Use long division to convert 6 7/15 to a decimal.(1 point)
1) ≈6.47
2) ≈0.46
3) 6.715
4) ≈6.14285
To convert the mixed number 6 7/15 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
Multiply the whole number (6) by the denominator (15) and add the numerator (7). Place the sum over the denominator.
6 7/15 = (6 x 15 + 7)/15 = (97/15)
Step 2: Perform the long division.
Divide the numerator (97) by the denominator (15). Write down the quotient and the remainder.
6.4
______________
15 | 97
The quotient is 6, so write down 6 as the whole number part of the decimal. The remainder is 7, which we place after the decimal point.
Step 3: Continue the long division.
Place a decimal point after the 6 and add a zero after it. Bring down the next digit (0) and divide as before.
6.47
______________
15 | 97
Divide 70 (the remainder of 7 followed by the next digit 0) by 15. This gives a quotient of 4.
Step 4: Check for repeating decimals.
The long division terminates without any repeating patterns. Therefore, the final decimal representation is 6.47.
So, according to the long division, the correct option is 1) ≈6.47.
To convert the mixed number 6 7/15 to a decimal using long division, follow these steps:
Step 1: Write the mixed number as a fraction.
6 7/15 = (6 * 15 + 7) / 15 = 97/15
Step 2: Perform long division by dividing the numerator (97) by the denominator (15).
6.47 <-- The decimal part is found here
___________
15 | 97
Step 3: Divide 15 into 97. The quotient is the whole number part of the decimal, and the remainder is the numerator of the fractional part.
6.47
___________
15 | 97
90
-----
7
Step 4: Bring down the next digit from the dividend (which is 0) and continue with the division:
6.47
___________
15 | 97
90
-----
70
Step 5: Divide 15 into 70:
6.47
___________
15 | 97
90
-----
70
-----
0
Since the remainder is now 0, the division is complete.
Step 6: The final quotient is the answer:
6 7/15 = 6.47 (approximately)
Therefore, the correct answer is option 1) ≈6.47.
To convert 6 7/15 to a decimal using long division, we set up the division as follows:
```
0. 4 6
_______________
15 | 67
```
We start by dividing 15 into 67. The quotient will be the whole number part of the mixed number.
```
0. 4 6
_______________
15 | 67
- 60
-----
7
```
Since 15 is not divisible by 7, we bring down the next digit, which is 0, and place it after the decimal point. We then divide 15 into 70.
```
0. 4 6
_______________
15 | 67
- 60
-----
7
0
```
15 goes into 70 four times. We multiply 15 by 4 and subtract the result from 70.
```
0. 4 6
_______________
15 | 67
- 60
-----
7
0
- 60
-----
10
```
Since 15 is not divisible by 10, we bring down the next digit, which is 0, and divide 15 into 100.
```
0. 4 6 4
_______________
15 | 67
- 60
-----
7
0
- 60
-----
10
0
```
15 goes into 100 six times. We multiply 15 by 6 and subtract the result from 100.
```
0. 4 6 4
_______________
15 | 67
- 60
-----
7
0
- 60
-----
10
0
- 90
-----
10
```
Since the remainder is 10, which is the same as the divisor, we know that the division is repeating. Therefore, the decimal representation for 6 7/15 is approximately 6.46.
Thus, the correct answer is option 1) ≈ 6.47.