Example: $25.5 \div 0.5 = \_\_\_\_$

Method 1: Converting to Fractions

One way to divide decimals is to convert both numbers into fractions.

1. Rewrite decimals as fractions: $25.5$ is the same as $\frac{255}{10}$, and $0.5$ is the same as $\frac{5}{10}$.
   $$\frac{25.5}{0.5} = \frac{\left(\frac{255}{10}\right)}{\left(\frac{5}{10}\right)}$$
2. Multiply by the reciprocal: To divide fractions, you multiply the first fraction by the reciprocal (flipped version) of the second fraction.
   $$\frac{255}{10} \times \frac{10}{5}$$
3. Simplify: The $10$s in the numerator and denominator cancel each other out, leaving you with:
   $$\frac{255}{5} = 51$$

Method 2: Removing the Decimal Points

A faster way to solve this is to eliminate the decimal points by multiplying both the numerator and the denominator by the same power of 10 (in this case, 10).

1. Shift the decimal point: Since both numbers have one decimal place, you can move the decimal point one place to the right for both. This is equivalent to multiplying both by 10.
   $$\frac{25.5}{0.5} = \frac{255}{5}$$
2. Divide the whole numbers: Now, simply divide $255$ by $5$.
   $$\frac{255}{5} = 51$$

Final Answer: 51

Example: $27 \div 0.03$

1. Identify the shift: To make $0.03$ a whole number, you need to move the decimal two places to the right.

2. Balance the top: Since you moved the bottom two places, you must move the top two places. Think of $27$ as $27.00$.

   • $0.03$ becomes 3.

   • $27.00$ becomes 2700.

3. Divide: $2700 \div 3 = \mathbf{900}$.