Use long division to convert 2 7/16 to a decimal.(1 point
To convert 2 7/16 to a decimal using long division, we follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
To convert the whole number 2 into a fraction, we multiply it by the denominator of the fraction and add the numerator:
2 * 16 + 7 = 39
The improper fraction is 39/16.
Step 2: Perform long division.
We divide the numerator (39) by the denominator (16):
16) 39.000
16 x 2 = 32
39 - 32 = 7
Now, we bring down the 0 from the decimal:
16) 39.000
16 x 2 = 32
39 - 32 = 7
7.0000
We continue with the long division:
16) 39.000
16 x 2 = 32
39 - 32 = 7
7.0000
7.0000
Step 3: Continue the long division until the desired level of accuracy is achieved.
Since we have a repeating decimal, we can see that the decimal portion of the quotient will continue infinitely. For simplicity, let's round it to 2 decimal places.
16) 39.000
16 x 2 = 32
39 - 32 = 7
7.0000
7.0000
0.0000
0.0000
We see that the digits after the decimal point continue as zeros, forming a repeating pattern. So, 2 7/16 as a decimal is approximately 2.44.
To convert 2 7/16 to a decimal using long division, follow these steps:
Step 1: Write the mixed number as an improper fraction.
- Multiply the whole number by the denominator, then add the numerator.
- The result becomes the new numerator over the original denominator.
- In this case, 2 7/16 becomes (2 * 16 + 7) / 16 = 39/16.
Step 2: Perform long division.
- Divide 39 by 16, and write the quotient above the division bar.
- Write the remainder (if any) as a fraction on the right side of the division bar.
- In this case, 39 ÷ 16 = 2 remainder 7.
2.4375
-------------
16 | 39
-32
--
7
Step 3: Continue the long division process.
- Bring down the next digit from the original number (if available).
- Repeat the process of dividing and finding the remainder.
- In this case, we don't have any more digits, so the division process is complete.
Step 4: Express the remainder as a fraction over the original denominator.
- The remainder 7 becomes 7/16.
Step 5: Combine the quotient and the remainder fraction.
- The quotient is 2 and the remainder fraction is 7/16.
- The final decimal representation is 2.4375.
Therefore, 2 7/16 as a decimal is 2.4375.
To convert a mixed number like 2 7/16 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
- Multiply the whole number (2) by the denominator (16): 2 * 16 = 32
- Add the numerator (7) to the result: 32 + 7 = 39
- Write the sum over the original denominator: 39/16
Step 2: Perform long division.
- Place the dividend (39) inside the division bracket and the divisor (16) outside the bracket.
- Divide 39 by 16: 39 ÷ 16 = 2 with a remainder of 7.
- Write the quotient (2) above the division bracket.
- Write the remainder (7) as a fraction over the original denominator: 7/16.
Step 3: Combine the quotient and remainder to form the decimal.
- Divide the remainder (7) by the original denominator (16): 7/16 = 0.4375
- Add the quotient (2) to the decimal: 2 + 0.4375 = 2.4375
Therefore, 2 7/16 as a decimal is 2.4375.