1. Convert 0.8671875 to base 8 and base 16.
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Here are the conversions for each number:
1. Convert $0.8671875$ to base 8 and base 16.
To Base 8:
Step 1: Multiply the fractional part by 8.
$$0.8671875 \times 8 = 6.9375$$
The integer part is 6. The new fractional part is $0.9375$.
Step 2: Multiply the new fractional part by 8.
$$0.9375 \times 8 = 7.5$$
The integer part is 7. The new fractional part is $0.5$.
Step 3: Multiply the new fractional part by 8.
$$0.5 \times 8 = 4.0$$
The integer part is 4. The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
Reading the integer parts from top to bottom gives the base 8 representation.
$$0.8671875_{10} = \boxed{0.674_8}$$
To Base 16:
Step 1: Multiply the fractional part by 16.
$$0.8671875 \times 16 = 13.875$$
The integer part is 13 (which is D in hexadecimal). The new fractional part is $0.875$.
Step 2: Multiply the new fractional part by 16.
$$0.875 \times 16 = 14.0$$
The integer part is 14 (which is E in hexadecimal). The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
Reading the integer parts from top to bottom gives the base 16 representation.
$$0.8671875_{10} = \boxed{0.\text{DE}_{16}}$$
2. Convert $0.53515625$ to base 8 and base 16.
To Base 8:
Step 1: Multiply the fractional part by 8.
$$0.53515625 \times 8 = 4.28125$$
The integer part is 4. The new fractional part is $0.28125$.
Step 2: Multiply the new fractional part by 8.
$$0.28125 \times 8 = 2.25$$
The integer part is 2. The new fractional part is $0.25$.
Step 3: Multiply the new fractional part by 8.
$$0.25 \times 8 = 2.0$$
The integer part is 2. The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
$$0.53515625_{10} = \boxed{0.422_8}$$
To Base 16:
Step 1: Multiply the fractional part by 16.
$$0.53515625 \times 16 = 8.5625$$
The integer part is 8. The new fractional part is $0.5625$.
Step 2: Multiply the new fractional part by 16.
$$0.5625 \times 16 = 9.0$$
The integer part is 9. The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
$$0.53515625_{10} = \boxed{0.89_{16}}$$
3. Convert $0.626953125$ to base 8 and base 16.
To Base 8:
Step 1: Multiply the fractional part by 8.
$$0.626953125 \times 8 = 5.015625$$
The integer part is 5. The new fractional part is $0.015625$.
Step 2: Multiply the new fractional part by 8.
$$0.015625 \times 8 = 0.125$$
The integer part is 0. The new fractional part is $0.125$.
Step 3: Multiply the new fractional part by 8.
$$0.125 \times 8 = 1.0$$
The integer part is 1. The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
$$0.626953125_{10} = \boxed{0.501_8}$$
To Base 16:
Step 1: Multiply the fractional part by 16.
$$0.626953125 \times 16 = 10.03125$$
The integer part is 10 (which is A in hexadecimal). The new fractional part is $0.03125$.
Step 2: Multiply the new fractional part by 16.
$$0.03125 \times 16 = 0.5$$
The integer part is 0. The new fractional part is $0.5$.
Step 3: Multiply the new fractional part by 16.
$$0.5 \times 16 = 8.0$$
The integer part is 8. The new fractional part is $0.0$.
Since the fractional part is 0, we stop.
$$0.626953125_{10} = \boxed{0.\text{A08}_{16}}$$
