Question

give the correct number of significant figures for each of the following measured values (e.g., 1, 2, 3, ... or “amb” for ambiguous).
0.0230 s⁻¹
290 nm
21.6 ml
1.9500×10⁻³¹ kg
question 3
express the following measurements in scientific notation
(a) 0.00000745 mol
(b) 870,000,000 g (to 2 sig figs)
(c) 1458.2 j
7.45×10⁻⁶ mol; 8.7×10⁸ g; 1.4582×10⁴ j
7.45×10⁶ mol; 8.7×10⁸ g; 1.4582×10³ j
7.45×10⁷ mol; 8.7×10⁸ g; 1.4582×10⁴ j
7.45×10⁶ mol; 8.7×10⁹ g; 1.4582×10³ j
7.45×10⁻⁶ mol; 8.7×10⁸ g; 1.4582×10³ j

Explanation:

Step1: Determine significant - figures for 0.0230 s⁻¹

Leading zeros are not significant. Trailing zero after non - zero digits is significant. So, there are 3 significant figures.

Step2: Determine significant - figures for 290 nm

Trailing zero in a number without a decimal point is ambiguous. So, it is "amb".

Step3: Determine significant - figures for 21.6 mL

All non - zero digits are significant. So, there are 3 significant figures.

Step4: Determine significant - figures for 1.9500×10⁻³¹ kg

All digits in the coefficient are significant. So, there are 5 significant figures.

Step5: Express 0.00000745 mol in scientific notation

Move the decimal point 6 places to the right. So, it is 7.45×10⁻⁶ mol.

Step6: Express 870,000,000 g to 2 significant figures in scientific notation

Move the decimal point 8 places to the left and round to 2 significant figures. So, it is 8.7×10⁸ g.

Step7: Express 1458.2 J in scientific notation

Move the decimal point 3 places to the left. So, it is 1.4582×10³ J.

Answer:

0.0230 s⁻¹: 3
290 nm: amb
21.6 mL: 3
1.9500×10⁻³¹ kg: 5
0.00000745 mol: 7.45×10⁻⁶ mol
870,000,000 g (to 2 sig figs): 8.7×10⁸ g
1458.2 J: 1.4582×10³ J