Stoshastic processes and stochastic integration by Pivato M.

By Pivato M.

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For example, here 1 is divided by 3. Both the calculations and the answers in the division become identical after the second stage, and the answer repeats endlessly. 3 goes into 10 three times, with 1 left over add a decimal point to the answer line 0. 0 carry 1 3 does not divide into 1 3 does not divide into 1, so enter 0 on the answer line. Add a decimal point after 0, and carry 1. 00 3 goes into 10 three times, with 1 left over divide 10 by 3 10 divided by 3 gives 3, with a remainder of 1. Write the 3 on the answer line and carry the 1 to the next 0.

Write this across two columns. 3 Finally, count the decimal digits in the original numbers – there is 1. The answer will also have 1 decimal digit. 45 DECIMALS DIVISION Dividing one number by another often gives a decimal answer. Sometimes it is easier to turn decimals into whole numbers before dividing them. Short division with decimals Many numbers do not divide into each other exactly. If this is the case, a decimal point is added to the number being divided, and zeros are added after the point until the division is solved.

It cannot accurately be written out in full, so it is most simply expressed as the surd √5. △Not a surd The square root of 4 is not a surd. It is the number 2, a whole, or rational, number. Simplifying surds Some surds can be made simpler by taking out factors that can be written as whole numbers. A few simple rules can help with this. ▷ Square roots A square root is the number that, when multiplied by itself, equals the number inside the root. a × a = a 3× 3 = 3 multiply the surd by itself to get the number inside the square root ▷ Multiplying roots Multiplying two numbers together and taking the square root of the result equals the same answer as taking the square roots of the two numbers and mutiplying them together.

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