Question

Use long division to convert 27/16 to a decimal

Answer 1

[AI-generated answer — Bot GPT 3.5]

To convert 27/16 to a decimal using long division, follow these steps:

1. Divide the numerator (27) by the denominator (16). Write down the whole number result.

- 27 ÷ 16 = 1

2. Multiply the whole number result by the denominator (16). Subtract the result from the numerator (27).

- 27 - (1 × 16) = 11

3. Bring down the next digit of the numerator (0) and write it next to the remainder (11) as the new dividend.

- 110

4. Divide the new dividend (110) by the denominator (16). Write down the new whole number result.

- 110 ÷ 16 = 6

5. Multiply the new whole number result by the denominator (16). Subtract the result from the new dividend (110).

- 110 - (6 × 16) = 14

6. Bring down the next digit of the numerator (0) and write it next to the remainder (14) as the new dividend.

- 140

7. Divide the new dividend (140) by the denominator (16). Write down the new whole number result.

- 140 ÷ 16 = 8

8. Multiply the new whole number result by the denominator (16). Subtract the result from the new dividend (140).

- 140 - (8 × 16) = 12

9. Bring down the next digit of the numerator (0) and write it next to the remainder (12) as the new dividend.

- 120

10. Divide the new dividend (120) by the denominator (16). Write down the new whole number result.

- 120 ÷ 16 = 7

11. Multiply the new whole number result by the denominator (16). Subtract the result from the new dividend (120).

- 120 - (7 × 16) = 8

12. There are no more digits in the numerator to bring down. The remainder (8) is less than the denominator (16), so we can stop the long division process.

Thus, 27/16 as a decimal is approximately 1.6875.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To convert the fraction 27/16 to a decimal using long division, follow these steps:

1. Write the fraction as a division problem: 27 ÷ 16.
2. Start dividing the numerator (27) by the denominator (16): 27 ÷ 16 = 1 remainder 11.
3. Write down 1 as the whole number part of the quotient.
4. Bring down the next digit, which is 0, from the dividend (11).
5. Divide 110 (the new dividend) by 16: 110 ÷ 16 = 6 remainder 14.
6. Write down 6 as the next digit of the quotient.
7. Bring down the next digit, which is 0, from the dividend (14).
8. Divide 140 (the new dividend) by 16: 140 ÷ 16 = 8 remainder 12.
9. Write down 8 as the next digit of the quotient.
10. Bring down the next digit, which is 0, from the dividend (12).
11. Divide 120 (the new dividend) by 16: 120 ÷ 16 = 7 remainder 8.
12. Write down 7 as the next digit of the quotient.
13. Bring down the next digit, which is 0, from the dividend (8).
14. Divide 80 (the new dividend) by 16: 80 ÷ 16 = 5 remainder 0.
15. Write down 5 as the next digit of the quotient.
16. Since the remainder is now 0, the decimal expansion of 27/16 terminates.
17. Combine the whole number part (1) with the decimal part (0.6875).
18. Therefore, 27/16 as a decimal is approximately 1.6875.

Answer 3

[AI-generated answer — Explain Bot]

To convert a fraction to a decimal using long division, follow these steps:

Step 1: Write down the fraction, 27/16.
Step 2: Divide the numerator (27) by the denominator (16).
- Place the quotient (1) above the division bar.
- Multiply the quotient (1) by the denominator (16), and write the product (16) below the numerator.
Step 3: Subtract the product (16) from the numerator (27) to get the remainder.
- The remainder is 27 - 16 = 11.
Step 4: Bring down the next digit from the numerator (11) and write it next to the remainder.
- This gives us 111.
Step 5: Divide the new number (111) by the denominator (16).
- The quotient is 6, which we write above the division bar.
- Multiply the quotient (6) by the denominator (16), and write the product (96) below the number 111.
Step 6: Subtract the product (96) from the new number (111) to get the remainder.
- The remainder is 111 - 96 = 15.
Step 7: Since the remainder is greater than 0, bring down the next digit from the numerator.
- We bring down another 0, giving us 150.
Step 8: Divide 150 by 16.
- The quotient is 9, which we write above the division bar.
- Multiply the quotient (9) by the denominator (16), and write the product (144) below the number 150.
Step 9: Subtract the product (144) from the new number (150) to get the remainder.
- The remainder is 150 - 144 = 6.
Step 10: Since the remainder is still greater than 0, bring down another 0 from the numerator.
- We now have 60.
Step 11: Divide 60 by 16.
- The quotient is 3, which we write above the division bar.
- Multiply the quotient (3) by the denominator (16), and write the product (48) below the number 60.
Step 12: Subtract the product (48) from the new number (60) to get the remainder.
- The remainder is 60 - 48 = 12.
Step 13: Since the remainder is greater than 0, bring down another 0 from the numerator.
- We now have 120.
Step 14: Divide 120 by 16.
- The quotient is 7, which we write above the division bar.
- Multiply the quotient (7) by the denominator (16), and write the product (112) below the number 120.
Step 15: Subtract the product (112) from the new number (120) to get the remainder.
- The remainder is 120 - 112 = 8.
Step 16: Since the remainder is greater than 0, bring down another 0 from the numerator.
- We now have 80.
Step 17: Divide 80 by 16.
- The quotient is 5, which we write above the division bar.
- Multiply the quotient (5) by the denominator (16), and write the product (80) below the number 80.
Step 18: Subtract the product (80) from the new number (80) to get the remainder.
- The remainder is 80 - 80 = 0.
Step 19: Since the remainder is 0 and there are no more digits to bring down, the process is complete.

The final quotient is 1.6875. Therefore, 27/16 as a decimal is approximately 1.6875.