What is the positive difference between the squares of 2.5 and 2.1 to 1 significant figures?

Analyze the question: We need the positive difference between 2.5² and 2.1², then round it to 1 significant figure.

Concept: The difference of two squares: a² − b² = (a − b)(a + b)

Solution:

• 2.5² = 6.25
• 2.1² = 4.41

Difference = 6.25 − 4.41 = 1.84

Check with the formula: (2.5 − 2.1)(2.5 + 2.1) = 0.4 × 4.6 = 1.84 ✓

Round to 1 significant figure: The first significant digit is 1, and the next digit is 8, so we round up: 1.84 ≈ 2

Matching the options:

• A (–2.0) is negative, so it is not valid because the question asks for the positive difference.
• B (–184) and C (–1.84) are negative, so they are not valid.
• D (2) matches our answer.
• E (18.4) is the wrong magnitude.

Tip: Always read the instruction at the end of the question ("to 1 significant figure"). Option C (-1.84) is the unrounded value with the wrong sign, which is a trap for students who stop at the exact answer. Also use (a − b)(a + b) to speed up calculations like this.