Final answer:
To express 0.00513 mg between 0.1 and 1000, we convert it to micrograms, resulting in 5.13 µg, which satisfies the specified range.
Step-by-step explanation:
To represent 0.00513 mg as a number between 0.1 and 1000 using an appropriate prefix, we must first understand the metric prefixes and their corresponding powers of ten. Since 1 milligram (mg) is equal to 10-3 grams (g), we can express 0.00513 mg in grams as 0.00513 x 10-3 g. However, we need to find a prefix that scales this value into the desired range.
Remembering the powers of ten, micrograms (µg) are equal to 10-6 grams, so we can convert milligrams to micrograms by multiplying by 103 (since -3 minus -6 equals 3). Therefore, 0.00513 mg is equivalent to 0.00513 x 103 µg, or 5.13 µg, which lies between 0.1 and 1000.