Final answer:
The decimal number 43 can be converted to binary as 101011, to octal as 53, and to hexadecimal as 2B. Understanding powers of 10 and their applications in scientific notation is essential to perform numerical system conversions.
Step-by-step explanation:
To convert the number 43 in decimal to other numerical systems, we proceed as follows:
- Binary: To convert to binary, divide the number by 2 and record the remainder. Repeat with the quotient until the quotient is zero. 43 in binary is 101011.
- Octal: To convert to octal, divide the number by 8 instead of 2 and record the remainders. 43 in octal is 53.
- Hexadecimal: For hexadecimal which is base 16, divide by 16. 43 in hexadecimal is 2B.
Understanding the power of 10 is useful in these conversions. For example, 10³ represents 1000, or 10 multiplied by itself three times. Powers of 10 are also used in scientific notation to express very large or very small numbers, such as 1.23 x 10⁹ for 1,230,000,000.
When multiplied together, powers of 10 are simply added. This applies to scientific notation as well. For instance, (4.506 × 10⁴) × (1.003 × 10²) can be calculated as 4.506 × 1.003 multiplied by 10⁴⁵².