The number of significant figures in 50000.020 × 10⁻³ is _____________.

Solution

Chemistry ma’am · 4 steps

Ignore the power of ten and count the digits in 50000.020. Every one of them counts here.

1. Drop the exponent. The factor 10⁻³ only moves the decimal point. It never changes the number of significant figures, so look only at 50000.020.
2. Zeros in between. The first non-zero digit is 5 and the last is 2. The five zeros sandwiched between them are all significant. That gives 1 + 5 + 1 = 7 digits so far.
3. Trailing zero. The final 0 comes after the decimal point and to the right of a non-zero digit, so it is significant too. It tells you the value is measured to that place.
4. So. The digits 5, 0, 0, 0, 0, 0, 2, 0 are all significant, giving 8 significant figures.

The common slip: 7. Dropping the last zero after the 2 as if it were meaningless gives 7. A trailing zero after a decimal point is significant.

The idea to keep. Powers of ten never change the count. Zeros between non-zero digits always count, and trailing zeros count only when the number has a decimal point.

Answer from the NTA final answer key. Solution by PrepWiser.