Practice exercise 1
Convert the following masses into kilograms.
a) [tex]$58475 \mu g$[/tex]
b) 406 dg
e) 945 Dg
f) 1854 mg
i) 40500 g

Express the following masses into decigram.

Convert micrograms to kilograms: 58475 μg = 0.000058475 k g
Convert decigrams to kilograms: 406 d g = 0.0406 k g
Convert decagrams to kilograms: 945 D g = 9.45 k g
Convert milligrams to kilograms: 1854 m g = 0.001854 k g
Convert grams to kilograms: 40500 g = 40.5 k g
Convert micrograms to decigrams: 58475 μg = 0.58475 d g
Convert decagrams to decigrams: 945 D g = 9450 d g
Convert milligrams to decigrams: 1854 m g = 18.54 d g
Convert grams to decigrams: 40500 g = 405000 d g
The mass 406 dg remains the same in decigrams: 406 d g ​

Explanation

Problem Analysis We are asked to convert several masses into kilograms and express them in decigrams. Let's tackle the kilogram conversions first.

Micrograms to Kilograms a) Convert 58475 μg to kg: To convert micrograms ( μg ) to kilograms (kg), we need to remember that 1 g = 1 0 6 μg and 1 k g = 1000 g = 1 0 3 g . Therefore, 1 k g = 1 0 9 μg .
58475 μg = 58475 × 1 0 − 9 k g = 0.000058475 k g

Decigrams to Kilograms b) Convert 406 d g to kg: To convert decigrams (dg) to kilograms (kg), we need to remember that 1 g = 10 d g and 1 k g = 1000 g . Therefore, 1 k g = 10000 d g .
406 d g = 10000 406 ​ k g = 0.0406 k g

Decagrams to Kilograms e) Convert 945 D g to kg: To convert decagrams (Dg) to kilograms (kg), we need to remember that 1 D g = 10 g and 1 k g = 1000 g . Therefore, 1 k g = 100 D g .
945 D g = 1000 945 × 10 ​ k g = 9.45 k g

Milligrams to Kilograms f) Convert 1854 m g to kg: To convert milligrams (mg) to kilograms (kg), we need to remember that 1 g = 1000 m g and 1 k g = 1000 g . Therefore, 1 k g = 1 0 6 m g .
1854 m g = 1 0 6 1854 ​ k g = 0.001854 k g

Grams to Kilograms i) Convert 40500 g to kg: To convert grams (g) to kilograms (kg), we need to remember that 1 k g = 1000 g .
40500 g = 1000 40500 ​ k g = 40.5 k g

Micrograms to Decigrams Now, let's express the given masses in decigrams (dg). Since the problem does not specify which masses to convert, we will convert all the original masses to decigrams. a) 58475 μg to dg: 1 g = 1 0 6 μg and 1 g = 10 d g . Therefore, 10 d g = 1 0 6 μg .
58475 μg = 1 0 6 58475 ​ × 10 d g = 0.58475 d g

Decigrams to Decigrams b) 406 d g is already in decigrams, so 406 d g = 406 d g .

Decagrams to Decigrams e) 945 D g to dg: 1 D g = 10 g and 1 g = 10 d g . Therefore, 1 D g = 100 d g .
945 D g = 945 × 100 d g = 94500 d g

Milligrams to Decigrams f) 1854 m g to dg: 1 g = 1000 m g and 1 g = 10 d g . Therefore, 10 d g = 1000 m g .
1854 m g = 1000 1854 ​ × 10 d g = 18.54 d g

Grams to Decigrams i) 40500 g to dg: 1 g = 10 d g .
40500 g = 40500 × 10 d g = 405000 d g

Final Results In summary: Kilogram conversions: a) 58475 μg = 0.000058475 k g b) 406 d g = 0.0406 k g e) 945 D g = 9.45 k g f) 1854 m g = 0.001854 k g i) 40500 g = 40.5 k g


Decigram conversions: a) 58475 μg = 0.58475 d g b) 406 d g = 406 d g e) 945 D g = 9450 d g f) 1854 m g = 18.54 d g i) 40500 g = 405000 d g
Examples
Understanding unit conversions is crucial in many real-world applications. For instance, when cooking, you might need to convert grams to milligrams to accurately measure spices. In construction, converting decagrams to kilograms helps in calculating the weight of materials. In medicine, precise conversions between micrograms and grams are essential for drug dosages, ensuring patient safety. These conversions enable accurate measurements and facilitate effective communication across various fields.

Answered by GinnyAnswer | 2025-07-03

We converted various masses into kilograms and then expressed them in decigrams, accurately following metric conversion conventions.
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Answered by Anonymous | 2025-07-04