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ivolga24 [154]
3 years ago
15

0.11 as a fraction and in the simplest form

Mathematics
2 answers:
weeeeeb [17]3 years ago
6 0
The simplest form it can be put into is 11/100 but the approximate value is 10.91 or even closer is 1/9
vovangra [49]3 years ago
5 0
Considering that the last 1 in 0.11 is located in the hundredths place, the simplest from of this fraction is 11/100 because it cannot be reduced.

*If you have any questions, feel free to ask me! I'd be happy to help you anytime!
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Answer:

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c is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if (x+y)^{2} = x^{2} + 2\cdot x\cdot y  + y^{2}. From statement, we must fulfill the following identity:

a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}

By Associative and Commutative properties, we can reorganize the expression as follows:

a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2} (1)

Then, we have the following system of equations:

x = a (2)

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y = c (4)

By (2) and (4) in (3), we have the following expression:

(b^{2} - 1) = 2\cdot a \cdot c

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b = \sqrt{1 + 2\cdot a\cdot c}

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, a, b, c > 1. If a, b and c are prime numbers, then  2\cdot a\cdot c must be an even composite number, which means that a and c can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, b must be a natural number, which means that:

1 + 2\cdot a\cdot c \ge 4

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But the lowest possible product made by two prime numbers is 2^{2} = 4. Hence, a\cdot c \ge 4.

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

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c is another arbitrary prime number. (3)

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b = \sqrt{1 + 2\cdot (2)\cdot (2)}

b = 3

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