$deciaml to integer fraction converter$

$deciaml to integer fraction converter$

Does this happen for all fractions? Let us look at the decimal for 3 22.įollowing the same division process, we get a 1 on top with a remainder of 8, a 3 on top with a remainder of 14, a 6 on top with a remainder of 8, a 3 on top with a remainder of 14 … but wait! We have already seen these remainders, and we know that the next number on top is a 6 with a remainder of 14 again. In the table, H means your guess was too high and L means your guess was too low.īecause the decimal for the number 7 16 ends, you can get the exact number by guessing one digit at a time in the decimal. The table below shows a possible way this could happen. If you are playing the guess-the-number game, you can arrive at this decimal version of 7 16 in several short steps. At this point, we are done with our long division and we can say that 7 16 = 0.4375. After we have done this four times, we get a remainder of 0, which has zero 16’s in it. We continue this process, bringing down zeros after each remainder and asking how many 16’s are in the resulting number. Next, we subtract 48 from 60 to get a remainder of 12. Since 16 × 3 = 48, we write a 3 above the second 0. In this case, 6 is called the remainder.įor the next step, we bring down the next 0 from 7.00. Then we subtract 64 from 70 and get 6 left over. Since 16 × 4 = 64, we write a 4 above the 0 in 7.0. (Really, we are asking how many 1.6’s are in 7.0, but this is equivalent to asking how many 16’s are in 70). Here is how it works for the fraction 7 16:įor the first step of the division, we ask how many 16’s are in 70. We can turn a fraction into a decimal by dividing the numerator by the denominator. Let us look at these numbers in a different way and think about them as decimals instead. The position of the number you are trying to guess, 3 22, is marked by the vertical black line segment. The dot at the end of each line segment is your guess. With each guess, you halve the range where Jordan’s number might be. Your friend Jordan asks you to guess a number between 0 and 1.Or are you doomed to be guessing forever? This seems like it is taking a long time! Will you ever guess the right number? Perhaps it would help if you change your strategy. One representation of this game is shown in Figure 1. Continuing with your strategy, you guess 1 8, 3 16, 5 32, 9 64, …. Jordan says 1 4 is still high, so you know the answer must be on the number line between 0 and 1 4. Jordan tells you your guess is high, so you know the answer is somewhere on the number line between 0 and 1 2. You try starting exactly in the middle and guess 1 2. You have to guess a number somewhere along the number line from 0 to 1. What if fractions are allowed? Suppose Jordan picks a number between 0 and 1, for example 3 22. However, during that class, you realize that you have been assuming Jordan will always pick an integer.

$deciaml to integer fraction converter$

You march off to your second class victoriously, confident that you will be prepared for Jordan’s next challenge. But then you realize: there is nothing special about −100 and 100! If you start with a number between −10, you know you will eventually guess the correct number even if it takes a few more guesses. If Jordan’s number is −32, and you have already figured out that −33 is too low and −31 is too high, then you know the answer is −32. You guess, and by going higher and lower you get closer and closer to the target. You decide to take the bait, and you quickly discover that this does not change the game much. Feeling pleased that you are getting closer, you ask, “How about 75?” “You got it!” Jordan replies, and you march triumphantly off to your first class of the day.īut after class, you again run into Jordan, who has apparently been thinking about ways to stump you: why stick to positive numbers? What if you also allow negative numbers? “Now I am thinking of a number between negative 100 and 100,” Jordan says gleefully. On Monday morning, your friend Jordan walks up to you and says, “I’m thinking of a number between 1 and 100.” Being a good sport, you play along and guess 43. What makes fractions so special? We explore how we can recognize the decimal representation of fractions and how fractions can be used to approximate any real number as closely as we wish. Centuries later, while we regularly use numbers that cannot be written as fractions, those numbers that can be written as fractions remain powerful tools. Legend has it that the first person in ancient Greece who discovered that there are numbers that cannot be written as fractions was thrown overboard from a ship.

$deciaml to integer fraction converter$

Deciaml to integer fraction converter