Question

the movement of the progress bar may be uneven because qu more or less (including zero) depending on your answer. divide: 32.068 ÷ 0.2 160.34 1, 603.4 1.6034 16, 034

Explanation:

Step1: Convert divisor to integer

To divide by a decimal, we can move the decimal point of the divisor (0.2) to the right until it becomes an integer. So, 0.2 becomes 2 (we moved the decimal point 1 place to the right). We must do the same to the dividend (32.068), moving its decimal point 1 place to the right, which gives us 320.68.

Step2: Perform the division

Now we divide 320.68 by 2.
$320.68\div2 = 160.34$? Wait, no, wait. Wait, 320.68 divided by 2: 2 goes into 3 once (1), 2 into 12 six times (6), 2 into 0 zero, 2 into 6 three times (3), 2 into 8 four times (4). Wait, no, 320.68 divided by 2: 320 divided by 2 is 160, 0.68 divided by 2 is 0.34. So 160 + 0.34 = 160.34? Wait, no, wait, the original dividend after moving the decimal was 320.68? Wait, no, 32.068 with decimal moved 1 place right is 320.68? Wait, 32.068 * 10 = 320.68, and 0.2 * 10 = 2. So now we have 320.68 ÷ 2. Let's do the division: 2 into 3 is 1, remainder 1. Bring down 2: 12, 2 into 12 is 6. Bring down 0: 2 into 0 is 0. Bring down 6: 2 into 6 is 3. Bring down 8: 2 into 8 is 4. So we get 160.34? Wait, but wait, 0.2 times 160.34 is 32.068? Let's check: 160.34 * 0.2. 160 * 0.2 = 32, 0.34 * 0.2 = 0.068. So 32 + 0.068 = 32.068. Yes, that's correct. Wait, but wait, the options include 1,603.4. Wait, did I make a mistake in moving the decimal? Wait, 0.2 is one decimal place, so we multiply numerator and denominator by 10: (32.068 * 10) / (0.2 * 10) = 320.68 / 2 = 160.34? But wait, 32.068 divided by 0.2: another way, dividing by 0.2 is the same as multiplying by 5 (since 1/0.2 = 5). So 32.068 * 5. Let's calculate that: 32 * 5 = 160, 0.068 * 5 = 0.34. So 160 + 0.34 = 160.34. Wait, but the option 1,603.4 is there. Wait, maybe I messed up the decimal movement. Wait, 0.2 is one decimal place, so we need to move the decimal of the divisor 1 place, so divisor becomes 2, dividend becomes 320.68? Wait, no, 32.068 has three decimal places? Wait, 32.068: the decimal is after 32, so moving one place right: 320.68 (correct, because 32.068 * 10 = 320.68). Then 320.68 ÷ 2. Wait, 320.68 divided by 2: 320 divided by 2 is 160, 0.68 divided by 2 is 0.34, so total 160.34. But let's check 0.2 * 1603.4: 1603.4 * 0.2 = 320.68. Oh! Wait a minute! I see my mistake. I moved the decimal of the dividend only 1 place, but 32.068 * 10 is 320.68, but 0.2 * 10 is 2. But 32.068 ÷ 0.2 is the same as (32.068 * 10) ÷ (0.2 * 10) = 320.68 ÷ 2? Wait, no, that's not right. Wait, 0.2 is 2 tenths, so dividing by 2 tenths is the same as multiplying by 5 (since 1 / (2/10) = 10/2 = 5). So 32.068 * 5. Let's calculate 32.068 * 5: 32 * 5 = 160, 0.068 * 5 = 0.34, so 160 + 0.34 = 160.34? But 0.2 * 1603.4 = 320.68, which is 10 times 32.068. Wait, I see the mistake! Oh no, I moved the decimal of the dividend 1 place, but 0.2 is one decimal place, so we need to move the decimal of the dividend one place to the right, making it 320.68? Wait, no, 32.068 with decimal moved one place right is 320.68? Wait, 32.068 * 10 = 320.68, and 0.2 * 10 = 2. So 320.68 ÷ 2. But 320.68 ÷ 2 is 160.34, but 0.2 * 1603.4 = 320.68, which is 10 times 32.068. Wait, I think I messed up the number of decimal places. Wait, 0.2 is 1 decimal place, so we multiply numerator and denominator by 10^1 = 10. So (32.068 * 10) / (0.2 * 10) = 320.68 / 2 = 160.34. But let's check with another method. 32.068 ÷ 0.2. Let's write this as 32.068 / 0.2. Multiply numerator and denominator by 1000 to eliminate all decimals: (32.068 * 1000) / (0.2 * 1000) = 32068 / 200. Now simplify 32068 ÷ 200. Divide numerator and denominator by 4: 8017 / 50 = 160.34. Yes, that's correct. So the answer is 160.34? Wait, but the option is 160.34? Wait, the first option is 160.34, the second is 1,603.4. Wait, maybe I made a mistake in the decimal movement. Wait, 0.2 is 2 tenths, so dividing by 2 tenths is the same as multiplying by 5. So 32.068 * 5: 32 * 5 = 160, 0.068 * 5 = 0.34, so 160.34. So the correct answer is 160.34, which is the first option. Wait, but let's check 0.2 * 1603.4: 1603.4 * 0.2 = 320.68, which is 10 times 32.068. So that would be if we moved the decimal two places, but we only needed to move one. So my initial calculation was correct. So the answer is 160.34.

Answer:

A. 160.34