0.1 + 0.01 + 0.001 = ?

Correct — B. Give every number three decimal places, then add column by column.

Pad with zeros: 0.1 = 0.100 and 0.01 = 0.010
Add: 0.100 + 0.010 + 0.001 = 0.111

Check in fractions: 100⁄1000 + 10⁄1000 + 1⁄1000 = 111⁄1000 = 0.111 → option (b)

Why the others are wrong

• (a)
  0.123 — 0.123 has 2 hundredths and 3 thousandths, but the sum has one of each: one tenth, one hundredth and one thousandth.
• (c)
  0.121 — 0.121 puts 2 in the hundredths place, but 0.01 is the one number with a non-zero hundredths digit, so that column adds to 1.
• (d)
  0.211 — 0.211 puts 2 in the tenths place, but 0.1 is the one number with a non-zero tenths digit, so that column adds to 1.

Adding decimals is adding by place value. Pad each number with zeros to the same number of decimal places so the points line up, then add column by column.

Here each number holds a single 1 in a different place: tenths, hundredths, thousandths. Each column adds to 1, so there is nothing to carry, and the sum reads 0.111.

Key facts

• 0.1 = 1⁄10, 0.01 = 1⁄100 and 0.001 = 1⁄1000.
• Zeros after the last decimal digit do not change a value: 0.1 = 0.100.
• For multiplication the decimal places are counted, not lined up: 0.1 × 0.01 = 0.001.

Common traps

• Right-aligning the numbers as if they were whole numbers: the decimal points must line up, which puts each 1 in its own column.
• Confusing 0.111 with the recurring 0.111…, which equals 1⁄9: this sum stops at the thousandths place.

No directly related past PYQ was found.