Tools of the Trade Calculators Scientific Notation Significant

Tools of the Trade Calculators, Scientific Notation, Significant Figures

Scientific Notation • Shorthand for writing LARGE or SMALL numbers • To write a number in scientific notation: – Use POWERS OF 10 – Move the decimal point • Each place to the left INCREASE power of 10 • Each place to the right DECREASE power of 10

Scientific Notation Examples – express in scientific notation 2. 137423 x 104 21374. 23 3. 4567 x 102 345. 67 4. 562 x 10 -3 0. 004562 5. 93 x 10 -6 0. 00000593

Calculator • Must have a calculator EVERY day – Do NOT need a graphing calculator – Need trigonometric functions • Good things to know about calculators… – Different calculators use different rules! – Force correct order using PARENTHESES – Use EXPONENTIAL notation

Exponential Notation 3, 000 Can be entered into the calculator as: 3 x 10 ^ 6 3 E 6 BETTER METHOD The calculator treats this as a SINGLE number – no PARENTHESES needed!!!

Exponential Notation Example a = 7 x 102 b = 3. 5 x 10 -4 What is the product of a and b? Using exponential notation, you can say: 7 E 2 x 3. 5 E-4 without parentheses!

Significant Figures Ignore all LEADING zero’s Decimal point? YES Count ALL remaining digits as significant NO Count remaining digits (except trailing zero’s) as significant

Significant Figures Examples 003456000 4 045. 6000 6 00. 000035 2 2340000 3 0. 0400 3

Adding with Significant Figures • Line numbers up • Circle the LAST SIGNIFICANT DIGIT in each • Result only goes as far as the LEFT MOST circle 100. 2546 + 57. 34 157. 5946 9. 45670 + 3. 23256 12. 68926 157. 59 144000 + 34642 178642 0. 00067 + 0. 1340 0. 13467 179000 0. 1347

Multiplying with Significant Figures • Result has the same number of significant figures as the measurement with the LEAST significant figures. 2 4 4456. x 45. 5 56000. x 122. 0567 7 200520 200000 6835175. 2 6835200 2 3 4. 09 x 4. 0 3 1 0. 002 x 256. 16. 36 16. 0. 512 0. 5