Express 1975 correct to 2 significant figures

Analyze the question: You are asked to round 1975 to 2 significant figures. Significant figures are counted from the first non-zero digit on the left.

Concept:

1. Find the first 2 significant digits.
2. Look at the next digit (the 3rd significant figure). If it is 5 or more, round up. If it is less than 5, leave the digits as they are.
3. Keep the place value by filling with zeros.

Solution:

• 1975 has digits 1, 9, 7, 5.
• The first 2 significant figures are 1 and 9, giving 19__.
• The next digit is 7, which is 5 or more, so we round up the 9.
• 19 becomes 20, so the first two significant digits are 2 and 0.
• Restoring the place value (thousands): 20 followed by two zeros gives 2,000.

Check: 1975 is closer to 2000 (difference 25) than to 1900 (difference 75). ✔

Why not the others?

• A (20) has the wrong magnitude, since it loses the place value.
• B (1,900) rounds down, which ignores the 7.
• C (1,980) is 3 significant figures, not 2 (and it is not even rounded correctly).

Answer: D. 2,000

Tip: When rounding to a given number of significant figures, always check the digit right after the last one you keep. Then put back zeros so the number stays the same size. Do not drop the place value, as in option A.