Question

divide
19\overline{)38.57}

Explanation:

Step1: Divide 38 by 19

Since \( 19\times2 = 38 \), we write 2 above the 8 in 38.57. So, the first digit of the quotient is 2.

Step2: Bring down the decimal and the next digit

Now, we bring down the 5 (after the decimal). The number becomes 0.5 (because 38 - 38 = 0, and we bring down the 5). But we are dividing by 19, and 19 goes into 5 zero times. So we write 0 next to the 2, making it 2.0.

Step3: Bring down the 7

Now we bring down the 7, so the number we have is 57 (since we had 0.5 and now bring down 7, it's 5.7? Wait, no. Wait, let's correct. After 38 divided by 19 is 2, with remainder 0. Then we bring down the 5 (the tenths place), so we have 0.5 (since the remainder is 0, and we're now looking at the decimal part). But 19 doesn't go into 5, so we put a 0 in the tenths place of the quotient. Then we bring down the 7 (the hundredths place), so now we have 57 (because 0.5 becomes 5.7? Wait, no, when dividing decimals, we can think of 38.57 as 3857 hundredths. So \( 38.57\div19=\frac{3857}{100}\div19=\frac{3857}{100\times19}\). But maybe better to do long division step by step.

Wait, let's start over. The dividend is 38.57, divisor is 19.

• 19 goes into 38 two times (19*2=38). Subtract 38 from 38, we get 0.
• Now, bring down the 5 (the tenths place). So we have 0.5 (since the remainder is 0, and we're now at the tenths place). 19 goes into 5 zero times. So we write 0 in the tenths place of the quotient.
• Now, bring down the 7 (the hundredths place). So now we have 57 (because we had 0.5 and now bring down 7, making it 5.7? Wait, no, when we bring down the 7, we have 57 (as in 57 hundredths? Wait, no, the decimal is 38.57, so after 38, we have.57, which is 5 tenths and 7 hundredths. So after dividing 38 by 19 (getting 2), we have a remainder of 0, then we bring down the 5 (tenths place), so we have 0.5 (since the remainder is 0, and we're now dealing with the decimal part). Since 19 doesn't go into 5, we put 0 in the tenths place, then bring down the 7 (hundredths place), so now we have 57 (as 5 tenths and 7 hundredths is 57 hundredths). Now, 19 goes into 57 three times (19*3=57). So we write 3 in the hundredths place of the quotient.

So putting it all together: 2 (units place), 0 (tenths place), 3 (hundredths place). Wait, but let's check: 192.03 = 192 + 19*0.03 = 38 + 0.57 = 38.57. Yes! So \( 38.57\div19 = 2.03 \).

Wait, let's do the long division properly:

    2.03
  _______
19|38.57
   38
   ---
    0.57
    0
    ---
    57
    57
    ---
     0

So step by step:

1. 19 into 38: 2, 2*19=38, subtract 38-38=0.
2. Bring down the 5 (after the decimal), now we have 0.5 (since remainder is 0, and we're at the tenths place). 19 into 5: 0, 0*19=0, subtract 5-0=5.
3. Bring down the 7, now we have 57 (since we had 5 tenths and now bring down 7 hundredths, making 57 hundredths). 19 into 57: 3, 3*19=57, subtract 57-57=0.

So the quotient is 2.03.

Answer:

\( 2.03 \)