The question asks for the value of the expression $(0.2)^3 - (0.02)^3$. We need to calculate the cubes of the two decimal numbers and then find their difference.
Calculation Steps for $(0.2)^3 - (0.02)^3$
- Calculate the first term: $(0.2)^3$ This means multiplying 0.2 by itself three times: $0.2 \times 0.2 \times 0.2 = 0.04 \times 0.2 = 0.008$
- Calculate the second term: $(0.02)^3$ This means multiplying 0.02 by itself three times: $0.02 \times 0.02 \times 0.02 = 0.0004 \times 0.02 = 0.000008$
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Subtract the second term from the first term:
We need to calculate $0.008 - 0.000008$.
To subtract, align the decimal points and add trailing zeros to the first number:
$0.008000$
So, $(0.2)^3 - (0.02)^3 = 0.007992$.
$- 0.000008$
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$0.007992$
The calculated value is 0.007992, which matches one of the given options.
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The value of \(\frac{1}{4} + \frac{{[{{(20.35)}^2} - {{(8.35)}^2}] \times 0.0175}}{{{{(1.05)}^2} + (1.05)(27.65)}}\) is:
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