Sure, let's solve the problem step-by-step.
Given:
- The weight of an adult blue whale is about 199 metric tons.
- 1 metric ton = 1000 kilograms (kg).
### Part (a)
Write the weight of the blue whale in kilograms.
Step:
1. Convert the weight from metric tons to kilograms.
2. Since 1 metric ton = 1000 kg, multiply the weight in metric tons by 1000.
Calculation:
[tex]\[ \text{Weight in kilograms} = 199 \text{ metric tons} \times 1000 \text{ kg/metric ton} = 199,000 \text{ kg} \][/tex]
So, the weight of the blue whale in kilograms is 199,000 kg.
### Part (b)
Express the weight in kilograms in scientific notation.
Step:
1. Convert 199,000 kg to scientific notation.
2. Scientific notation is of the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
Calculation:
[tex]\[ 199,000 \text{ kg} = 1.99 \times 10^5 \text{ kg} \][/tex]
So, the weight in kilograms in scientific notation is [tex]\( 1.99 \times 10^5 \)[/tex] kg.
### Part (c)
Convert the weight to grams and express it in scientific notation.
Step:
1. Convert the weight from kilograms to grams.
2. Since 1 kilogram = 1000 grams, multiply the weight in kilograms by 1000.
3. Then, convert the weight in grams to scientific notation.
Calculation:
[tex]\[ \text{Weight in grams} = 199,000 \text{ kg} \times 1000 \text{ g/kg} = 199,000,000 \text{ g} \][/tex]
Now, express 199,000,000 grams in scientific notation:
[tex]\[ 199,000,000 \text{ g} = 1.99 \times 10^8 \text{ g} \][/tex]
So, the weight in grams is [tex]\( 1.99 \times 10^8 \)[/tex] g.
### Summary:
1. The weight of the blue whale in kilograms is 199,000 kg.
2. The weight in kilograms in scientific notation is [tex]\( 1.99 \times 10^5 \)[/tex] kg.
3. The weight in grams is [tex]\( 1.99 \times 10^8 \)[/tex] g.
