Okay, so I need to convert the fraction 57/160 into a terminating decimal. Hmm, let me think about how to do this. I remember that a fraction will convert to a terminating decimal if its denominator, after simplifying the fraction, has no prime factors other than 2 or 5. So first, I should check if 57/160 is already in its simplest form. Let's see, 57 and 160. The factors of 57 are 3 and 19, right? Because 3 times 19 is 57. And 160 is 16 times 10, which is 2^5 * 5. So the denominator is 2^5 * 5, and the numerator is 3*19. There are no common factors between 57 and 160, so the fraction is already simplified. That means the denominator is 2^5 * 5, which fits the criteria for a terminating decimal. Cool, so the decimal will terminate.

Now, how do I convert 57 divided by 160 into a decimal? I can do long division. Let me try that. So 160 goes into 57 zero times. We add a decimal point and a zero, making it 570. How many times does 160 go into 570? Let's see, 160 times 3 is 480, and 160 times 4 is 640, which is too big. So 3 times. 3 times 160 is 480. Subtract that from 570, we get 90. Bring down another zero, making it 900. How many times does 160 go into 900? 160 times 5 is 800, 160 times 6 is 960, which is too big. So 5 times. 5 times 160 is 800. Subtract from 900, we get 100. Bring down another zero, making it 1000. 160 goes into 1000 six times because 160*6=960. Subtract 960 from 1000, we have 40. Bring down another zero, making it 400. 160 goes into 400 exactly 2.5 times, but since we can't have a decimal here, wait, no. Wait, 160*2=320. Subtract 320 from 400, we get 80. Bring down another zero, making it 800. 160 goes into 800 exactly 5 times. So now, putting it all together:

0.
3 (from 160 into 570)
5 (from 160 into 900)
6 (from 160 into 1000)
2 (from 160 into 400)
5 (from 160 into 800)

Wait, but let me check the steps again because I might have messed up the remainders. Let's go step by step.

57 divided by 160: 160 doesn't go into 57, so we write 0. Then add a decimal point and a zero, making it 570.

160 into 570: 3 times (3*160=480). Subtract 480 from 570: 90. Bring down a zero to make 900.

160 into 900: 5 times (5*160=800). Subtract 800 from 900: 100. Bring down a zero to make 1000.

160 into 1000: 6 times (6*160=960). Subtract 960 from 1000: 40. Bring down a zero to make 400.

160 into 400: 2 times (2*160=320). Subtract 320 from 400: 80. Bring down a zero to make 800.

160 into 800: 5 times (5*160=800). Subtract 800 from 800: 0. So done.

Putting the digits together after the decimal: 3, 5, 6, 2, 5. So the decimal is 0.35625. Let me verify that. Let's check 0.35625 multiplied by 160.

0.35625 * 160: 0.35625 * 100 = 35.625, 0.35625 * 60 = 21.375. So 35.625 + 21.375 = 57. Exactly. So that's correct. Therefore, 57/160 is 0.35625 as a decimal. So the answer is 0.35625. Wait, but the question says "convert to a terminating decimal." So that's already done. So the final answer is 0.35625. Let me just check once more with another method. Maybe using prime factors.

Since the denominator is 160, which is 2^5 * 5. To convert to decimal, we can multiply numerator and denominator by 5^3 to make the denominator 10^5. Wait, let's see. Wait, 160 is 2^5 * 5. To make it 10^n, we need to have denominator as 2^n * 5^n. So current denominator is 2^5 * 5. To make it 10^5, we need to multiply numerator and denominator by 5^4. Wait, 10^5 is 2^5 * 5^5. So denominator is 2^5 *5, so we need to multiply by 5^4 to get 5^5. Then denominator becomes 10^5, which is 100000. Then numerator is 57 * 5^4. Let's compute that.

5^4 is 625. So 57 * 625. Let's compute 57*600 = 34200, 57*25=1425. So total is 34200 +1425=35625. So numerator is 35625, denominator is 100000. So 35625/100000 is 0.35625. Yep, same result. So that's correct. So 57/160 is 0.35625 as a terminating decimal. Therefore, the answer is 0.35625. I think that's correct. Let me do another check. 0.35625 * 160. Let's compute 0.35625 * 160. 0.35625 * 100 = 35.625, 0.35625 * 60 = 21.375. 35.625 + 21.375 = 57. Correct. So yes, the answer is 0.35625. Therefore, the final answer is 0.35625, which as a fraction is 35625/100000, simplifying to 57/160. Therefore, the decimal is 0.35625.
Therefore, $\frac{57}{160}$ as a terminating decimal is $\boxed{0.35625}$.
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