Question

1.4777…
1.474747…
1.474777…
1.477477477…
1.\overline{47}
1.\overline{477}
1.474\overline{7}
1.4\overline{7}

Explanation:

Step1: Analyze \(1.4777\ldots\)

The decimal \(1.4777\ldots\) has the digit \(7\) repeating after the hundredths place. So its repeating decimal notation is \(1.4\overline{7}\) (the bar is over the \(7\) in the thousandths place and beyond).

Step2: Analyze \(1.474747\ldots\)

The decimal \(1.474747\ldots\) has the sequence \(47\) repeating. So its repeating decimal notation is \(1.\overline{47}\) (the bar is over \(47\)).

Step3: Analyze \(1.474777\ldots\)

The decimal \(1.474777\ldots\) has \(47\) first and then \(7\) repeating. So its repeating decimal notation is \(1.474\overline{7}\) (the bar is over the last \(7\) and subsequent \(7\)s).

Step4: Analyze \(1.477477477\ldots\)

The decimal \(1.477477477\ldots\) has the sequence \(477\) repeating. So its repeating decimal notation is \(1.\overline{477}\) (the bar is over \(477\)).

Answer:

• \(1.4777\ldots\) connects to \(1.4\overline{7}\)
• \(1.474747\ldots\) connects to \(1.\overline{47}\)
• \(1.474777\ldots\) connects to \(1.474\overline{7}\)
• \(1.477477477\ldots\) connects to \(1.\overline{477}\)