Mastering Significant Figures in Logarithms: A Comprehensive Guide

[mathzeroh]

significant figures help needed badly!

hows everyone doing in this fine evening?

ok i just had some questions on "sig figs" as the pros call it (unfortunately that's not me ) ok, i'll try to explain as clearly as i can here:

in this manual i have that explains sig figs, it says the following about Siginificant Figures in Logarithms:

...The characteristic consists of the digits to the lft of the decimal point and the mantissa consists of the digits to the right of the decimal point. the mantissa of a log should have the same number of sig. figs. as does the original number. Some esamples are:

log 2=0.3 (1sig fig in 2)
log 2.0=0.30 (2 sig figs in 2.0)
log 2.00=0.300 (3 sig figs in 2.00)
log 2.0 X 10^4=4.30 (2 sig figs in 2.0)
log 2.00 X 10^(-5)=-4.699 (3 sig figs in 2.00)



now my questions concern the red bold faced part of the above examples. if it says that there's "3 sig figs in 2.00" then why does it report a four sig fig carrying number -4.699??

it said that the same rule was applied to antilogs, but again, same problem a little further down in the examples:

... antilog 3.4771 = 3.000 X 10^3 (4 sig figs in the mantissa)

uh yea i see that but so what?? isn't it supposed to have FIVE sig figs because of the "characteristic"??


also, can somebody please tell me if i did these correctly:

Round to four sig figs:

273.15 -> 273.2 *(bcuz the "1" is an odd number, you would round up to the nearest even number, right? and if it was already an even number followed by a 5 and nothing else following the 5, you would leave it alone as a "1" and just drop the five, right??
12.652 -> 12.65
19.9743 -> 19.97
4.32156 -> 4.322
0.019807 -> 0.01981



Thanks!

 

[learningphysics]

hows everyone doing in this fine evening?

ok i just had some questions on "sig figs" as the pros call it (unfortunately that's not me ) ok, i'll try to explain as clearly as i can here:

in this manual i have that explains sig figs, it says the following about Siginificant Figures in Logarithms:

...The characteristic consists of the digits to the lft of the decimal point and the mantissa consists of the digits to the right of the decimal point. the mantissa of a log should have the same number of sig. figs. as does the original number. Some esamples are:

log 2=0.3 (1sig fig in 2)
log 2.0=0.30 (2 sig figs in 2.0)
log 2.00=0.300 (3 sig figs in 2.00)
log 2.0 X 10^4=4.30 (2 sig figs in 2.0)
log 52.00 X 10^(-5)=-4.699 (3 sig figs in 2.00)



now my questions concern the red bold faced part of the above examples. if it says that there's "3 sig figs in 2.00" then why does it report a four sig fig carrying number -4.699??

The mantissa (digits after the decimal) should have the same number of digits: 699 is 3 digits.

it said that the same rule was applied to antilogs, but again, same problem a little further down in the examples:

... antilog 3.4771 = 3.000 X 10^3 (4 sig figs in the mantissa)

uh yea i see that but so what?? isn't it supposed to have FIVE sig figs because of the "characteristic"??

According to the rule at the top of your posted it is supposed to have 4 digits because the mantissa has 4 digits (you shouldn't be taking the number of digits of the characteristic)

also, can somebody please tell me if i did these correctly:

Round to four sig figs:

273.15 -> 273.2 *(bcuz the "1" is an odd number, you would round up to the nearest even number, right? and if it was already an even number followed by a 5 and nothing else following the 5, you would leave it alone as a "1" and just drop the five, right??
12.652 -> 12.65
19.9743 -> 19.97
4.32156 -> 4.322
0.019807 -> 0.01981

The above look good to me.

Thanks![/QUOTE]

 

[mathzeroh]

OH, so ur not supposed to count the number to the left of the decimal point, only the number to the right are considered part of the mantissa, the quantity of which is determined by the amount of sig. figs. in the characteristic? right? :)

 

[learningphysics]

OH, so ur not supposed to count the number to the left of the decimal point, only the number to the right are considered part of the mantissa,

Yes.

the quantity of which is determined by the amount of sig. figs. in the characteristic? right? :)

I don't understand what you mean here.