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If 0.225225тАЛ=K22.5тАЛ, then the value of K is:
0.0225
0.225
2.25
0.00225
0.0225
Observe the ratio: the numerator 225 becomes 22.5 (divided by 10). To maintain equality, the denominator 0.225 must also be divided by 10, resulting in 0.0225.
We are given the proportion: 225 / 0.225 = 22.5 / K
baтАЛ=dcтАЛтЯ╣d=ab├ЧcтАЛ
Observe the ratio: the numerator 225 becomes 22.5 (divided by 10). To maintain equality, the denominator 0.225 must also be divided by 10, resulting in 0.0225.
Students often misplace the decimal point during division or multiply by 10 instead of dividing by 10.
Set up the equation
Represent the given proportion as an algebraic equation to solve for K.
0.225225тАЛ=K22.5тАЛ
Isolate K
Cross-multiply the terms to isolate K on one side of the equation.
K=22522.5├Ч0.225тАЛ
Simplify the values
Divide 22.5 by 225, which gives 0.1.
K=0.1├Ч0.225
Calculate final result
Multiply 0.1 by 0.225 to obtain the final value of K.
K=0.0225
A is correct because the cross-multiplication of the given proportion leads to the value 0.0225.
Understanding decimal shifts is crucial in Chemistry for molarity calculations and in Physics for unit conversions involving scientific notation.
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