 106.6 we're not plane about how many significant figures are in the numbers that were starting with we're only looking at decimal places so after we do our calculation we want to make sure that our answer only has one decimal place when you multiply and divide you can't significant figures but when you add subtract you look at decimal places there is one notable exception to these rules it is acceptable to keep one or two extra digits during intermediate steps of a calculation to minimize round errors in the calculation but the final answer must be reported with the proper number of significant figures look at example please rank in order from the most to the least the number of significant figures in the following numbers I'm going to give you a second to take a look at these and if you need more time you can stop the video and it started again when you have your answer Choice a has two significant figures Choice be also has two while choicy has three significant figures Sandy has four since we're supposed to write these in order from greatest to least the correct answer will be a the next class if we need to take a look at is scientific notation it's often beneficial to write numbers very large or very small numbers using scientific notation so let's take a look at the examples provided if you have 6370000 the correct way to represent this number in scientific notation is 6.37 X 10 to the 6th making sure you have units we would include meters at the end  how do we get this number it we moved the decimal from the end of the where to ride in front of the six when we did that we moved it to the left which indicates a positive exponent and we moved at 6 places and that's where the six came from please also note that original number only had three significant figures so are number written in scientific notation also has three significant figures  for doing the same method for the bottom example if we move our decimal from where it's at 2 but there's one digit to the left of the decimal we would have 7.5 in our base times 10 and we would have moved our decimal to the right which ended say negative and in this situation removed at 6 places also so you have a -6 include the units and that's our number in scientific notation if you think you need a little extra practice here you can see tactics box 1.2 or come in and see me and myself for Miss Loveland and will be glad to help you what the scores were also going to make sure that all of our values and answers have units at the units used on the AP test or going to be them 30 minutes and you probably already are familiar with units such as time with the unit seconds length meters and mass in kilograms what come across several new units throughout the year as well what also throughout the class find out that there is several large and very number a very small numbers that often get assigned a prefix to note to denote the power of 10 table 1.2 out of your Nextbook show some common prefixes used throughout this course and you do need to realize that they give you these prefixes on your on the AP sheet in formula chart and I'm sure your reference that throughout the year your textbook not only use the metric system it also uses push system you might have to make conversions between these two units of measurement and table 1.3 in your textbook show some very common useful conversion units that you might have to use throughout the year but what about conversions you're going to have to convert from prefixes which units from metric to english throughout the year please make sure that you are proficient at doing conversions and if you need some extra help please come in and get that take a look at it real quick example that would be common to this class so you'll have something to reference we want to convert 85 km per hour into where's per second please note that we want to take from kilometers and converted to meters as well as hours into seconds since we're starting with a we write that and then we need to make sure we write the units correctly it's meat kilometers divided by hours does go to which unit we're going to convert first have just pick one so in this case is take a look at kilometers I want to get rid of kilometers so I'm going to put it and the denominator leaving a blank on top  and that's where I put the meters meters in the numerator kilometers is in it I need to make my conversion factor equal to one so in 1 km there are 1000 M please know now that are units of kilometers will cancel we do the same thing with ours but here in our Base number we start with ours and the denominator so we need to put ours in the numerator leaving the blank in the denominator Laurel put seconds making this conversion factor equal to one 1 hours equal to 3600 seconds now or ours will cancel out leaving us with only the units of meters on top and seconds on bottom all you have to do now is do the calculation and you can pick up your calculator and I'll leave the rest to you hope this video is helped have a great day

Uploaded by Nicole Comstock.

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Section 1.4 Lecture Video (Sig Figs, Sci Notation and Units)

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