Scientific Notation Chemistry Honors
Used to easily write very large or very small numbers: 1 mole of a substance consists of 602,000,000,000,000,000,000,000 particles (we ll come back to this in Chapter 11) Rather than writing 21 zeroes, we write 6.02 10 23 The mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 910 9 kg 9.109 10 31 kg Consists of two parts: coefficient A 10 n exponent Coefficient must be 1 A <10 (one non-zero digit to left of decimal point) and can be negative Exponent indicates the magnitude of the absolute value of the original number and is positive if the number >1 (large) and negative if it is <1 (small)
Converting to Scientific Notation Large Numbers (>1) will have positive exponents Move the decimal point n spaces to the left so the coefficient has only one digit to the left Since number (coefficient) decreased, exponent is positive: exponent = n e.g. 56,100 kg Scientific Notation: 5.61 10 4 kg Note that units come after the exponent Negative numbers have negative coefficients Can convert non-scientific notation numbers with exponents Moving dec. pt. to left decreases coefficient, so exponent must increase by m: 289 10 4 m move dec. pt. 4 spaces left; n = 4 move dec. pt. 2 spaces left; increase n by 2 Scientific Notation: 2.89 10 6 m
Small Numbers (<1) will have negative exponents Move the decimal point n spaces to the right so the coefficient has only one digit to the left Since number (coefficient) increased, exponent is negative: exponent = n e.g. 0.000 032 1 s Scientific Notation: 3.21 10 5 s move dec. pt. 5 spaces right; n = 5
Converting to Decimal Notation Positive Exponents are large numbers (>1) Move the decimal point to the right by the number of spaces equal to n to make the coefficient larger Pad to the new decimal location with zeroes e.g. 9.83 10 6 g Decimal notation: 9,830,000 g Negative exponents are small numbers (<1) move the decimal point to the left by the number of spaces equal to n to make the coefficient smaller Fill back with zeroes to the new decimal point e.g. 5.727 10 4 m Decimal notation: 0.0005727 m n = 6; move dec. pt. 6 spaces right n = 4; move dec. pt. 4 spaces left note the number of zeroes is one less than n
Calculation For addition and subtraction, exponent and units must match: e.g. What is 5.68 10 3 km +2.8 10 2 km? Change 2.8 10 2 km 0.28 10 3 km first (exponent 1 so coefficient 1) 5.68 10 3 km + 0.28 10 3 km = 5.96 10 3 km For multiplication & division, operate on coefficient, exponent, units separately, convert to valid scientific notation if needed Remember, multiplying adds exponents, dividing subtracts e.g. what is 60 10 3 cm 4 10 2 cm? 240 10 5 cm 2 = 2.4 10 7 cm 2 (coefficient 2 so exponent 2)
Sci. Not. on a Calculator We use the special EE ( 2nd, ) exponent key to enter scientific notation Instead of entering 1 10^2, we will enter 1 EE 2 Only press EE once a single E will appear in the display EE replaces 10^ do NOT enter any part of it Avoids order of operation errors Parentheses will work, but the EE key is more efficient Still need to group calculations in denominator in parentheses Use the ( ) key to change exponent to When reading & writing your calculator answer, convert E back to 10 with the correct exponent.
Entering/Exiting Sci. Not. Mode You generally will not be required to be in scientific notation mode To set your calculator to scientific notation: Press MODE Select Sci ; press ENTER Press QUIT ( 2nd MODE ) to exit. To return to decimal mode Press MODE Select Normal & press ENTER Press QUIT ( 2nd MODE ) to exit.