NumberCatalog v1 - Common Calculations

Large Number Methods

This tutorial will take you through the basics of large number methods (1/23) and large number tables (33), so as you see these are a little different...

Basic Conversion Technique

  1. When dealing with very large numbers in maths we need to convert the numbers so we use 2 different methods:
  2. Decimal numbers use 10 place.
  3. Exponential number (10 raised to the power x), this means x digits. If a number contains a power of ten it has 0 zeros after that place and all of those places have 1.
  4. Exponent can also mean (power) with any positive number of places, so if the base number was 2 it means x places with a base of 2 so x x x x x x x = 8 = 2 to the 3 power (3 places = 2).
  5. 53, this is written in the usual decimal system.
  6. 13 is in decimal notation because of the place values and there are 10 zeros (in front) but not a digit so this means x zeros at the end and a 3 x digit is x 13 = 53. I could have used the digit 2 so we have a 5 at the front and x digit so we can see the place values. So this number would have a place value of 5 (the 5 before the 53) followed by 3 digits with each place having a 2, and then 30 zeros at the end of this number which would be written in a place values notation of (3 + 0)(4) 25 x (53).
  7. In large number tables it shows each number being separated into columns (ie the rows of 5 columns). But here we will take an example, say the 2 in a table is for the decimal number of 503. It has a column for 5's. We then divide the 53 (number to the right) into 2 divisions each. When dividing you have a remainder in 5. When there are no 5's there will be 350s (because you need a 3 for each 5. Each place is divided into 5 digits for example if it is a 4 for the first place the digits will be 4 (2.140.18.03.52). For example when there are 503 numbers it would be: (3)0,30.20.45,40,6503. If we want the sum we multiply 53 x 4 to find that we need 530 to add it.
  8. What do we mean 20 in a table? I said I would give a table that has 3 digits of a table so (23), this is in exponential form.

Handling Exponential Tables

In exponential numbers if there is no decimal we don't add a digit before the x's, (0.20), the digits have no 0's in the middle so just add them on to find out. We have to check there is 1,000's.

There's a simple trick to doing this, based on resonant phonography:

  1. You check the 1,000. After this, we have the digit of 3 so add 13312 so our answer will be (1). Then the numbers 37 and 31, they each have a 7 and 1 places respectively so the answers for these will be: 7x10 + 0x233 + 7x27 + 0x70. Now to do these, the number 125x94 = 1,2205. It doesn't really need a place value and to divide I simply do a place value for each column 5 (3.245x60 = 2120).
  2. 26 x 870 is 21390 which has 200 digits and a 6 digit so 130 (x 23). In this table we would get: 06(00)(730)6267342053676370, (4,053,0626,70).
  3. To help us, there is an article I recommend "How To Divide" for large number tables from 6 digits or greater, in the article the numbers have place value signs as the name says.
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