Help stuck in Converting Fahrenheit of 135; to Celsius and Kelvin. Using Significant Figures!?

135°F = 57.2°C = 330.4K

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first.. let's cover sig figs

rules for what IS a sig fig and what IS NOT a sig fig

.. (1).. all non-zero digits are sig figs.. 1,2,3,4,5,6,7,8,9

.. (2).. zeros may or may not be significant,..

.. . .....(a) zeros between two non-zero digits are significant.. ex. 9091

.. . .. . (b) zeros to the right of a decimal point and right of any nonzero

. .. ... . .. .digit are significant.. . 1.900... .the zeros are sig figs

. .. .. ..(c) zeros to the right of a decimal point and left of all non-zero

.. .. .. . .. ..digits are NOT significant... . example.. 0.000012 has 2 sig figs

. .. .. . (d) zeros to the LEFT of the decimal point and RIGHT of the rightmost

.. .. .. .. . ..non-zero digit MAY be significant.. example "9200" has 2, 3, or 4

.. .. .. . . ..sig figs depending on whether 0, 1, or 2 of those zeros is a sig fig

.. .. .. . ... We indicate if those zeros are sig figs with 4 different ways

.. .. . . . . .(i) by drawing a line over the rightmost significant zero

.. .. .. .. .. . . ..912Ō000 has 4 sig figs... the 9, 1, and 2 + the left most zero

... .. ... .. .. .. 9120Ō00 has 5 sig figs... the leftmost 5 digits

.. .. .... .. . . ...91200Ō0 has 6 sig figs

... .. ... . .. ... .912000Ō has 7 sig figs

... . .. .. ..(ii) by adding a decimal point.. this indicates ALL those zeros are significant

.. .. ... .. . .. .. "9120." has 4 sig figs

.. ... ... ... .. .. "91200." has 5 sig figs... note the decimal point

.. .. .. .. .. . ...."912000." has 6 sig figs

.. ... ... ....(iii) by stating the number of sig figs...

.. .. . .. .. .. .. ..."91200 with 4 sig figs"... means only the leftmost zero is significant

.. .. .. .. . .(iv) by writing in scientific notation

.. .. .. . .. .. .. .. ."9.12x10^6".... has 3 sig figs

.. .. .. . .. .. .. .. ."9.120x10^6".... has 4 sig figs

.. .. .. . .. .. .. .. ."9.1200x10^6".... has 5 sig figs

.. .. .. . .. .. .. .. ."9.12000x10^6".... has 6 sig figs

.. (3) exact numbers have infinite sig figs for the purposes of calculations.

examples

.. 6.022x10^23... 4 sig figs.. . .rule 2(a) above

.. 8.314 J/molK.. .4 sig figs,.. . rule 1

.. 32.0 g/mol.. .. . 3 sig figs... . rule 2(b) above

.. 0.012g.. ..... .. ..2 sig figs.. .. rule 2(c) above

.. "520.".. . .. .. ...3 sig figs.. . .rule 2(d)(ii)

... 520 without the decimal point.. ambiguous.. assume the zeros are NOT sig figs

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math operations on sig figs.. there are 3 you need to know. 2 are common, 1 isn't but we'll cover it anyway.

math operation #1 : Multiplication / division

. .. in mult / div, the result is limited to the number of sig figs in the factor

.. . with the least number of sig figs

.... ... .example...

.. .. ... .. .8.314 x 96 x10^3 = 8.0 x10^5.. .. .. . 96 has 2 sig figs and limits the result to 2

.. .. ... .. .8.314 x 96.0 x10^3 = 7.98 x10^5... ..96.0 has 3 sig figs and limits the result to 3

.. .. ... .. .8.314 x 96.00 x10^3 = 7.981 x10^5.. 96.00 has 4 sig figs.

math operation #2:.. addition / subtraction

.. in addition and subtraction, the result is limited to the same "precision" as the addend

.. with the lowest precision.

.. ... example

.. .. ... .. 273.15.. the 273.15 is precise to the 0.01's column

..... . .. .+.25... .. .the 25 is precise to the 1's column

.. .. .. .------------

... .. .. . .298.... . ..the result is limited to the 1's column.... the 1's column is

.. ... ... .. .. .. .. . . .lower precision than the 0.01's column

and finally

math operations #3 : log functions

.. sig figs in log functions are treated differently, the number of sig figs in the

.. number you're logging = the number of sig figs right of the decimal point in the result

....example

.. . .. .log(10.595) = 1.02510.. . .. 10.595 has 5 sig figs... ".02510" has 5 sig figs

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your problem

the conversions are..

.. °C = (5/9) x (°F - 32)

.. K = °C + 273.15

and so

..(5/9) x (135 - 32) = (5/9) x (103) = 57.2.

.. .. . 5 and 9 and 32 are exact

.. .. . 135 is precise to the 1's column, so the result is limited to the 1's column

.. .... .so that 135 - 32 = 103

.. . ....then 103 has 3 sig figs, 5 and 9 have infinite sig figs, so the result is

.. . . ..limited to 3 sig figs

then converting to K

.. K = °C + 273.15 = 57.2 + 273.15 = 330.4 K

.. . .. ...the 57.2 is precise to the 0.1's column

.. . .. ...the 273.15 is precise to the 0.1's column, so the result is limited to the 0.1's column

135 degres farenheit is (135-32) 103 degrees above freezing.

degrees C = 103*(100/180) = 57

degrees K = degrees C + 273 = 330