Use long division to convert 2 7/16 to a decimal.(1 point) Responses 0.4375 0.4375 2.4375 2.4375 2.716 2.716 2.2857 2.2857
To convert 2 7/16 to a decimal using long division, we divide 7 by 16.
```
0.4375
__________
16| 7.0000
-64
_____
40
-32
_____
80
-80
_____
0
```
Therefore, 2 7/16 is equal to 2.4375 as a decimal.
To convert 2 7/16 to a decimal using long division, follow these steps:
1. Write down the whole number, 2, as the dividend (the number being divided).
2. Multiply the denominator (16) by the whole number (2) and add the numerator (7) to get the new dividend: 16 * 2 + 7 = 39.
3. Write down the divisor (16) as the divisor (the number doing the dividing).
4. Divide the new dividend (39) by the divisor (16) and write the quotient above the division line.
- The quotient is 2, so write 2 above the division line.
5. Multiply the divisor (16) by the quotient (2) and write the product below the dividend.
- The product is 16 * 2 = 32.
6. Subtract the product (32) from the new dividend (39) to get the new remainder.
- The remainder is 39 - 32 = 7.
7. Bring down the next digit (0) from the original number.
- Write 0 next to the remainder (7) to get 70.
8. Divide the new dividend (70) by the divisor (16) and write the new quotient above the division line.
- The quotient is 4, so write 4 below the 2 in the quotient.
9. Multiply the divisor (16) by the new quotient (4) and write the product below the new dividend.
- The product is 16 * 4 = 64.
10. Subtract the product (64) from the new dividend (70) to get the new remainder.
- The remainder is 70 - 64 = 6.
11. Since there are no more digits in the original number to bring down, the division is complete.
12. The quotient is 2.4375, so the decimal representation of 2 7/16 is 2.4375.
Therefore, the correct answer is 2.4375.
To convert a mixed number like 2 7/16 to a decimal, you can use long division. Here's how you can do it:
Step 1: Write down the mixed number 2 7/16 as an improper fraction. To do this, multiply the whole number (2) by the denominator (16) and add the numerator (7). This gives us (2 * 16) + 7 = 39. So, 2 7/16 can be written as the improper fraction 39/16.
Step 2: Perform long division. Divide the numerator (39) by the denominator (16). Place the quotient (whole number) on top and the remainder inside a new division problem.
16 │ 39
-
Step 3: Divide 16 into 39. The quotient is 2 (since 2 * 16 = 32), and the remainder is 7.
16 │ 39
- 32
----
7
Step 4: Since the remainder is not zero, bring down the next digit from the numerator. In this case, the next digit is 0.
16 │ 39
- 32
-----
70
Step 5: Divide 16 into 70. The quotient is 4 (since 4 * 16 = 64), and the remainder is 6.
16 │ 39
- 32
-----
70
- 64
-----
6
Step 6: Bring down another digit if available. In this case, there are no more digits in the numerator.
Step 7: The decimal representation of 2 7/16 is obtained by combining the quotient from Step 3 (2) with the decimal representation of the remainder. This is usually done by placing a decimal point in front of the remainder and adding zeros after it.
In this case, the remainder is 6, so the decimal representation is 0.6.
Step 8: Finally, we can write the decimal representation of 2 7/16 as 2.6.
Therefore, the correct answer is 2.6.