- Represent the division as a fraction: \(\frac{0.287}{0.1}\).
- Multiply both the numerator and the denominator by 10 to simplify the divisor: \(\frac{0.287 \times 10}{0.1 \times 10} = \frac{2.87}{1}\).
- Evaluate the quotient: \(\frac{2.87}{1} = 2.87\).
- Final result: \(\boxed{2.87}\).
Explanation
- Analysis of the Division Problem
The problem asks for the result of dividing the decimal 0.287 by the decimal 0.1. We can express this as the fraction \(\frac{0.287}{0.1}\). To make the division easier, we can eliminate the decimal in the divisor by multiplying both the numerator and the denominator by 10.
- Performing the Division
By multiplying both the numerator and the denominator by 10, we transform the division expression:
\[ \frac{0.287}{0.1} \times \frac{10}{10} = \frac{0.287 \times 10}{0.1 \times 10} = \frac{2.87}{1} \]
Dividing any number by 1 results in the original number. Thus, \(\frac{2.87}{1} = 2.87\). Alternatively, one can simply note that dividing by 0.1 is equivalent to multiplying by 10, so \(0.287 \times 10 = 2.87\).
Examples
Imagine you are measuring ingredients for a science project and you have 0.287 liters of a solution. If you need to distribute this solution into 0.1-liter vials, you can calculate how many vials you will fill by dividing 0.287 by 0.1. This operation, which gives you 2.87, shows that you can fill 2 full vials and a portion of a third one. Understanding how to divide by decimals helps in various practical tasks involving measurement, scaling, or resource allocation.