If \(155\over0.155\) = \(15.5\over k\), then the value of K is:
0.0155
Solving the Equation for K
The problem asks us to find the value of K given the equation:
\( \frac{155}{0.155} = \frac{15.5}{k} \)
We need to solve this equation to find the specific numerical value for k.
Step-by-Step Calculation
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Simplify the Left Side: First, let's simplify the fraction on the left side of the equation, which is \( \frac{155}{0.155} \).
To make the division easier, we can rewrite 0.155 as \( \frac{155}{1000} \).
So, the left side becomes:
\( \frac{155}{\frac{155}{1000}} \)
Dividing by a fraction is the same as multiplying by its reciprocal:
\( 155 \times \frac{1000}{155} \)
The 155 terms cancel out:
\( = 1000 \)
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Set Up the Simplified Equation: Now, we substitute the simplified value back into the original equation:
\( 1000 = \frac{15.5}{k} \)
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Solve for K: To isolate k, we can rearrange the equation. Multiply both sides by k:
\( 1000 \times k = 15.5 \)
Now, divide both sides by 1000:
\( k = \frac{15.5}{1000} \)
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Final Calculation: Perform the division:
\( k = 0.0155 \)
Conclusion
By following the steps of simplifying the initial fraction and then algebraically solving for k, we find that the value of k is 0.0155.
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