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2. The drachm, a Polish measure of mass, is equivalent to 15 other Polish units called denarii. A drachm is also approximately equal to 12.27 grams. Based on these relationships, to the nearest hundredth, 49 denarii are equivalent to how many decagrams? (10 grams = 1 decagram)

Sagot :

Let's solve this problem step by step.

1. Understanding the relationships:
- 1 drachm is equivalent to 15 denarii.
- 1 drachm is equivalent to approximately 12.27 grams.
- 10 grams are equivalent to 1 decagram.

2. Convert denarii to drachms:
- We are given 49 denarii.
- To find out how many drachms this is equivalent to, we divide the number of denarii by the number of denarii per drachm.

[tex]\[ \text{Drachms} = \frac{\text{Denarii}}{\text{Denarii per Drachm}} = \frac{49}{15} \approx 3.2667 \ \text{(rounded to 4 decimal places for intermediate values)} \][/tex]

3. Convert drachms to grams:
- We have approximately 3.2667 drachms.
- To find out how many grams this equates to, we multiply the number of drachms by the number of grams per drachm.

[tex]\[ \text{Grams} = \text{Drachms} \times \text{Grams per Drachm} = 3.2667 \times 12.27 \approx 40.082 \ \text{grams} \][/tex]

4. Convert grams to decagrams:
- We have approximately 40.082 grams.
- To find out how many decagrams this equates to, we divide the number of grams by the number of grams per decagram.

[tex]\[ \text{Decagrams} = \frac{\text{Grams}}{\text{Grams per Decagram}} = \frac{40.082}{10} \approx 4.0082 \][/tex]

5. Round to the nearest hundredth:
- We need to round the number of decagrams to the nearest hundredth.

[tex]\[ \text{Decagrams (rounded)} = 4.01 \][/tex]

Therefore, 49 denarii are approximately equivalent to 4.01 decagrams when rounded to the nearest hundredth.
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