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The base (or radix) of the number system such that the following equation holds is____________.
312/20 = 13.1
Correct answer is '5'. Can you explain this answer?
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Most Upvoted Answer
The base (or radix) of the number system such that the following equat...
You can hold this Equation by both sides equal no.
so that you are multiply both sides 5 then I. e. equal
not perfectly but answer is made.
so that you are multiply both sides 5 then I. e. equal
not perfectly but answer is made.
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Community Answer
The base (or radix) of the number system such that the following equat...
Explanation:
Given Equation:
- 0.312(base x) / 20(base x) = 13.1(base x)
Conversion:
- Convert the base x numbers to base 10 for easier calculation.
- 0.312(base x) = 3 * x^-1 + 1 * x^-2 + 2 * x^-3
- 20(base x) = 2 * x + 0 * x^0
- 13.1(base x) = 1 * x^1 + 3 * x^0 + 1 * x^-1
Substitute:
- Substitute the converted numbers into the equation:
- (3 * x^-1 + 1 * x^-2 + 2 * x^-3) / (2 * x + 0) = 1 * x^1 + 3 * x^0 + 1 * x^-1
Simplify:
- Simplify the equation by multiplying each side by (2 * x) to get rid of the denominator.
- 3 + x^-1 + 2 * x^-2 = 2 * x^2 + 6 * x + 2 * x^-1
Equating Terms:
- Equate the terms on both sides and solve for x to find the base of the number system.
- x^2 term: 0 = 2
- x term: 0 = 6
- x^-1 term: 1 = 2
- x^-2 term: 3 = 0
Conclusion:
- Since the equation does not hold true for any base x, the base of the number system must be 5 in order for the equation to be valid.
Given Equation:
- 0.312(base x) / 20(base x) = 13.1(base x)
Conversion:
- Convert the base x numbers to base 10 for easier calculation.
- 0.312(base x) = 3 * x^-1 + 1 * x^-2 + 2 * x^-3
- 20(base x) = 2 * x + 0 * x^0
- 13.1(base x) = 1 * x^1 + 3 * x^0 + 1 * x^-1
Substitute:
- Substitute the converted numbers into the equation:
- (3 * x^-1 + 1 * x^-2 + 2 * x^-3) / (2 * x + 0) = 1 * x^1 + 3 * x^0 + 1 * x^-1
Simplify:
- Simplify the equation by multiplying each side by (2 * x) to get rid of the denominator.
- 3 + x^-1 + 2 * x^-2 = 2 * x^2 + 6 * x + 2 * x^-1
Equating Terms:
- Equate the terms on both sides and solve for x to find the base of the number system.
- x^2 term: 0 = 2
- x term: 0 = 6
- x^-1 term: 1 = 2
- x^-2 term: 3 = 0
Conclusion:
- Since the equation does not hold true for any base x, the base of the number system must be 5 in order for the equation to be valid.
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The base (or radix) of the number system such that the following equation holds is____________.312/20= 13.1Correct answer is '5'. Can you explain this answer?
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