represent each of the following to three significant figures and express each answer in SI units using an appropriate prefix:
a)1568(10^5)mm
b)0.005 63 mg
a)1.57 x 10^5 m
b)5.63 x 10^-9 kg
a) To express 1568(10^5) mm to three significant figures, we need to simplify the number and convert it to SI units with an appropriate prefix.
First, let's convert 1568 mm to meters by dividing by 1000:
1568 mm ÷ 1000 = 1.568 m
Next, let's express 10^5 in scientific notation:
10^5 = 100,000
Finally, multiplying 1.568 m by 100,000 gives us the final answer:
1.568 m × 100,000 = 156,800 m
To express the answer in SI units with an appropriate prefix, we'll use the kilo (k) prefix, which represents a thousand. So the answer is:
156.8 kM
b) Similarly, to express 0.005 63 mg to three significant figures and SI units, we need to convert the number to grams and use an appropriate prefix.
First, let's convert 0.00563 mg to grams by dividing by 1000:
0.00563 mg ÷ 1000 = 0.00000563 g
Next, let's express the answer using an appropriate prefix. In this case, the micro (µ) prefix represents a millionth. So the answer is:
5.63 µg