Significant Figures and Scientific notation Chapter 2 review Significant Figures and Scientific notation

Scientific notation (SN) Rules for SN Nx10n N-any number between 1-9.9 n- how many places decimal point moves big # are positive small #are negative

Examples Starting with the decimal move it over six places Starting with the last zero move the decimal over eight places 0.0000082 = 8.2 x 10-6 Starting with the decimal move it over six places

Rules for counting significant Figures 1-9 always SF 0 in front NEVER SF 0 in middle ALWAYS SF 0 at end SF if decimal exists 0 at the end without decimal are “ambiguous” not SF 0.0035 100.155 2 SF are present b/c 0 in front do not count 6 SF are present 0 in middle are SF

Rule Number one examples Numbers 1-9 are always significant figures 1,756 = 4 significant figures 3,987.954 = 8 significant figures 2,999,675,843 = 10 significant figures Always

Rule number two examples Zero’s in front are never significant figures 0.00032 = 2 significant figures 0.00374 = 3 significant figures 0.0008 = 1 significant figure Never

Rule number three examples Zero’s in the middle are always significant figures 3045 = 4 significant figures 40098 = 5 significant figures 403 = 3 significant figures Always

Rule number four examples Zero’s at the end are always a significant figure if there is a decimal point 230.000 = 6 significant figures 4.00 = 3 significant figures 38.00 = 4 significant figures Always

Rule number five examples Zero at the end is ambiguous and is not a significant figure 23000 = 2 significant figures 200 = 1 significant figure 13400 = 3 significant figures Never

Adding/subtracting Significant figures Keep as many SF as the least precise number Add/subtract all the numbers according to rules of SF Ex. 12.439 + 9.375 15.7 37.514 12,000 - 34.56 1250.000 Least precise Least precise 13,284.56 1.3x104 37.5 or 3.75x101

Multiply/divide significant figures Keep the lowest number of SF Ex. (125)(0.23)=28.75 29 (least number of SF) 0.4248 =0.0075053 56.6 2 sf 3 SF 7.18x10 -3

Rounding If the number you are rounding is followed by 5,6,7,8,9 then round the number up If the number you are rounding is followed by 0,1,2,3,4 then leave it Ex. 2,158,346 in scientific notation to three SF 2.16 x 106 (round up because of the 8 after the 5) Ex.100.015 round to 3 SF 100. (round to 100. because of the 0 after decimal)

Exact numbers Exact numbers are those that have defined values or are integers that result from counting numbers of objects. Exact numbers have infinite number of SF Example: one dozen eggs is exactly 12 eggs 1000 grams is exactly 1 kilogram 2.54 centimeters is exactly 1 inch

Inexact numbers Inexact numbers are approximate numbers or numbers obtained from measurements. Example: One mile is 1.6093 kilometers One ounce is 28.35 grams One kilogram is 2.2046 pounds