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Question 51

The number of significant figures in 50000.020 $$\times 10^{-3}$$ is ______


Correct Answer: 8

Solution

We need to find the number of significant figures in $$50000.020 \times 10^{-3}$$.

The number of significant figures is determined by the coefficient $$50000.020$$, not by the power of 10. The multiplication by $$10^{-3}$$ only shifts the decimal point and does not change the number of significant figures.

In the number $$50000.020$$, we count the significant figures:

The digit 5 is significant (non-zero digit). The four zeros between 5 and the decimal point (0, 0, 0, 0) are significant because they are between a non-zero digit and the decimal point (or equivalently, they are captured between significant digits once we note the trailing digits after the decimal). The digit 0 after the decimal point is significant. The digit 2 is significant (non-zero digit). The trailing 0 after 2 is significant because it comes after the decimal point.

Counting: $$5, 0, 0, 0, 0, 0, 2, 0$$ — that gives us 8 significant figures.

The answer is $$\boxed{8}$$.

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