2 How many jumps does it take? Ladder Method123KILO 1000 UnitsHECTO 100 UnitsDEKA 10 UnitsDECI 0.1 UnitMeters Liters GramsCENTI 0.01 UnitMILLI UnitHow do you use the “ladder” method?1st – Determine your starting point.2nd – Count the “jumps” to your ending point.3rd – Move the decimal the same number of jumps in the same direction.4 km = _________ mStarting PointEnding PointHow many jumps does it take?4.1__.2__.3__.= 4000 m
3 Conversion Practice Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm14 km = _______ m 109 g = _______ kg 250 m = _______ kmCompare using <, >, or =.56 cm m 7 g mg
5 Scientific Notation Essential Questions How do I write numbers in scientific notation?How do I calculate with scientific notation?When would I use scientific notation?
6 The table shows relationships between several powers of 10. Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left.Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.
7 You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.
8 Additional Example 1: Multiplying by Powers of Ten Since the exponent is a positive 4, move the decimal point 4 places to the right.140,000B. 3.6 10-5Since the exponent is a negative 5, move the decimal point 5 places to the left.
9 Powers of 10 are used when writing numbers in scientific notation Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.
10 Additional Example 2: Writing Numbers in Scientific Notation Write the number in scientific notation.AThink: The decimal needs to move 3 places to get a number between 1 and 10.7.09 10-3Think: The number is less than 1, so the exponent will be negative.So written in scientific notation is 7.09 10–3.
11 Additional Example 2: Writing Numbers in Scientific Notation Write the number in scientific notation.B. 23,000,000,000Think: The decimal needs to move 10 places to get a number between 1 and 10.2.3 1010Think: The number is greater than 1, so the exponent will be positive.So 23,000,000,000 written in scientific notation is 2.3 1010.
12 Significant Figures (sig. figs) Rules: All non-zero #’s are significant Some zeros are significant; others are place holders
13 Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12A piece of paper is measured 11 inches tall.Being able to locate, and count significant figures is an important skill.
14 Atlantic-Pacific Rule Ask yourself: self, is there a decimal?PACIFIC ATLANTIC(Present) (Absent)Start from LEFT Start from RIGHT& count all #’s from & count all #’s fromfirst nonzero first nonzero
15 Practice Makes Perfect! How many sig figs?PRESENTStart from LEFT and count all #’s from first nonzero4.0010.0203100.ABSENTStart from RIGHT and count all #’s from first nonzero4001503000100443331
16 Sig. Figs in Scientific Notation All #’s (excluding x 10xx) ARE significantHow many sig. figs?:3.2 x 1033.20 x 103Put in scientific notation w/ sig. figs
17 Sig. Fig. Calculations Multiplication/Division Rules: The measurement w/ the smallest # of sig. figs determines the # of sig. figs in answerLet’s Practice!!!6.221cm x 5.2cm = cm24 2How many sig figs in final answer???And the answer is… cm2
18 Rounding ruleslook at the number behind the one you’re rounding. If it is 0 to 4 don’t change it If it is 5 to 9 make it one bigger round to four sig figs to three sig figs to two sig figs to one sig fig