Use long division to convert 2 7/16 to a decimal.
A. 2.2857
B. 0.4375
C. 2.716
D. 2.4375
The correct answer is D. 2.4375.
To convert 2 7/16 to a decimal using long division, follow these steps:
1. Write the mixed number as an improper fraction.
2 7/16 = (2 * 16 + 7)/16 = 39/16
2. Perform long division of 39 by 16:
2.4375
__________
16 | 39
-32
_______
70
-64
______
60
-48
______
120
-112
______
80
-80
______
0
The division completely ends without any remainder. The quotient is 2.4375.
To convert the mixed number 2 7/16 to a decimal using long division, follow these steps:
1. Write the mixed number as a fraction: 2 7/16 = (2 * 16 + 7) / 16 = 39/16.
2. Set up the long division problem with the numerator (39) inside the division symbol and the denominator (16) outside the division symbol, like this:
2.4375
___________
16 | 39
3. Begin the long division by dividing the first digit of the numerator (3) by the denominator (16). The result is the whole number part of the decimal. In this case, 3 divided by 16 is 0. The decimal will start with 0.
2.4375
___________
16 | 39
0
4. Bring down the next digit from the numerator, which is 9, and place it to the right of the remainder. This gives you 9 as the new dividend.
2.4375
___________
16 | 39
09
5. Divide the new dividend (9) by the denominator (16). Since 9 is smaller than 16, add a decimal point to the result from step 3 and divide as you would with decimals. Place a 0 in the quotient and multiply the divisor (16) by 0, then subtract from the dividend (9).
2.4375
___________
16 | 39
09
-00
6. Bring down the next digit from the numerator, which is 0 in this case. Place it to the right of the previous remainder.
2.4375
___________
16 | 39
090
7. Divide the new dividend (90) by the denominator (16). This time, 90 is larger than 16, so we continue the long division.
2.4375
___________
16 | 39
090
- 80
8. Bring down the next digit from the numerator, which is 0 in this case. Place it to the right of the previous remainder.
2.4375
___________
16 | 39
0900
9. Divide the new dividend (900) by the denominator (16).
2.4375
___________
16 | 39
0900
- 0800
10. Bring down the next digit from the numerator, which is 0 in this case. Place it to the right of the previous remainder.
2.4375
___________
16 | 39
09000
11. Divide the new dividend (9000) by the denominator (16).
2.4375
___________
16 | 39
09000
- 08000
12. Bring down the next digit from the numerator, which is 0 in this case. Place it to the right of the previous remainder.
2.4375
___________
16 | 39
090000
13. Divide the new dividend (90000) by the denominator (16).
2.4375
___________
16 | 39
09000
- 08000
01000
14. Continue bringing down zeros and dividing until the remainder becomes zero:
2.4375
___________
16 | 39
09000
- 08000
01000
- 01000
0000
15. The long division is complete when the remainder becomes zero. The quotient is 2.4375.
Therefore, the correct answer is D. 2.4375.
To convert 2 7/16 to a decimal using long division, you would divide the numerator (the top number) of the fraction by the denominator (the bottom number). Here's how you can do it step by step:
Step 1: Convert the whole number part to a fraction.
Since 2 is the whole number part of the mixed number, you can write it as 2/1.
Step 2: Add the fraction form of the mixed number to the fraction part.
Add 2/1 to 7/16. To do this, you need to find a common denominator for both fractions, which in this case is 16. Rewriting the fractions with a common denominator, you have 2/1 + 7/16 = 32/16 + 7/16 = 39/16.
Step 3: Perform the long division.
Divide the numerator (39) by the denominator (16) using long division.
```
2.4375
_______
16|39.0000
-32
---
70
-64
---
60
-48
---
120
-112
----
80
```
Step 4: Read the quotient as the decimal.
The quotient of the long division is 2.4375.
Therefore, the decimal form of 2 7/16 is 2.4375 (D).