Question

What is the rational number equivalent to 1.28 repeating

Answer 1

The repeating decimal 1.282828... is equivalent to the rational number 127/99, which is found by setting the decimal to a variable, multiplying by 100 to shift the decimal, subtracting the original number to eliminate the repeating part, and then simplifying the result.

Step-by-step explanation:

The rational number equivalent to 1.28 repeating is found by expressing the number as a fraction. To do this, let ‘x’ represent the repeating decimal 1.282828.... First, we'll write it out like this:

x = 1.282828...

Now, multiply both sides by 100 to shift the decimal two places to the right:

100x = 128.282828...

Subtract the original equation (x = 1.282828...) from this new equation:

99x = 127

Divide both sides by 99 to solve for x:

x = 127/99

So, the rational number equivalent to 1.28 repeating is 127/99.

Answer 2

100*1.2828...= 128.28282828..( so on..)
100x=128.28

then you do 100x - x = 128.2828...- 1.2828..

then we subtract the .282828... part

99x = 127

then divide boths sides by 99 and then x=127/99