Verified Answer :
- A percent is a ratio defined as \(x\% = \frac{x}{100}\).
- Dividing the percentage value by \(100\) directly converts the percent to its decimal form.
- Moving the decimal point two places to the left is an arithmetic equivalent of dividing by \(100\).
- The correct methods are: \(\boxed{\text{Divide the percent by 100, and remove the percent sign; Move the decimal point two places to the left, and remove the percent sign}}\).
Explanation
- Definition of Percent to Decimal Conversion
To convert a percentage to a decimal, we must understand the definition of the term "percent." The word "percent" is derived from Latin, meaning "per hundred" or "by the hundred." Therefore, \(x\%\) is mathematically equivalent to the ratio \(\frac{x}{100}\). To convert this ratio into a decimal form, we perform the division of \(x\) by \(100\).
- Evaluating the Conversion Methods
Now, let us examine the provided methods for converting a percent to a decimal:
- Multiplying the percent by \(100\) (Option 1) is incorrect because it changes the value by a factor of \(10,000\), not \(0.01\).
- Moving the decimal point two places to the right (Option 2) is equivalent to multiplying by \(100\), which is also incorrect.
- Dividing the percent by \(100\) (Option 3) matches our definition \(\frac{x}{100}\), making this method correct.
- Moving the decimal point two places to the left (Option 4) is a standard arithmetic shortcut for dividing by \(100\). Since moving a digit one place to the right relative to the decimal point corresponds to multiplying by \(10\), moving it two places to the left corresponds to dividing by \(10^2 = 100\). Thus, this method is also correct.
- Conclusion
Based on the evaluation, the valid ways to convert a percent to a decimal are dividing by \(100\) and moving the decimal point two places to the left. Therefore, the correct statements are the third and fourth options. In summary, for any value \(x\%\), the decimal form is \(\frac{x}{100}\). This is achieved by either direct division or by shifting the decimal point two positions to the left. Both of these operations are valid and yield the same result. The final answer includes the two correct methods.
Examples
Imagine you are calculating the tip for a restaurant bill. If the tip percentage is \(15\%\), you can calculate the decimal value by moving the decimal point in \(15.0\) two places to the left, resulting in \(0.15\). You then multiply the bill amount by this decimal to find the tip. Understanding this conversion is essential for quick mental math and accurate financial calculations in daily life, such as applying discounts, calculating interest rates, or adjusting recipe measurements.