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Why does 39 divided by 99 equal 0.39393939 repeating?
Simply because the solution to your sum produces a repeating decimal. Just as 22/7 (The value of Pi as a fraction) produces the repeating decimal 3.142857
Why is point nine repeating equal to one?
To answer that question we should first talk about why any non-termination decimal number is equal to whatever it is. And to talk about that, we should first talk about the value of ordinary terminating decimals. Consider a terminating decimal, say 0.314. This decimal represents the sum of the fractions 3/10 + 1/100 + 4/1000; and longer (but still terminating) decimals can be computed in a similar way. But how do we decide what value a non-terminating decimal represents, say 0.314159265458979... and so on with a never-ending sequence of digits? By analogy, it should be equal to 3/10 + 1/100 + 4/1000 + 1/10,000 + ... and so on; but how can we figure out what such a never-ending sum adds up to? Well, one way of looking at it is as follows: Whatever value the decimal has, we know that (say)0.314 is off by no more than 0.001, since 0.314159... - 0.314 = 0.000159..., and 0.000159... is clearly < 0.001. Likewise, 0.3141 is off by no more than 0.0001, and 0.31415 is off by no more than 0.00001, and so on. In other words, the sequence of (terminating) decimals, 0.3, 0.31, 0.314, 0.3141, 0.31415, etc. gives us a list of better and better approximations to the ultimate value of the non-terminating decimal; and in fact by taking enough decimal places, the error in the approximation can be made as small as you like. If you've studied calculus, you may recognize this sort of discussion--it means that the value of the non-terminating decimal acts like the limit of the sequence of terminating decimals. In fact, it just *is* the limit of the sequence. So mathematicians have chosen to define the value of a non-terminating decimal as the limit of the sequence of approximations. Now we can talk about the specific case of 0.9 repeating: It turns out that the limit of the sequence 0.9, 0.99, 0.999, ... is just equal to 1, exactly (which should not be too hard to convince yourself of) and therefore the value of the non-terminating decimal 0.9 repeating is, by definition, equal to 1.
What does binary 100000001 plus binary 11010111 equal?
111011000 (decimal 472). The sum is 257+215.
What is the sum of the first 8192 terms of the binary sequence?
Expressed in decimal, the sum of the numbers 1 to 8192 is 33558528 - expressed in binary, this number is equal to 10000000000001000000000000.
How many decimal places are in the product of 4.97 and 3.456?
Generally speaking, with the exception of trailing zeroes, the number of decimal places in the answer of a multiplication sum is equal to the sum of the number of decimal places in the question. Therefore, 4.97 x 3.456 contains five decimal places in total, therefore the answer contains five decimal places. In this instance, 4.97 x 3.456 = 17.17632.
What is a terminating fraction?
To sum this answer up you half to turn the fraction into a decimal and if it ends that is terminating but if it keeps going it is called a repeating decimal EXAMPLES Terminating- 5/10=.5 Repeating- 1/3=.3333 (bar notation over the 3)
Why does 39 divided by 99 equal 0.39393939 repeating?
Simply because the solution to your sum produces a repeating decimal. Just as 22/7 (The value of Pi as a fraction) produces the repeating decimal 3.142857
Which of the following is always irrationalhe sum of two fractions the product of a fraction and a repeating decimal the sum of a terminating decimal and the square root of a perfect square the produ?
None of the items in the list.
Does the addition of two repeating decimal equal to a repeating decimal?
Not necessarily. 1/3 = 0.333... 1/6 = 0.166... Their sum is 1/2 or 0.5 certainly not
What is the sum of the digits of the repeating decimal?
Infinity.
Why is point nine repeating equal to one?
To answer that question we should first talk about why any non-termination decimal number is equal to whatever it is. And to talk about that, we should first talk about the value of ordinary terminating decimals. Consider a terminating decimal, say 0.314. This decimal represents the sum of the fractions 3/10 + 1/100 + 4/1000; and longer (but still terminating) decimals can be computed in a similar way. But how do we decide what value a non-terminating decimal represents, say 0.314159265458979... and so on with a never-ending sequence of digits? By analogy, it should be equal to 3/10 + 1/100 + 4/1000 + 1/10,000 + ... and so on; but how can we figure out what such a never-ending sum adds up to? Well, one way of looking at it is as follows: Whatever value the decimal has, we know that (say)0.314 is off by no more than 0.001, since 0.314159... - 0.314 = 0.000159..., and 0.000159... is clearly < 0.001. Likewise, 0.3141 is off by no more than 0.0001, and 0.31415 is off by no more than 0.00001, and so on. In other words, the sequence of (terminating) decimals, 0.3, 0.31, 0.314, 0.3141, 0.31415, etc. gives us a list of better and better approximations to the ultimate value of the non-terminating decimal; and in fact by taking enough decimal places, the error in the approximation can be made as small as you like. If you've studied calculus, you may recognize this sort of discussion--it means that the value of the non-terminating decimal acts like the limit of the sequence of terminating decimals. In fact, it just *is* the limit of the sequence. So mathematicians have chosen to define the value of a non-terminating decimal as the limit of the sequence of approximations. Now we can talk about the specific case of 0.9 repeating: It turns out that the limit of the sequence 0.9, 0.99, 0.999, ... is just equal to 1, exactly (which should not be too hard to convince yourself of) and therefore the value of the non-terminating decimal 0.9 repeating is, by definition, equal to 1.
What does binary 100000001 plus binary 11010111 equal?
111011000 (decimal 472). The sum is 257+215.
What is .1111111111 as a fraction?
The repeating decimal .1111111111 can be represented as the fraction 1/9. This is because the decimal 0.1 can be expressed as 1/10, and when we have a repeating decimal like .1111111111, it is equivalent to 1/10 + 1/100 + 1/1000 + ... which simplifies to 1/9 using the formula for the sum of an infinite geometric series.
What is the sum of the first 8192 terms of the binary sequence?
Expressed in decimal, the sum of the numbers 1 to 8192 is 33558528 - expressed in binary, this number is equal to 10000000000001000000000000.
How do you write seven and three hundredths in decimal form?
Expressed as a decimal, 7 3/100 is equal to 7.03.
Does all the numbers have to repeat in order to be a rational number?
For a number to be rational you need to be able to write it as a fraction. To answer your question, it must repeat as a decimal or else terminate which can be thought of as repeating zeroes. Further, every repeating decimal can be written as a fraction and you can find the fraction by using the formula for the sum of an infinite geometric series.
518 is 77 of what sum?
672.72 repeating
