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Suppose that you've taken up astronomy recently and would like to know the gravitational force acting between the Earth and the Moon. For the calculations, we need the masses of the two objects (denote the Earth's by M₁ and the Moon's by M₂) and the distance between them (denoted by R). We have: Conversely, if we divide the initial number by 10, which is equal to multiplying it by 1/10 = 10⁻¹, we'll get We said that the number b should be between 1 and 10. This means that, for example, 1.36 × 10⁷ or 9.81 × 10⁻²³ are in standard form, but 13.1 × 10¹² isn't because 13.1 is bigger than 10. We could, however, convert it to standard form by saying that: We've spent quite some time together with the standard form calculator, enough to know that we can't leave the answer like this. We haven't learned how to write a number in standard form for nothing. Teenagers head out to Crystal Lake, NJ where they encounter murderous Jason and his handy machete...In the first section, we mentioned that the standard form converter is most useful when we're dealing with very large or very small numbers. So, why don't we take one object from each side of the spectrum: a planet and an atom. But there's more! We have multiplication and division in the formula, and the standard form exponents make these two operations very easy to calculate. By the well-known, well-remembered, and totally not forgotten the moment the test was over formulas, multiplying two powers with the same base is the same as adding the exponents, while dividing corresponds to subtracting them. In other words, if we separate the 10s to some powers from the other numbers, we'll get: Now, this is more like it! We don't know about you, but for us, short is beautiful, in mathematics at least. It might seem artificial to write a sum of the products, like 1×100 or 4×1, but that's just what the expanded form is.
fruits = [ 'orange' , 'apple' , 'pear' , 'banana' , 'kiwi' , 'apple' , 'banana' ] >>> fruits . count ( 'apple' ) 2 >>> fruits . count ( 'tangerine' ) 0 >>> fruits . index ( 'banana' ) 3 >>> fruits . index ( 'banana' , 4 ) # Find next banana starting at position 4 6 >>> fruits . reverse () >>> fruits ['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange'] >>> fruits . append ( 'grape' ) >>> fruits ['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange', 'grape'] >>> fruits . sort () >>> fruits ['apple', 'apple', 'banana', 'banana', 'grape', 'kiwi', 'orange', 'pear'] >>> fruits . pop () 'pear' For our non-American friends out there, the standard form is usually quite a different thing. Outside of the USA (especially in the UK), we say that a number is in its standard form if it's a single value that involves no arithmetic operations whatsoever. This notion is connected to the expanded form, and we explain it all in detail in the dedicated section. Also, note how you can switch between the two variants in the advanced section by choosing the appropriate option in the field " Have the calculator use..." For instance, take the number 154.37. It is in its standard form in the decimal base. That means 1 is the hundreds digit, 5 is that of tens, 4 of ones, 3 of tenths, and 7 of hundredths. Having the number written the way it is, makes us see it as a whole, and we don't really think of the individual digits, do we? which is the number we had initially but with the point two places to the right. This movement by 2 is shown by the power in the standard form exponents. Welcome to the standard form calculator, where we'll learn how to write a number in standard form. "What is the standard form?" Well, we'll get to the standard form definition soon enough. But let's just say that standard form in math and physics (quite often called scientific notation) is a neat way of dealing with very large or very small values. It's quite troublesome to write all the zeros of a number in every line of our calculations. Preferably, we can use standard form exponents and write the same thing with just a few symbols. That's why we made this standard form converter – to help you with just that.Anyway, if scientists had to write all of those zeros every time they calculated something about our planet, they'd waste ages! It's much easier to recall how to write a number in standard form and say that the mass of Earth is, in fact, So I can't complain that there's little character development or that the movie is riddled with clichés and stereotypes because this film is wise enough to dispense with the myriad BS and get to the elements that Friday' fans enjoy. Good choice. My only big complaint is the fact that Harry Manfredini's iconic theme music wasn't featured much, if any, in the movie. I did miss that ki-ki-ki ma-ma-ma. Still, we might wish to decompose it even further. After all, we wanted to see the digits themselves (i.e., as one-digit numbers) and not some " complicated" expression like 0.07. Therefore, we can also write: There is a valuable lesson here: writing numbers in standard form is not always the way to go. It's all about simplicity of notation, but, at the end of the day, it pretty much boils down to a matter of personal preference (or your teacher's if you're writing a test).
This time, we indeed see the digits as the first factors in each multiplication. Moreover, the second factors have a lot in common - they consist of a single 1 with some zeros (possibly none). and the circumference is... actually, the 40,075 km doesn't look that bad, does it? Well, we could use a length converter and change it to 4.0075 × 10⁴ km, but is it better that way? If we needed to change it to millimeters, then maybe it'd be a better idea, but the kilometer form seems perfectly usable.Now that we've seen how to write a number in standard form, it's time to convince you that it's a useful thing to do. Of course, we know that you're most probably learning all of this for the pure pleasure of grasping yet another part of theoretical mathematics, but it doesn't hurt to take a look at physics or chemistry from time to time. You know, those two minor branches of mathematics.
Now, this looks even worse than the previous example; it doesn't have commas in between! Thankfully, there are tools - like our standard form calculator - to make our lives easier. So, what is the standard form of the above numbers?
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vec = [ - 4 , - 2 , 0 , 2 , 4 ] >>> # create a new list with the values doubled >>> [ x * 2 for x in vec ] [-8, -4, 0, 4, 8] >>> # filter the list to exclude negative numbers >>> [ x for x in vec if x >= 0 ] [0, 2, 4] >>> # apply a function to all the elements >>> [ abs ( x ) for x in vec ] [4, 2, 0, 2, 4] >>> # call a method on each element >>> freshfruit = [ ' banana' , ' loganberry ' , 'passion fruit ' ] >>> [ weapon . strip () for weapon in freshfruit ] ['banana', 'loganberry', 'passion fruit'] >>> # create a list of 2-tuples like (number, square) >>> [( x , x ** 2 ) for x in range ( 6 )] [(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)] >>> # the tuple must be parenthesized, otherwise an error is raised >>> [ x , x ** 2 for x in range ( 6 )] Before we give some examples of writing numbers in standard form in physics or chemistry, let's recall from the above section the standard form math formula: The expanded form is a way to write a number as a sum, each summand corresponding to one of the number's digits. In our case, the sum would be:
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