whats 6 and 7/15 as a decimal using long division
To convert 6 and 7/15 to a decimal using long division, follow these steps:
1. Write 6 as a whole number.
2. Place the decimal point directly after the 6.
6.
3. Convert 7/15 to a decimal. To do this, divide 7 by 15 using long division:
0.4
-----------
15 | 7.00
-7.5
-----
25
-25
-----
0
The decimal equivalent of 7/15 is 0.4.
4. Append the decimal equivalent of 7/15 to the right of the decimal point:
6.4
Therefore, 6 and 7/15 as a decimal using long division is 6.4.
To convert 6 and 7/15 to a decimal using long division, follow these steps:
1. Write 6 as the whole number and 7/15 as the fraction.
Whole number: 6
Fraction: 7/15
2. Place the dividend (7) inside the long division bracket and the divisor (15) outside the bracket.
_____
15 | 7
3. Since 7 is less than 15, we can't divide it evenly. To proceed, place a decimal point after the whole number and add a zero after it, making the dividend become 70.
0.
_____
15 | 70
4. Divide 70 by 15. The quotient is 4 and the remainder is 10.
0.4
_____
15 | 70
- 60
-----
10
5. Bring down the next digit of the dividend (0) and write it next to the remainder (10) to get 100.
0.46
_____
15 | 700
- 60
-----
100
6. Divide 100 by 15. The quotient is 6 and the remainder is 10.
0.4666...
_____
15 | 700
- 60
-----
100
- 90
-----
10
7. The remainder is 10. Since the remainder is the same as the divisor, the division will repeat indefinitely. To indicate that the decimal is recurring, place a horizontal line (called a vinculum or overbar) above the recurring digits and add dots above the repeating digit(s).
The decimal representation of 6 and 7/15 is 0.4666... (with a vinculum above 6).
To convert a mixed number like 6 and 7/15 to a decimal using long division, you can follow these steps:
Step 1: Write the whole number part (6) as a decimal without any fractional part: 6.0
Step 2: Divide the numerator of the fractional part (7) by the denominator (15).
- Place the quotient (the result of the division) as the next digit after the decimal point: 6.0<quotient>
- Multiply the quotient by the denominator (15) and subtract it from the numerator (7).
Step 3: Bring down a zero and repeat the process, continuing until you have obtained the desired level of precision.
- Multiply the remainder (the result of the subtraction) by 10 and divide it by the denominator (15).
- Place the new quotient as the next decimal digit: 6.0<quotient1>...<quotient2>...
- Multiply the new quotient by the denominator (15) and subtract it from the remainder.
- Repeat the process until you've reached the desired level of precision or until the remainder becomes zero.
- If the remainder becomes zero before the desired level of precision is reached, you can choose to stop there.
By applying these steps, we can convert 6 and 7/15 to a decimal using long division:
Step 1: Write 6 as 6.0 (no fractional part).
Step 2: Divide 7 by 15. The quotient is 0.4666..., which we'll round to four decimal places as 0.4667.
Therefore, 6 and 7/15 as a decimal using long division is approximately 6.4667.