Makars Problem Solving Essentials & Sig Digs (2016)

What does the term significant digit mean? SIGNIFICANT means important, and DIGIT means numbers. The number of significant digits depends on: the precision of your measurement tool and how accurately it is used the precision of the measurement and the math involved. There is a difference between 10g and 10.0g; 10.0g is much more accurate. Rules for Determining Significant Digits Rules Examples The following are ALWAYS SIGNIFICANT All Non-zero Numbers/Integers All Zeros to the Right of Numbers/Integers (trailing zeros) All Zeros Between Numbers/Integers All values in a Scientific Notation before the ×10# 123456 has 6 sig digs 10000.00 has 7 sig digs 123000045 has 9 sig digs 4.560×104 has 4 sig digs The following are NEVER SIGNIFICANT All Zeros to the left of the decimal in numbers less than 1 (leading zeros) All Zeros to the right of the decimal but to the left of the first integer (again, leading zeros) 0.56789 has 5 sig digs 0.0001234 has 4 sig digs The following are EXCEPTIONS that are NEVER SIGNIFICANT Exact conversion factors have infinite sig digs Counted Numbers have infinite sig digs 100cm/1m = infinite 12 eggs = infinite Rules for Determining Significant Digits when Applying Mathematics Rules Examples Addition and Subtraction All answers are rounded to the fewest number of decimal places in any of the numbers involved in the operation. 1.05+2.6 = 3.7 6.50-3.258 = 3.24 Multiplication, Division, and Combinations with Add./Sub. All answers are rounded to the fewest number of sig digs found in any of the numbers involved in the operation. 10.00÷2.5 = 7.5 2.2×50.00 = 1.1×102 (6.5+10.5)×1.50 = 26 Makar’s Problem Solving Essentials (Every time you are asked to solve a mathematical science problem that involves the use of an equation, you may be asked to include all (or perhaps, most) of the steps described below) Givens: Make sure you write down all of the variable/ information/data given to you in the problem. Don’t forget to include all correct units, sig digs, signs(+/-), directions [ ] Equation: Write down the equation or manipulated equations needed to solve the problem. Make sure that the equations are manipulated so the term/variable you are solving for is located on the left side of the equation. Ensure that you have used the correct symbols to represent the variables in the equation. Add variables to this list as they are introduced. eg. time = t or distance = d or displacement = speed = v or ?v velocity = or acceleration = Substitution: Substitute your known/given values into your equation. Don’t forget to include all correct units, sig digs, signs(+/-), directions [ ] Solution: Solve the equation. Don’t forget to include all correct units, sig digs, signs(+/-), directions [ ] Paraphrase: Write a proper sentence/paraphrase that answers the problem. Don’t forget to include all correct units, sig digs, signs(+/-), directions [ ]