Foamma 0.5" x 30" x 72" High Density Upholstery Foam Cushion (Seat Replacement, Upholstery Sheet, Foam Padding) @ Spinger Ltd (0.5" x 30" x 72")

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But what do we do if the dimensions are expressed in units other than feet — like yards, inches, or even centimeters and meters? Well, you need to convert them. There are two ways of doing this — either you convert the units before the volume calculation or after:

Both types of integrals are tied together by the fundamental theorem of calculus. This states that if is continuous on and is its continuous indefinite integral, then . This means . Sometimes an approximation to a definite integral is desired. A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram|Alpha can solve a broad range of integrals How Wolfram|Alpha calculates integrals 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: Wolfram|Alpha computes integrals differently than people. It calls Mathematica's Integrate function, which represents a huge amount of mathematical and computational research. Integrate does not do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions. 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: As other people (who are probably real mathematicians) have implied, as you get further on in your mathematical career, the less useful is to think of mathematical constructs being real. Instead it's helpful to think of them being useful (or in some cases elegant but of no practical use - although that's largely what people thought of number theory, before the invention of public key cryptography).

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?

Conversely, if we divide the initial number by 10, which is equal to multiplying it by 1/10 = 10⁻¹, we'll getThere 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). F = 0.00000000006674 N·m²/kg² × 5,972,000,000,000,000,000,000,000 kg × 73,480,000,000,000,000,000,000 kg / (384,400,000 m)².

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, Don't ask us how they found the mass of the Earth, as there isn't any scale big enough to weigh the entire planet. As for the circumference, talk to Eratosthenes. 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.To return to your original question though: imagine you have a number line and want to double a number, x. You get an imaginary rope, cut it to length x then lay it out from 0 to x then from x to 2x. This is easily generalized to multiplying by any natural number, a. Convert the volume directly to cubic feet unit. You may find this method easier, as you only need to divide or multiply once: 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.

As you can see, we had five digits, so we got five terms. What is more, consecutive digits appear in consecutive summands; we simply add a few zeros in the correct places to make it all jump to the right spot when we add it all up.

After converting the units, you'll have all of the dimensions in feet, so a simple multiplication will give us the result in cubic feet.