Why is it necessary to have whole numbers when constructing a stem and leaf diagram?
930802
not necessary to have whole numbers...you can have decimals like 2.79 5.5 3.2 like these..all these depends on the key you used to represent the data
932232
Hello,\n\nThe symbols in relationship to the numbers change each time. \nThe symbol you choose is the correct one  for all answers. No matter the number you choose there is one correct symbol for all answers.
701990
Okay, this is corny, but say you were arranging a number of something on a table, and you wanted to make a square. You would take the square root of however many you have, and then you would know how many to put in the first row, and you could just line up each column after that to match. Or, if you wanted to stack them in a cube, you would take the cube root.
383124
I believe the book is incorrect as well.\n\nThere are some real-world problems that start and end with numbers that do not belong to the set of Reals.  Consider the Quaternion.  A Quaternion is like a "super imaginary number", it is of the form, a + b*i + c*j + d*k, where i^2 = j^2 = k^2 = -1\n\nThis type of number can be used to represent the position and orientation of an object in 3D.  Since objects do have positions and orientations, it is not unreasonable to represent this with a Quaternion (even though many people don't know what it is).
112490
Because the numbers after the decimal (to the right of) represent less than one. One times a number is that number. Less than one times a number is only a fraction of that number.\n\nMake sense?
326552
Sometimes they're just easier to write out.  "The fourth root of x raised to the 9th" in radical form is a 4 on the outside and an x^9 inside.  But in decimal form, it's x^9/4.  For some, drawing that radical sign is a pain and looks sloppy after a while, whereas fractions are easier to write and understand (no confusing that with a division sign!).\n\nOther times it's easier to work with mathematically.  Consider:\n\ncuberoot(x)/x^4\n\nThat doesn't look like it's simplified as is, but in exponent form, you can do more to it.  cuberoot(x) = x^(1/3), so\n\nx^(1/3)/x^4 = x^(-11/3)\n\nExponents vs. radicals is great when multiplying or dividing numbers or variables with the same base.  If you're multiplying, you simply add the bases:\n\nsqrt(x) * cuberoot(x) = x^1/2 * x^1/3 = x^5/6\n\nAnd if you're dividing, as in my first example, you subtract the bases.
699709
Rather than tackle all these topics where no one else can see, I will briefly summarize some thoughts here for you.  Of course, you'll get much more from checking out a good Beginning Calculus study aid (like "Schaum's Outline" series) at your local bookstore.\n\nINTERVAL NOTATION\n\nWe can use brackets [ ] and parentheses ( ) to denote portions of the x-axis or any other continuous set of numbers.\n\nExamples are probably best to learn from.  I'll say it in English, then write the interval using notation.\n\n"All the numbers from 0 to 5, but not including 5 itself."  [0,5)\n\nSee how the parenthesis ) means "not including this number"?  And the [ means "include the zero" on the left-hand side of the interval.\n\n"Numbers greater than 6 but less than 11."\n(6,11)\nHere, neither of the interval's endpoints is included in the set, but everything in between is.\n\nIf I could write the symbol for "infinity" I could come up with open-ended intervals:\n"All the numbers smaller than -3" would be the interval (-inf,-3)\n\nIMPORTANT:  When infinity is one of the 'endpoints', a parenthesis is ALWAYS used.  Because you can never 'include' infinity.\n\nLIMITS\n\nThis is normally a lengthy topic, and limits can seem complicated because there are so many different occasions where limits apply.  Even the notation is funny-looking (like an arrow --> that means 'approaches') and takes a while to get used to.\n\nBut the simplest way to think of a limit is as "a possible value that is being approached somehow."  We could speak of x values becoming closer and closer to, say, 15 -- and 15 might turn out to be "the limit" in the problem, in which case x might eventually EQUAL 15 and stop there (or x might just get arbitrarily CLOSE to 15 and something stops it from BEING 15).\n\nIf we choose simple functions like y=3x and then ask "What will be the limit of this function as x approaches 7?" ... the answer is very straightforward.  21!  Because there's nothing to stop x from being 7, and it doesn't frankly matter whether it 'got there' after being 7.1 or 6.9.  The function has no holes (discontinuities) or breaks (asymptotes) or restrictions (such as x<5) ... so life was really easy with y=3x!\n\nBut for functions that are more "interesting" or have funky graphs right around a particular x-value, it pays to be aware how the limit (the y-value) may be a challenge to discover.  The limit may even CHANGE as we let x approach from the 'left' (below) or the 'right' (above).\n\nHere's the last example:\n\nf(x)=(x-1)/(x+5)\nBeing a rational function, f is defined only for values of x that are permitted ... and, like any fraction, the denominator may NEVER be 0.  That eliminates x=-5.  In interval notation, we'd say that the permissible values of x come from the set (-inf,-5) U (-5,inf).  As you can see, sometimes 'interval notation' is not so brief!\nIn those cases, we often simply write x / -5 (where the 'equal sign' has a slash drawn through it).\nNevertheless, f(x) has values we can calculate for every other possible value of x besides -5!  If you graph f(x), you will see that the function behaves 'strangely' right around x=-5.  Those are asymptotes ... a break in the graph that cannot be "fixed" simply by filling in a missing hole!  You could say the function f(x) "increases without limit" or "decreases without limit" on either side of x=-5 ... some teachers prefer "f has infinite limits."\n\nMAXIMA and MINIMA\nThese are merely the greatest and least values that a function might attain over a given interval.  Sometimes a function's least or greatest value occurs at the interval's endpoint(s).  But just as often, the 'lowest' (valley) or 'highest' (peak) might occur somewher
342027
hahahah that doesn't make sense in order for two sides of an equation to be equal the numerical value of each side must be the same.  Whats with all the equals signs!
845089
Ok, your question makes absolutely no sense.  Why say we can only use 1 through 16, and then say we can only use 1?\nSome ways, assuming I translated your question correctly, would include 16 + 16 +1 +1, and 16 + 15 + 3.... There are almost an infinite number of ways to add to 34 with the numbers 1-16, so please rephrase your question.
858824
Data can be shown in a variety of ways including graphs, charts and tables. A Stem and Leaf Plot is a type of graph that is similar to a histogram but shows more information. The Stem-and-Leaf Plot summarizes the shape of a set of data (the distribution) and provides extra detail regarding individual values. The data is arranged by place value. The digits in the largest place is referred to as the stem and the digits in the smallest place are referred to as the leaf (leaves). The leaves are always displayed to the left of the stem. Stem and Leaf Plots are great organizers for large amounts of information.
609782
root, stem, leaf and flower
1060197
Grappling with the axiomatic logic is not suitable for most of\nus and these readings are difficult.  Let me attempt an inadequate simplifi-\ncation.  I would say a number "belongs to a concept" and is an\nextension of that concept and then statements about numbers correspond to\n"identities of concept".\n\nIn the sense of counting, one apple and one orange represent identical\nconcepts even if apples are not oranges, so we write 1 = 1.  Now 1 + 1 or\nfor that matter 1 + 1 + 1 + 1 + 1 + 1 (repeating)  are represented in the\nsense of identity by other symbols which, if arabic numerals are used, we\nwrite as 2 or 5.  The symbols are just compact notation for representation\nof an identical "concept".  I would say that number is not anything\nphysical nor is it subjective.  This may not be very satisfying but deep\nphilosophical questions about numbers may always remain unanswered in very\nsatisfying ways.
602685
Not necessarily. If you can turn them into decimals, sometimes it's easier to compare them.\nFor instance, 4/8 = .5 and 5/9 = .55. Obviously 5/9 is a little larger, and you don't have to do all the math.
971505
When graphing, the open circle indicates "less than" and "greater than", the closed circle indicates "less than or equal to" and "greater than or equal to".  In your case, you need a CLOSED circle at -1/2 and shade to the left since the numbers to the left of -1/2 are less in value.  The arrow placed at the end indicates that ALL numbers in that direction are less than or equal to -1/2.
454426
i have a great logical reasoning for that.... here goes:\n1. there are two 2s, so you overlap them, making just one two. \n2. take the plus sign out for a second.\n2 1/2. the plus sign consists of 2 sticks, one horizantal and one vertical. \n3. the vertical came become a one and place it on the left of the 2. ( it makes 12)\n4. the other horizantal line can be used as a minus sign. \n5. Now, in the equal sign, it consists of two lines, both horizantal. \n5 1/2. if you leave one, and make the other diagonal, and attach in together, it makes a seven. \n6. so.. so far, it's is like this: 12-7=?\n7. ultimately, the answers five\nso there you have it, it sounds a little weird and strange, but it's really impossible to have a logical reasoning for 2+2=5... hehe
262787
that's as low as it'll go, nothing can be divided out of anything in the numerator or the denominator.  That's because there's not any like terms.  In other words, c nor d is in both parts of either the top or the bottom.  I hope you understood that, but trust me on this one.  Calculus us hard.
317809
absolute values are important in higher levels of analysis when using wide ranges of numbers, also it help when we try to have equations of only real numbers make sense sometimes, i.e. various sorts of root equations