Sure, let's solve the given problem step-by-step.
We are given a value of [tex]\(0.024\)[/tex], and we need to find the expression [tex]\(0.024^2 \times \frac{12}{45}\)[/tex].
1. Square the given value:
[tex]\[
0.024^2 = 0.024 \times 0.024 = 0.000576
\][/tex]
2. Calculate the fraction:
[tex]\[
\frac{12}{45}
\][/tex]
Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 3):
[tex]\[
\frac{12 \div 3}{45 \div 3} = \frac{4}{15}
\][/tex]
3. Multiply the squared value with the simplified fraction:
[tex]\[
0.000576 \times \frac{4}{15}
\][/tex]
4. Perform the multiplication:
We multiply [tex]\(0.000576\)[/tex] by [tex]\(\frac{4}{15}\)[/tex]:
[tex]\[
0.000576 \times \frac{4}{15} = 0.000576 \times 0.2667 \approx 0.0001536
\][/tex]
So, the detailed step-by-step solution to the expression [tex]\( 0.024^2 \times \frac{12}{45} \)[/tex] results in:
[tex]\[
(0.024^2, 0.024^2 \times \frac{12}{45}) = (0.000576, 0.0001536)
\][/tex]
