Significant Digits & Rounding

RULES FOR DETERMINING SD 1) NON ZERO NUMBERS ARE ALWAYS SIGNIFICANT. 2) A ZERO BETWEEN TWO NUMBERS IS SIGNIFICANT. 3) ZEROS USED TO SPACE THE DECIMAL POINT ARE NOT SIGNIFICANT. 4) ANY ZEROS AFTER THE DECIMAL POINT AND AFTER A NUMBER ARE SIGNIFICANT.

EXAMPLES OF RULES NON ZERO NUMBERS 234 = 3 SD 1987 = 4 SD 12 = 2 SD

2) ZEROS BETWEEN 204 = 3 SD 1907 = 4 SD 101.0101 = 7 SD EXAMPLES OF RULES 2) ZEROS BETWEEN 204 = 3 SD 1907 = 4 SD 101.0101 = 7 SD

EXAMPLES OF RULES 3) SPACING THE DECIMAL POINT 2340 = 3 SD 198700 = 4 SD 0.0012 = 2 SD

4) AFTER THE DECIMAL POINT 0.002340 = 4 SD .001907 = 4 SD EXAMPLES OF RULES 4) AFTER THE DECIMAL POINT (BOTH CONDITIONS MUST BE TRUE) 0.002340 = 4 SD .001907 = 4 SD .0001020= 4 SD

WORKSHEET 1) 208 =3 2) 1876 =4 3) 2.00 =3 4) 420 =2 5) 14227 =5 6) 2000 =1 7) 123.55 =5 8) 28.90 =4 9) 0.00509 =3

WORKSHEET 10) 60558 = 5 11) 1800 =2 12) 4.8217 = 5 13) 192003 = 6 14) 0.01360 = 4 15) 1,000,000.0 =8 16) 3044.04 = 6 17) 1.0969 =5 18) 25020 = 4

WORKSHEET CONTINUED 19) 0.0000001 = 1 20) 259.95 = 5 21) 7.50 = 3 22) 0.0193= 3 23) 1607 =4 24) 1611.0 = 5 25) 6.010 = 4

ROUNDING OFF TO 3 SD MAKE SURE YOUR ANSWER HAS 3 SD THEN LOOK AT THE 4TH DIGIT TO DETERMINE IF YOU ROUND UP OR LEAVE IT ALONE

The answer should have 3 digits 123 ROUNDING EXAMPLES 123.567 The answer should have 3 digits 123 Look at the 5 and then round up to 124

ROUNDING EXAMPLES 1,437 USE THE COMMA TO KEEP THE DECIMAL POINT IN THE PROPER PLACE. THE 7 ROUNDS UP THE 3 TO A 4. USE A ZERO TO PLACE THE DECIMAL POINT. 1,440

ROUNDING EXAMPLES 0.004563 THE ZEROS IN FRONT ARE NOT SD BUT THEY ARE USED TO SPACE THE DECIMAL POINT. 0.00456

1)    1.00794 2)    6.941 3)    9.0121821 4)    10.811 5)    12.011 6)    14.00674 7)    15.9994 8)    18.998 9)    20.1797 10) 22.989768

11) 0.0040078 12) 0.000114818 13) 208.98037 14) 1,274 15) 21,643 16) 157,678 17) 1,456.852 18) 145.78 19) 114.865 20) 132.905453

WORKSHEET ROUNDING 1) 1.01 9) 20.2 2) 6.94 10) 23.0 1) 1.01 9) 20.2 2) 6.94 10) 23.0 3) 9.01 11) 0.00401 4) 10.8 12) 0.000115 5) 12.0 13) 209 6) 14.0 14) 1,270 7) 16.0 15) 21,600 8) 19.0 16) 158,000

ROUNDING WORKSHEET CONT. 17) 1,460 18) 146 19) 115 20) 133

HOMEWORK Choose 10 from the top determine the number of SD. Choose 10 from the bottom Round off to 3SD

SD HOMEWORK 1) 33.40=4 2) 405=3 3) 0.678=3 4) 6.104=4 5) 501.0=4 6) 23500=3 7) 0.069080=5

SD HOMEWORK 8) 0.0897=3 9) 237.80=5 10) 0.4090=4 11) 0.70320=5 12) 860=2 13) 937,000=3 14) 0.29070=5 15) 41030=4

SD HOMEWORK 16) 0.0939=3 17) 569,300=4 18) 0.008030=4 19) 0.740070=6 20) 302900=4

ROUNDING HOMWEORK 1) 121.842= 122 2) 112.417= 112 3) 35.589= 35.6 4) 50.917= 50.9 5) 0.22374= 0.224 6) 204.812= 205

ROUNDING HOMWEORK 7) 0.00001839= 0.0000184 8) 0.1148= 0.115 9) 101.42= 101 10) 20.742= 20.7 11) 0.23876= 0.239 12) 186,271= 186,000 13) 441,237= 441,000 14) 207.12= 207

ROUNDING HOMWEORK 15) 63.5846= 63.6 16) 0.006998= 0.00700 17) 107.981= 108 18) 0.0006354= 0.000635 19) 0.001279= 0.00128 20) 0.010294= 0.0103