Change 0.125 x 10^5 mm^2 to m^2 leaving in standard form.
Understand the Problem
The question asks us to convert an area of 0.125 x 10^5 square millimeters (mm²) to square meters (m²). The final answer should be expressed in standard form (scientific notation). 1 mm = 0.001 m, so 1 mm^2 = (0.001 m)^2 = 0.000001 m^2 = 10^-6 m^2
Answer
$1.25 \times 10^{-2} \, m^2$
Answer for screen readers
$1.25 \times 10^{-2} , m^2$
Steps to Solve
- Convert $mm^2$ to $m^2$
We know that $1 , mm = 10^{-3} , m$. Therefore, $1 , mm^2 = (10^{-3} , m)^2 = 10^{-6} , m^2$. To convert $0.125 \times 10^5 , mm^2$ to $m^2$, we multiply by the conversion factor $10^{-6}$: $$0.125 \times 10^5 , mm^2 = 0.125 \times 10^5 \times 10^{-6} , m^2$$
- Simplify the expression
Now, we simplify the powers of 10: $$0.125 \times 10^5 \times 10^{-6} = 0.125 \times 10^{5-6} = 0.125 \times 10^{-1} , m^2$$
- Express in standard form
Standard form (scientific notation) requires the coefficient to be between 1 and 10. We can rewrite $0.125$ as $1.25 \times 10^{-1}$: $$0.125 \times 10^{-1} = 1.25 \times 10^{-1} \times 10^{-1} = 1.25 \times 10^{-1 + (-1)} = 1.25 \times 10^{-2} , m^2$$
$1.25 \times 10^{-2} , m^2$
More Information
The area in square meters is $1.25 \times 10^{-2} , m^2$. This is equivalent to 0.0125 square meters.
Tips
A common mistake would be forgetting to square the conversion factor when converting from $mm^2$ to $m^2$. Another mistake could be incorrectly simplifying the powers of 10. Finally, not expressing the final answer in standard form would be an error.
AI-generated content may contain errors. Please verify critical information
