The question asks for the simplified value of the expression: $ \frac{0.01404}{24^2+6^2-144} $ We need to calculate the denominator first and then perform the division.
Denominator Calculation
First, calculate the squares in the denominator:
- $24^2 = 576$
- $6^2 = 36$
Now, substitute these values back into the denominator expression:
$ \text{Denominator} = 24^2 + 6^2 - 144 $ $ \text{Denominator} = 576 + 36 - 144 $Perform the addition and subtraction:
$ \text{Denominator} = 612 - 144 $ $ \text{Denominator} = 468 $Fraction Simplification
Now substitute the calculated denominator back into the original fraction:
$ \frac{0.01404}{468} $To simplify this, we can perform the division. It's helpful to write the numerator in scientific notation:
$ 0.01404 = 1.404 \times 10^{-2} $The expression becomes:
$ \frac{1.404 \times 10^{-2}}{468} $Now, divide the numbers:
$ \frac{1.404}{468} = 0.003 $So the expression simplifies to:
$ 0.003 \times 10^{-2} $Convert $0.003$ to scientific notation:
$ 0.003 = 3 \times 10^{-3} $Combine the terms:
$ (3 \times 10^{-3}) \times 10^{-2} $Using the rule of exponents ($a^m \times a^n = a^{m+n}$):
$ 3 \times 10^{-3 + (-2)} $ $ 3 \times 10^{-5} $The simplified value is $3 \times 10^{-5}$.
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Important Questions from Simplification
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
