Μπακάλικα μαθηματικά
Δημοσιεύτηκε: Τρί Φεβ 06, 2007 4:06 pm
Βρηκα σ ενα site ενα τυπο ο οποιος ειχε βρει διαφοροθσ τροποθσ να υπολογιζει με το μυαλο αλγοριθμους,ριζες,τετραγωνα(για μεγαλα νουμερα μιλαμε!).Πραθετο ενα απο ολα που εχει γραψει,για τους αλγοριθμους:
1. When someone gives you any positive number, you should immediately 'write' that number in scientific notation in your head.
2. Next, focus only on the exponent of the number (written in scientific notation). This number will be the basis of you answer.
3. Estimate the logarithm of the abscissa in your head (thats the number between 1 and 9.999999..., not part of the exponent). Note: you'll need to memorize the table below (its not that hard).
4. Add the logarithm of the abscissa to the exponent you found in step 2.
What follows are the values for the logs you'll need to have memorized for step 3...
log[1]= 0
log[2]= .30
log[3]= .48
log[4]= .60
log[5]= .70
log[6]= .78
log[7]= .85
log[8]= .90
log[9]= .95
As an example, lets find the logarithm of 29,012. Written in scientific notation, that would be 2.9012 X 10^4. So, the exponent is 4. Now, we need to concentrate on the abscissa (2.9012 is very very close to 3). From our table above (which we have memorized for the trick), the logarithm of 3 is 0.48. So, we add the exponent (4), to the log of the abscissa (0.48), to get a value of 4.48. A calculator reveals how good this method is (4.46 out to two decimal places).
This method works because scientific notation is a base 10 system for writing out numbers. With some practice, you'll get a feel for how to massage your guesses for numbers that aren't exactly in the table (for instance: 2.5).
1. When someone gives you any positive number, you should immediately 'write' that number in scientific notation in your head.
2. Next, focus only on the exponent of the number (written in scientific notation). This number will be the basis of you answer.
3. Estimate the logarithm of the abscissa in your head (thats the number between 1 and 9.999999..., not part of the exponent). Note: you'll need to memorize the table below (its not that hard).
4. Add the logarithm of the abscissa to the exponent you found in step 2.
What follows are the values for the logs you'll need to have memorized for step 3...
log[1]= 0
log[2]= .30
log[3]= .48
log[4]= .60
log[5]= .70
log[6]= .78
log[7]= .85
log[8]= .90
log[9]= .95
As an example, lets find the logarithm of 29,012. Written in scientific notation, that would be 2.9012 X 10^4. So, the exponent is 4. Now, we need to concentrate on the abscissa (2.9012 is very very close to 3). From our table above (which we have memorized for the trick), the logarithm of 3 is 0.48. So, we add the exponent (4), to the log of the abscissa (0.48), to get a value of 4.48. A calculator reveals how good this method is (4.46 out to two decimal places).
This method works because scientific notation is a base 10 system for writing out numbers. With some practice, you'll get a feel for how to massage your guesses for numbers that aren't exactly in the table (for instance: 2.5).
