Convert 0.125 * 10^5 mm² to m²
Understand the Problem
The question is asking to convert an area from square millimeters (mm²) to square meters (m²). The given area is expressed in scientific notation. We need to apply the correct conversion factor to obtain the equivalent area in square meters.
Answer
$0.0125 \, \text{m}^2$
Answer for screen readers
$0.0125 , \text{m}^2$
Steps to Solve
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Understand the conversion factor
We know that $1 , \text{m} = 1000 , \text{mm}$. Therefore, $1 , \text{m}^2 = (1000 , \text{mm})^2 = 10^6 , \text{mm}^2$. This means that $1 , \text{mm}^2 = 10^{-6} , \text{m}^2$.
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Rewrite the given area
The given area is $0.125 \times 10^5 , \text{mm}^2$.
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Apply the conversion
To convert from $\text{mm}^2$ to $\text{m}^2$, multiply by the conversion factor $10^{-6}$: $$ 0.125 \times 10^5 , \text{mm}^2 \times \frac{10^{-6} , \text{m}^2}{1 , \text{mm}^2} = 0.125 \times 10^5 \times 10^{-6} , \text{m}^2 $$
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Simplify the expression
Using the properties of exponents, we have: $$ 0.125 \times 10^5 \times 10^{-6} , \text{m}^2 = 0.125 \times 10^{5-6} , \text{m}^2 = 0.125 \times 10^{-1} , \text{m}^2 $$
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Calculate the final value
$$ 0.125 \times 10^{-1} , \text{m}^2 = 0.0125 , \text{m}^2 $$
$0.0125 , \text{m}^2$
More Information
The area $0.125 \times 10^5 , \text{mm}^2$ is equivalent to $0.0125 , \text{m}^2$. This conversion is essential in many fields, including engineering, physics, and construction, where measurements often need to be expressed in different units for calculations and design purposes.
Tips
A common mistake is using the linear conversion factor (1 m = 1000 mm) directly for area, rather than squaring it to get the correct area conversion factor ($1 , \text{m}^2 = 10^6 , \text{mm}^2$). Another common mistake is errors in scientific notation, particularly when multiplying or dividing by powers of 10.
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