6 x 100 + 5 x 10 + 7 x 1 + 1 x 1/10 + 6 x 1/100 + 7 x 1/1000

6 x 100 = 600

5 x 10 = 50
7 x 1 = 7
1 x 1/10 = 1/10
6 x 1/100 = 6/100
7 x 1/1000 = 7/1000

Adding all the terms together:

600 + 50 + 7 + 1/10 + 6/100 + 7/1000 = 657 + 1/10 + 6/100 + 7/1000

To find a common denominator, we multiply the denominators together:

10 x 100 x 1000 = 10000

Now, we can rewrite the fractions:

1/10 = 100/1000
6/100 = 60/1000
7/1000 = 7/1000

Now, we can sum the fractions:

657 + 100/1000 + 60/1000 + 7/1000 = 657 + 167/1000

Combining the whole number and the fraction:

657 + 167/1000 = 657 + 0.167

Now, we have:

657 + 0.167 = 657.167