__ Describe and explain personal strategy which could be used to determine the measurement of the circumference of a DVD using a referent for metric units.

Here's a personal strategy using a referent for metric units to determine the circumference of a DVD:<br /><br />**1. Choosing a Referent:**<br /><br />A good referent for this task would be a standard ruler or a measuring tape marked in centimeters (cm) or millimeters (mm). Most people have access to one of these. A standard credit card could also work as its length and width are fairly consistent.<br /><br />**2. Understanding the Relationship between Diameter and Circumference:**<br /><br />The key mathematical relationship we need is that the circumference (C) of a circle is equal to pi (π) multiplied by its diameter (D): C = πD. Pi (π) is approximately 3.14.<br /><br />**3. Measuring the Diameter:**<br /><br />* **Using a Ruler/Measuring Tape:** Place the ruler across the center of the DVD, making sure it passes through the widest point. Read the measurement in centimeters (or millimeters for greater precision). This is the diameter.<br />* **Using a Credit Card:** Carefully align the long edge of the credit card across the diameter of the DVD. Mark the points where the edges of the card touch the DVD. Then, measure the distance between these marks using the ruler/measuring tape. This gives you the diameter. A standard credit card is approximately 8.56 cm long. If the DVD's diameter is roughly equal to the credit card's length, you can use 8.56 cm as an *approximate* diameter.<br /><br />**4. Calculating the Circumference:**<br /><br />Once you have the diameter (D), multiply it by pi (π ≈ 3.14) to calculate the circumference (C). For example, if the diameter is 12 cm, the circumference would be approximately 12 cm * 3.14 = 37.68 cm.<br /><br />**5. Improving Accuracy:**<br /><br />* **Multiple Measurements:** Take the diameter measurement a few times and average the results to reduce error.<br />* **Smaller Units:** If using a ruler, measure in millimeters for greater precision and then convert to centimeters if needed.<br />* **String Method:** Alternatively, wrap a piece of string snugly around the circumference of the DVD. Mark the point where the string overlaps. Then, lay the string flat and measure its length with the ruler. This directly measures the circumference, bypassing the need to measure the diameter.<br /><br />**Example using a credit card as a referent (approximate):**<br /><br />Let's say the DVD's diameter is approximately the same as the length of a credit card.<br /><br />1. **Referent:** Credit card length ≈ 8.56 cm<br />2. **Diameter (D):** ≈ 8.56 cm<br />3. **Circumference (C):** C = πD ≈ 3.14 * 8.56 cm ≈ 26.88 cm<br /><br />Therefore, the approximate circumference of the DVD is 26.88 cm. Remember, this method using a credit card provides only an *estimate* because it assumes the DVD's diameter is exactly the same as the card's length. Using a ruler or the string method will provide a more accurate measurement.<br />