The density of gold is 19.3 g/ml. what is gold’s density in decigrams per liter?
The Correct Answer and Explanation is:
To convert the density of gold from grams per milliliter (g/ml) to decigrams per liter (dg/L), we need to follow a series of unit conversions.
Step 1: Understand the conversion factors
- 1 g = 10 dg (since a decigram is 1/10 of a gram).
- 1 ml = 1 cm³.
- 1 liter (L) = 1000 ml.
Step 2: Convert the density of gold
We are given that the density of gold is 19.3 g/ml. Let’s break this down:
- Convert grams to decigrams:
Since 1 g = 10 dg, multiply the given density by 10: 19.3 g/ml×10=193 dg/ml19.3 \, \text{g/ml} \times 10 = 193 \, \text{dg/ml}19.3g/ml×10=193dg/ml - Convert milliliters to liters:
1 ml = 0.001 L, so to convert from milliliters to liters, multiply by 1000: 193 dg/ml×1000=193,000 dg/L193 \, \text{dg/ml} \times 1000 = 193,000 \, \text{dg/L}193dg/ml×1000=193,000dg/L
Final Result:
Thus, the density of gold in decigrams per liter (dg/L) is 193,000 dg/L.
Explanation:
We started with the given density of gold in grams per milliliter (19.3 g/ml). We converted grams to decigrams (since there are 10 decigrams in a gram) and milliliters to liters (1000 milliliters in a liter). This conversion gave us a final result of 193,000 decigrams per liter. This is a straightforward application of unit conversion principles to transform one set of measurement units into another.
