Arrange in ascending order: 12.142, 12.124, 12.104, 12.401, 12.214.
12.104 < 12.124 < 12.142 < 12.214 < 12.401
Step 1: Look at the whole number part.
All numbers have whole part \(12\). So we compare the decimal places.
Step 2: Compare the tenths place.
\(12.142\) → tenths \(1\)
\(12.124\) → tenths \(1\)
\(12.104\) → tenths \(1\)
\(12.401\) → tenths \(4\)
\(12.214\) → tenths \(2\)
The smallest tenths digit is \(1\). So the three smallest (in some order) are:
\(12.104, 12.124, 12.142\).
Step 3: For those three, compare the hundredths place.
\(12.104\) → hundredths \(0\)
\(12.124\) → hundredths \(2\)
\(12.142\) → hundredths \(4\)
Since \(0 < 2 < 4\), we get:
\(12.104 < 12.124 < 12.142\).
Step 4: Compare the remaining two numbers.
\(12.214\) → tenths \(2\)
\(12.401\) → tenths \(4\)
Since \(2 < 4\), we have:
\(12.214 < 12.401\).
Final answer (ascending):
\(\underline{12.104 < 12.124 < 12.142 < 12.214 < 12.401}\)