2nd. The TI-30XIIS Calculator and Fractions, Mixed Numbers and Decimals These are the buttons we will be using to calculate fractions.
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1 The TI-30XIIS Calculator and Fractions, Mixed Numbers and Decimals These are the buttons we will be using to calculate fractions. FRACTION A!! ON Let s start with the basic arithmetic operations: Ø ADDITION:!! +!! Start with 3 A!! 4 Continue with + 1 A!! 5 = Ø SUBTRACTION:!!!! 1 A!! 3-2 A!! 5 = Ø MULTIPLICATION:!!!! 5 A!! 4 X 2 A!! 3 = Ø DIVISION:!!!!" 4 A!! 7 6 A!! 13 =
2 Mixed numbers These are the buttons we will be using to calculate mixed numbers and improper factions. 2 nd FRACTION to access A b c ó d c FRACTION A b c The answer from the division problem above was a mixed number 1 _ 5 / 21. To convert from a mixed number to a improper fraction use the A b c button to access the A b c ó d c function. Ø Having 1 _ 5 / 21 on the screen, 2 nd A b c = Your screen should look like: 26 / 21 To convert back to a mixed number just press 2 nd A b c again. To input a mixed number, you need to use A b c key twice. Ø 3!! is input by pressing 3 A b c 3 A b c 4 = To work with mixed numbers and proper fractions, you just need to input each using the appropriate buttons. Let s work 2!!!! Ø Input 2 A b c 1 A b c 4 2 A b c 5 = A b yields 45 / 8. These buttons allow you to go back and forth between mixed numbers c and improper fractions.
3 Decimal/Fraction Conversions These are the buttons we will be using to work with decimal conversions and percent. PRB to access F ód FRACTION ( to access % A b c There are times the decimal rather than the fractional value is needed. To convert a fraction to a decimal or back the PRB buttons must be pressed. Ø To change 5 5 to a decimal, input the mixed number as before 5 A b 8 c Now PRB press and the answer will change to a decimal. 5 A b c 8: If you press A b c again the answer reverts to the mixed number. Suppose the fraction does not represent a terminating decimal? If the problem is looking for an exact answer, you are better leaving your work in fractional form. If the problem is asking for an approximate answer, you may convert to a non-termination decimal as a LAST step. Fractions which have non-terminating decimal representation are given with the line above the repeating numbers.! becomes 0. 6! becomes !" becomes 1.416!!!" Ø Pressing the PRB again changes decimal to one with 10 decimal places rounding the answer in the last place becomes becomes becomes
4 Ø Pressing the PRB again changes decimal back to its fractional form. To work a problem involving percent you will need to access the % function by first using and then (. Ø To take 25% of 468: Press 25 ( X 468 = Ø To take To take 12!! % of 325: press 12 A b c 1 A b c 3 ( 325 = This answer can be changed to the mix number 40 1 A b c or PRB. 12 or the decimal equivalent by using Changing from percent to fraction or decimal is possible by just inputting the percent and pressing =. Ø Find 48% as a fraction and a decimal: 48 ( = Ø Find 53!! % as a fraction and a decimal: 53 A b c 1 A b c 3 3 ( =
5 The TI-30X IIS Calculator and Exponents ARROWS ^ x 2 PARENTHESIS Squaring a number can be done easily using a x 2 key. Cubing a number or raising it to any power can be achieved by using ^ key followed by number 3. Ø Squaring: input the number and then x 2 =, 4 2 is found by inputting: 4 x 2 = Cubing or raising a number to the third power: input the number and then ^3 =, 4 3 is found by inputting: 4 ^3 = Raising a number to a power greater than 3: input the number and then ^ (the power desired) =, (-3) 4 is found by inputting: ( (-)3 ) ^ 4 = Note: if you did not put the -3 in parentheses, the orders of operation raises the 3 to the fourth power and then makes it negative, hence the answer will be -81. Be careful that you always put negative numbers in parentheses when raising them to powers. You can also take values to fractional exponents: 8 2/3 can be found by inputting: 8 ^ (2 3) =
6 Taking a root can be done easily using option, which is achieved by pressing x 2. Any other root (n-root), can be calculated by pressing (the root desired) ^. Square root: the number =, is found by inputting: x 2 36 = Cube root: the number =, is found by inputting: 3 ^ 64 = Taking a root higher than a cube root: (the root desired) ^ (the value) =, is found by inputting: 4 ^ 1296 = Since the root symbol works like a grouping symbol, there is no need to use parentheses for negative values. is found by inputting: 5 ^ (-)32 = Remember that you can t take an even root of a negative number. If you do you will get an error message.
7 The TI-30XIIS Calculator and Orders of Operation ARROWS PRB PARENTHESIS x 2 (-) The calculator always uses the correct orders of operation. You need to ensure that what you are inputting is correct. Simplify the following expression without using the calculator and then input it into your calculator to see if you have the same answer x 2 = The calculator will give an answer of 4. If you multiplied before dividing you have an answer of 1. Remember multiplication and division are done in order from left to right. Since the division comes first, you should divide first and then multiply. This is why it is very important to input the problem correctly. It you wanted to multiply first you need to input the expression with parenthesis such as 16 (8 x 2) =. It is very important to place grouping symbols where appropriate. To simplify the expression, there are two option: 1 st - input the expression as a single line using in place of the fraction bar and ensuring that the numerator and denominator are both in parenthesis: (56 4(20 13) ) ( (2+6) x 2-2(37-6) ) =
8 Using Orders of Operation in Formulas 2 nd - input the numerator expression 56 4(20 13), then press = key. Now you have calculated the value of the numerator. Press divide key and enter the denominator expression ( (2+6) x 2-2(37-6) ) = The orders of operation become important when substituting values into a formula. 1. Quadratic formula: ; solve 4x 2 + 5x 3 = 0 using the quadratic formula (a = 4; b = 5; c = -3) hence you need to input the following expression: (NOTE: you can only compute one value at a time, so begin with the positive root.) input the expression as a single line using in place of the fraction bar and ensuring that the numerator and denominator are both in parenthesis: ( (-)5 + x 2 (5x (-)3) ) ( 2 4) = This is the decimal value. If you want a result in a fraction form, press PRB = Whenever you want to reenter the previous expression to make a simple change, press the right arrow key and the previous expression will appear on the screen. To calculate the other root, the sign before the square root in the previous expression is the only entry that needs to be changed. Press the right arrow to access the previous expression. Using the right arrow key to move the cursor on the + and hit. This removes the + and inputs. (Be sure that you use the subtraction button and not the (-) button.)
9 The TI-30X IIS Calculator and Scientific notation DRG π % PARENTHESIS ^ x 2 x!! (-) These are the buttons we will be using to calculate in scientific notation. Make sure that your calculator is set to display numbers in scientific notation by clicking DRG and using arrow keys to underline SCI. Hit enter and you are good to go. We will be using the x!! button to input the numbers in scientific notation. Inputting values in scientific notation: input the number, press x!!, input the power, press =. Input 3.24 x 10 6 : 3.24 x!! 6 = Input 4.65 x 10-4 : 4.65 x!! (-) 4 =
10 Scientific notation is used when dealing with very large and very small numbers in applications. The volume of a sphere is given by the formula: 4 3 π r3. 1. Given the radius of the Earth is meters, find its volume. Type 4 3. Now press π Now input (6.30 x!! 6) ^ 3. A ^ key allows you to raise a number to any power. In this example we are raising radius to cube power. 2. Given that the radius of the Sun is meters, find the volume of the sun. Input: 4 3 π (6.96 x!! 8) ^ 3 = 3. How many Earths will fit into the Sun? This requires the volume of the sun to be divided by the volume of the earth. Input: 1.41 x!! x!! 21 = When working with very small amounts like the mass of a water molecule which is , negative numbers are used in the exponent. Make sure that you use negative sign key (-) rather than minus key. 4. The total mass of the earth is kilograms and about 0.023% of the earth is water. If the mass of one water molecule is kilograms, how many water molecules are there on the earth? First find the amount of water on the earth and then divide by the size of one water molecule. Input: 5.98 x!! ( 3.00 x!! (-) 26 =
11 The gravitational pull between two bodies of mass M1 and M2 at the distance D is given by the formula!!!! F = G where G is the universal gravitational constant, G= !!!!!!!!!"! 5. Calculate the force between the Sun and the Earth, if mass of the Sun is M sun = kg and mass of the Earth is M earth = kg and the distance between them is D = m. Inputting these numbers formula becomes: F = !!! 2 10!" !" ( ! )! Ø Input 6.67 x!! (-) 11 2 x!! x!! 24 (1.496 x!! 8) x 2 =
12 The TI-30X IIS Calculator and Base e ARROWS e x PARENTHESIS ln: log base e (-) Many application problems require using the natural base or base e. The symbol e represents an irrational number similar to π. e Raising e to a power: e 5 is found by inputting: ln 5 = Raising e to a negative power: e -3 is found by inputting: ln (-) 3) =, The inverse function for exponentials is logarithms. For base e this requires using the natural log or ln. To take the natural log of a number 45, ln(45), is found by inputting: ln 45 ) =, Note that the calculator inserts the left parenthesis when you input ln. Remember that you can t take the log of a negative number so if you input ln(-45) you will get an error message.
13 The TI-30X IIS Calculator and Base 10 ARROWS 10 x log: base 10 PARENTHESIS (-) Many application problems require using the common base or base 10. Raising 10 to a power: 10 5 is found by inputting: log 5 =, Raising 10 to a negative power: 10-3 is found by inputting: log (-) 3 =, PRB changes the answer to a fraction. The screen will look like 1 / 1000 Raising 10 integer powers is just a matter of moving the decimal point, so a calculator is really only needed when raising 10 to a fractional exponent. 10 3/4 is found by inputting: log (3 4) =, Many applications involve using the inverse or common log (log base 10) function. To take the common log of a number: log the number ) =, log(45) is found by inputting: log 45 ) =
14 If you need to take the log to a base other than 10 or e, use the change of base formula first. Input log 34) log 3 ) =, hence 1. Applications involving base e: Population growth is given as P(t) = P o e kt where P o is the original population, k is the growth rate and t is the time. Suppose you are asked to find the population after 2 years given the original population was 2500 and the growth rate is 5%. The values you have are P o = 2500, t = 2 and k = 0.05, hence Input: 2500 ln ) = 2. Applications involving base 10: The measure of the intensity of an earthquake is given as a Richter Scale value using the equation where A is the amplitude of the ground s vibrations (in micrometers) and P is the time (in sec.) it takes for the ground to oscillate one time. Suppose that the ground oscillated 5000 micrometers every 0.2 sec., what is the Richter scale value? A = 5000 and P = 0.2 hence Input: log ) =
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