Question

the number 0.0010100 μm has 1 significant figures and an uncertainty of 2 (not in scientific notation). when the number is displayed in scientific notation it still has 3 significant figures, an uncertainty of 4, and is displayed as 5 a. 0.0001 x 10^-3 μm b. 0.0000001 μm c. 3 d. 4 e. 5 f. 7 g. 1.01 x 10^-3 μm h. 1.0100 x 10^-3 μm

Explanation:

Step1: Determine significant figures

Leading zeros are not significant. Non - zero digits and zeros between non - zero digits are significant. In 0.0010100, the significant figures are 1, 0, 1, 0, 0. So there are 4 significant figures.

Step2: Find uncertainty of non - scientific notation number

The last digit in a measured number represents the uncertainty. For 0.0010100, the uncertainty is in the fifth decimal place. The value of the uncertainty is 0.0000001 μm (B).

Step3: Scientific notation significant figures

When written in scientific notation, the significant figures are in the coefficient part. For 0.0010100 = 1.0100×10⁻³, the number of significant figures is still 4.

Step4: Uncertainty in scientific notation

The uncertainty is still related to the last significant digit. For 1.0100×10⁻³, the uncertainty is 0.0001×10⁻³ = 0.0000001 μm (B).

Step5: Write in scientific notation

0.0010100 in scientific notation is 1.0100×10⁻³ μm (H).

Answer:

1. D. 4
2. B. 0.0000001 μm
3. D. 4
4. B. 0.0000001 μm
5. H. 1.0100×10⁻³ μm