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
The value of {5 - 5 ÷ (10 - 12) × 8 + 9} × 3 + 5 + 5 × 5 ÷ 5 of 5 is:
What should come in place of the question mark (?) in the following question?
[((16 ÷ 4) × 4) ÷ 4] = ?
Simplify the following expression.
\(\frac{{6\frac{1}{2} + 2\frac{5}{7} \times \frac{{14}}{{19}} - \frac{1}{2} \div 2\ of\frac{1}{4}}}{{11 \times 12 \div 12 + 12}}\)
The value of \(\left( {\frac{7}{5} \div \frac{7}{{10}}of\frac{3}{4}} \right) \div \frac{4}{9} + \left( {\frac{7}{{16}} \div 10\frac{1}{2} \times 7\frac{1}{5}} \right) \times \frac{5}{{12}} \) is:
The value of \(\left( {{1 \over 2}} \right)\) [{–2(12 + 2)}10] is:
