WHAT WE HAVE LEARNED

SCIENTIFIC NOTATION

1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive. To write a number in scientific notation:

MULTIPLICATION When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x ) (2.1 x 10 5 ) Solution: Multiply 3.2 x 2.1. Add the exponents Answer: 6.7 x 10 2

DIVISION Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 10 6 ) by (1.7 x 10 2 ) Solution: Divide 6.4 by 1.7. Subtract the exponents Answer: 3.8 x 10 4

ADDITION AND SUBTRACTION To add or subtract numbers written in scientific notation, you must….express them with the same power of ten. Sample Problem: Add (5.8 x 10 3 ) and (2.16 x 10 4 ) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 10 3 =.58 x 10 4 so.58 x x 10 4 =? Answer: 2.74 x 10 4

DIMENSIONAL ANALYSIS

STEPS TO PROBLEM SOLVING Read problem Identify data Make a unit plan from the initial unit to the desired unit (good practice at beginning, not necessary as you get comfortable with this) Select conversion factors Change initial unit to desired unit Cancel units and check Do math on calculator Give an answer using significant figures

SIGNIFICANT FIGURES

WHAT IS A SIGNIFICANT FIGURE?  There are 2 kinds of numbers:  Exact: the amount of money in your account. Known with certainty.  Approximate: weight, height—anything MEASURED. No measurement is perfect.

CERTAIN AND ESTIMATED DIGITS  Always be some margin of error.  Usually the last digit in a number.  Comes from measurements falling between two known marks  EX: 324 g 324. pg  mL0.001 cm

HOW DO I KNOW HOW MANY SIG FIGS?  Rule: All digits are significant starting with the first non-zero digit on the left.

SIGNIFICANT FIGURES  Indicate precision of a measurement.  Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit  Counting Sig Figs  Count all numbers EXCEPT:  Leading zeros  Trailing zeros without a decimal point -- 2,500

SIGNIFICANT FIGURES  Calculating with Sig Figs  Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.  Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

SCIENTIFIC NOTATION  Converting into Sci. Notation:  Move decimal until there’s 1 digit to its left.  Places moved = exponent.  Large # (>1)  positive exponent Small # (<1)  negative exponent  Only include sig figs. 65,000 kg  6.5 × 10 4 kg

CONVERSIONS mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 BASE UNIT

FINISHER….  Change a speed of 72.4 miles per hour to meters per second.  Make sure to convert ALL units  Use correct number of sig figs.  The density of mercury is 13.6 g/mL. What is the mass in kilograms of a 2 L commercial flask of mercury?  Using correct number of sig figs.  27.2 kg