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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.

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?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: 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:

Conversely, if we divide the initial number by 10, which is equal to multiplying it by 1/10 = 10⁻¹, we'll get 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. Convert the volume directly to cubic feet unit. You may find this method easier, as you only need to divide or multiply once: Use Math Input above or enter your integral calculator queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral using plain English.

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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: 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.