0.4 recurring multiplied by 4

One point seven recurring.

0.4 recurring can be expressed as a fraction in the following way:

Let x = 0.44444.....

Multiply by 10

10x = 4.44444....

Subtract x from 10x

9x = 4

So x = 4/9

Now multiply this by 4 to get 16/9

If you want this as a decimal:

$${\frac{{\mathtt{16}}}{{\mathtt{9}}}} = {\mathtt{1.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$

or 1.77777777....   (i.e. the 7's recurr).

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