Use long division to convert 2 7/16 to a decimal.(1 point

Answer 1

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.