Presentation on theme: "Please turn in your Home-learning, get your notebook and Springboard book, and begin the bell-ringer! Test on Activity 6, 7 and 8 Wednesday (A day) and."— Presentation transcript:
1Please turn in your Home-learning, get your notebook and Springboard book, and begin the bell-ringer! Test on Activity 6, 7 and 8 Wednesday (A day) and Thursday (B day).
2Bell-Ringer # /30/14Write the following in either standard form or scientific notation.3.71 x 100Simplify the following. Write your answer in both scientific notation and standard form.x 105 – 3.26 x 105
3Properties of Exponents and Scientific Notation 10/30/14
4Different forms: Exponential Form: 45 x 43 or 5 9 5 6 Expanded Form: 45 x 43 = (4x4x4x4x4)(4x4x4)= 5∗5∗5∗5∗5∗5∗5∗5∗5 5∗5∗5∗5∗5∗5Standard Form:45 x 43 = 65,536= 625
5Multiplying with Exponents RULE: When multiplying two exponential expressions with the same base, you ADD the exponents.Example: 59 x 53 = 59+3 =512The bases are the same (5), therefore you add the two exponents (9+3).
6Dividing with Exponents RULE: When dividing two exponential expressions with the same base, you SUBTRACT the exponents.Example: = 38-6 = 32The bases are the same (3), therefore, you can subtract the exponents (8-6).
7Negative ExponentsWhen DIVIDING two exponential expressions that will result in an expression with a negative exponent, you have two options:Divide by subtracting the exponents.43 48 =43_8=4_52. Write the numerator and denominator in expanded form and simplify.= 4∗4∗4 4∗4∗4∗4∗4∗4∗4∗4 =4_5=HINT: You must know your rules for operations with integers in order to be able to successfully solve problems with negative exponents!
8Exponent of 0 and 1Anything raised to the power of zero (0) is always one (1).70 = 1Anything raised to the power of one (1) is always itself.71 = 7
9Powers of PowersWhen an exponential expression is raised to a power, you multiply the two exponents.(88)6 = 88x6 =848(1011)2 =1011x2 =1022
10Rules for Operations with Integers Examples(-9) + (-4) =(-7) + 4 =8 – 11 =15 – (-7) =(-5) x (-9) =(-90) ÷ 3=Addition (when the signs are the same)Keep the SignAddAddition (when the signs are different)Keep the sign of the number with the greater absolute value.Subtract the bigger number from the smaller number.Subtraction (Think L-C-O…Leave, Change, Opposite)Change the subtraction sign to addition sign.Change the sign of the second number.Follow Addition Rules.Multiplication/DivisionPositive & Positive = PositiveNegative & Negative = PositivePositive & Negative = NegativeNegative & Positive = Negative
11Scientific NotationScientific Notation: a way to write a number as a product of the number, a, and 10n, when 1≤ a <10 (a needs to be at least equal to 1 but less than 10) and n is an integer.a x 10n x 106Standard Form: a way to write a number using a digit for each place.591,157.21
12Convert from Scientific Notation to Standard Form: 5.12 x 106Step 1: Simplify 106106 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000Step 2: Multiply by 5.125.12 x 1,000,000 = 5,120,000Hint: The exponent tells you how many spaces to move the decimal. When converting from scientific notation to standard form and the exponent is positive, you move the decimal to the RIGHT and fill spaces with zeroes.
13Convert from Standard Form to Scientific Notation: 860,000Step 1: Identify the location of the decimal point in ,000. In all whole numbers, the decimal point is at the end (all the way to the right) of a number.860, Decimal PointStep 2: Move the decimal point to the left until you have a number that is greater than or equal to 1 and less than Count the number of places you moved the decimal point.860,000. the decimal is moved 5 placesStep 3: Rewrite the number in scientific notation. The number of places you moved the decimal is the exponent for the base of 10.8.6 x 105Remember: Scientific Notation requires that the value for “a” be at least 1 and less than 10.
14Scientific Notation: Power of Zero, Negative Exponents, and Ordering 4.5 x 100 = 4.5 x 1 = 4.5Negative ExponentsStandard form to Scientific notation: = 6.51 x 10-6Count the number of paces the decimal is moved to the right to make the number between 1 and 10, the number of places moved to the right is written as the exponent for 10 and should be negative.Scientific Notation to Standard form: 8.75 x 10-7 =Move the decimal to the left according to the number in the exponent.OrderingUse the values of the exponents to help determine the order. The smaller the exponent, the smaller the value. The greater the exponent, the greater the value.Write the number in standard form to check the order.Write the numbers in order in their original form (scientific notation).
15Scientific Notation: Estimation To estimate:Look for the greatest place value and round to that place value.Follow the rules for converting from standard form to scientific notation.Examples: ,145,956Step 1:Step 2:Solution:
16Multiplying in Scientific Notation (2.15 x 108) x (1.24 x 103)Step 1:(2.15 x 1.24) x (108 x 103)Step 2: =1011x1.242.666 x 1011Standard form: 266,600,000,000Step 1: use the commutative and associative properties of multiplication to regroup and reorder the multiplication problem.Step 2: MultiplySolution:
17Dividing in Scientific Notation 16.4 x 1094.1 x 105Step 1:16.4 = 44.1Step 2:109-5 =1044 x 104Standard form: 40,000Step 1: Divide the factors of a.a x 10n aStep 2: Then, apply the rules for dividing exponential expressions. (you subtract the exponents)n-nSolution: Rewrite the answer in scientific notation using the number in step 1 and 2.
18Adding/Subtracting in Scientific Notation Examples:8.5 x 108 – 6.2 x 1062.1 x x 105Step 1: To add or subtract in scientific notation, the exponents must be the same. If they are not the same, rewrite the terms so that the exponents are the same. To do so, determine the number by which to increase the smaller exponent by so it is equal to the larger exponent.Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left the same number of places.4.2 x x 103 same exponentsStep 2: Add or subtract the new factors (digits) for “a.” = 7.1Solution: Write the sum in scientific notation. If the answer is not in scientific notation (i.e. if “a” is not between 1 and10 ) convert it to scientific notation.7.1 x 103