To solve the equation 493 × 3432 × 1 and express each side in terms of base, we can start by simplifying the equation step by step.
The given equation can initially be simplified because multiplying by 1 does not change the value. Therefore, we can focus on simplifying 493 × 3432.
First, let’s perform the multiplication:
- 493 × 3432 = 169,596
Now, we have simplified our equation to 169,596.
Next, we can express 169,596 in terms of a base. The most commonly used bases are 10 (decimal), 2 (binary), and even 16 (hexadecimal). Let’s express this number in base 10:
- In base 10, 169,596 is simply 169,596.
If we want to express this in another base, we might choose binary (base 2). To convert 169,596 to binary:
- Divide 169,596 by 2 and note the quotient and the remainder.
- Continue dividing the quotient by 2 until the quotient is 0.
- The binary representation is found by reading the remainders from bottom to top.
After performing these calculations, 169,596 in binary is 10000101110110101100.
So, to summarize:
- The left side of the equation is 493 × 3432 × 1, which simplifies to 169,596.
- In base 10, it is 169,596.
- In binary (base 2), it is 10000101110110101100.
This process can be applied similarly if you want to explore other bases, such as base 16, where you would convert the decimal number to hexadecimal.
By understanding how to express numbers in different bases, you gain a clearer perspective on number representation in mathematics.