Arrange in ascending order: 0.011, 1.001, 0.101, 0.110.
0.011 < 0.101 < 0.110 < 1.001
Step 1: Write the numbers clearly.
We have: 0.011, 1.001, 0.101, 0.110
Step 2: Check the whole-number (ones) part first.
For three numbers the ones digit is (0): (0.011,; 0.101,; 0.110).
For one number the ones digit is (1): (1.001).
Numbers with ones digit (0) are smaller than the number with ones digit (1).
So (1.001) will be the largest.
Step 3: Compare only the numbers starting with 0.
Compare (0.011,; 0.101,; 0.110).
Look at tenths (first digit after the decimal).
(0.011) has tenths (= 0).
(0.101) has tenths (= 1).
(0.110) has tenths (= 1).
A smaller tenths digit means a smaller number, so (0.011) is the smallest of these three.
Step 4: Now compare (0.101) and (0.110).
Their tenths are the same ((1)), so check the next place: hundredths.
(;0.101:) hundredths (= 0)
(;0.110:) hundredths (= 1)
Since (0 < 1), we have (0.101 < 0.110).
Final order (smallest to largest):
(oxed{0.011 lt 0.101 lt 0.110 lt 1.001})
Why this works: When comparing decimals, compare place by place — ones ( ightarrow) tenths ( ightarrow) hundredths ( ightarrow) thousandths — and stop as soon as you find a difference.