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shutvik [7]
3 years ago
8

Hi I am Khine Mye and I want to ask you a question I don't know that is square root of 2 is 1.4 and how to get that 1.4 and plz

explain me step by step​
Computers and Technology
1 answer:
MrRissso [65]3 years ago
3 0

Divide the radicand into groups of two, starting

from the decimal point and going in either

direction. For rational radicands, add pairs of

zeroes to the right of the decimal point as

needed. If the number is irrational, you already

have an infinite sequence of pairs. Now that the

radicand is marked off in pairs, forget the

decimal point (except in the answer). Call each

new digit of the approximation D, and the

current best approximation of the square root R.

Find the largest integer whose square is less

than or equal to the leftmost group. Since

groups are at most two digits long, the integer

is one digit long: in this case, the leftmost group

is 2, so we begin with D = 1, R = 1.

2 -1 = 1, append the next pair of digits, giving

100.

Find the largest digit D such that D*(20*1+D) is

less than or equal to 100.

(HINT: estimate D by dividing 20*1 into 100 -

this approach might overestimate.)

The result is 4*(20*1+4) = 4*24 = 96, so D = 4, R

= 1.4.

100 - 96 = 4, append next pair of digits, result is

400.

400/(20*14) = 1 + fraction, 1*(20*14+1) =

%3D

1*281, so D = 1, R = 1.41.

400 - 281 = 119, appending next pair yields

11900.

11900/(20*141)

= 4 + fraction, 4*(20*141+4) =

4*2824 = 11296, so D = 4, R = 1.414, etc. etc.

What justifies this?

Suppose we know R, the best N-digit

approximation from this algorithm. Then the

next approximation will be 10*R + D, and D must

be the largest digit that satisfies

10R + D)? = (100R? + 20RD + D² )

(= 100R? + D(20R+ D) < radicand

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Answer:

import re

#section 1

while True:

   try:

       major=input('Enter Major: ')

       if re.search(r'^\d{1,4}$',major):

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       else:

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       try:

           if re.search(r'^\d{1,4}$',minor):

               sub1=input('Enter sub1: ')

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           try:

               if re.search(r'^\d{1,4}$',sub1):

                   sub2=input('Enter sub2: ')

               else:

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               try:

                   if re.search(r'^\d{1,4}$',sub2):

                       break

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               except:

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           except:

               print('enter a correct sub1')        

       except:

           print('Enter a correct minor ')            

   except:

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#section 2

sub1= f"{int(sub1):04d}"

sub2= f"{int(sub2):04d}"

major= f"{int(major):04d}"

minor= f"{int(minor):04d}"

if major == '0000' and minor == '0000' and sub1=='0000' and sub2=='0000':

   print('INVALID!!! Acount Number')

else:

   print('-----------------------')

   print('Your Account Number is')

   print(major, minor, sub1, sub2)

   print('-----------------------')

Explanation:

The programming language used is python 3

The Regular  Expression Module was imported to allow us perform special operations on string variables.

This is the pattern that was used to check if an input was valid or invalid re.search(r'^\d{1,4}$',string)

what this pattern does is that it ensures that:

  1. (\d) represents digits that is any number from 0-9.
  2. ( ^ ) ensures that it starts with a digit.
  3. ({1,4}) accepts digits with length ranging from 1-4. i.e you can enter at least one digit and at most four digits.
  4. ($) ensures that the input ends with a digit
  5. string is the text that is passed to the pattern

we also made use of fstrings

sub1= f"{int(sub1):04d}"

the above line of code takes 'sub1' in this case, and converts it temporarily to an integer and ensures it has a length of 4 by adding 0's in front of it to convert it to a four digit number.

These are the major though areas, but i'll explain the sections too.

#section 1

In this section the WHILE loop is used in conjunction with the TRY and EXCEPT block and the IF statement to ensure that the correct input is given.

The while loop will keep looping until the correct input is inserted  before it breaks and each input is tested in the try and except block using the if statement and the regular expression pattern I explained, as a result, you cannot input a letter, a blank space, a punctuation or numbers with length greater than 4, it has to be numbers within the range of 1-4.

#section 2

The second section converts each entry to a four digit number and checks with an if statement if the entry is all zeros (0000 0000 0000 0000) and prints invalid.

Otherwise, it prints the account number.

check the attachment to see how the script runs.

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