These are 12 questions and 12 answers, each with its explanation.
Answer:
(a) 5.432 g : 4 significant figures
(b) 40.319 g: 5 significant figures
(c) 146 cm: 3 significant figures
(d) 3.285 cm: 4 significant figures
(e) 0.189 s: 3 significant figures
(f) 429.3 mm: 4 significant figures
(g) 2873.0: 5 significant figures
(h) 990 ml: 2 significant figures
(i) 0.0000246 g: 3 significant figures
(j) 1.04 × 10¹² g: 3 significant figures
(k) 5.59 x 10⁻⁷ m: 3 significant figures
(l) 0.0000242 mg: 3 significant figures
Explanation:
The significant figures are the digits that are certain plus one digit that is uncertain.
In a measure, all the non-zero digits and the zeros between two non-zero digits are signficant (take this as the first rule).
That rule apply for the items (a) through (d).
With that rule, then, you get the answer for the first four questions.
(a) 5.432 g: all the digits are different from zero, so all 4 are significant.
(b) 40.319 g: all digits are non-zero, so all 5 are significant.
(c) 146 cm: all digits are non-zero, so all 3 are significant.
(d) 3.285 cm: all digits are non-zero, so all 4 are significant.
In a decimal number, the leading zeros before the first non-zero digit are not significant (second rule)
(e) 0.189 s: 3 significant figures
So, with the second rule, you have that the 0 before the perios is not significant, and with the first rule you get that the 3 decimal (which are non-zeros) are significant.
(f) 429.3 mm: 4 significant figures
For this number use the first rule: all the digits are non-zero, so the 4 digits are significant.
(g) 2873.0: 5 significant figures
Now our third rule: all the trailing zeros to the right of the decimal point are significant.
That means that the digit 0 after the decimal point is significant. Since the other 4 digits are non-zero, the first rule may you conclude that they are also significant. So, the 5 digits are significant.
(h) 990 ml: 2 significant figures
New (fourth rule): the zeros that are only place holders are not significant.
So, the last 0 in 990 is not significant, and only the two non-zero digits (99) are significant figures.
(i) 0.0000246 g: 3 significant figures
With this number use the second rule (the leading zeros before the first non-zero digit are not significant), so the three non-zero digits are the signiticant figures.
(j) 1.04 × 10¹² g: 3 significant figures
This number is written in scientific notation. Only the digits of the mantissa (the digits before the power of 10) are taken into account to determine the number of significant figures.
So, use the previous rules with the number 1.04: first rule, all the non-zero digits and the zeros between two non-zero digits are significant. So the 3 digits in 1.04 are significant.
(k) 5.59 x 10⁻⁷ m: 3 significant figures
This number is also written in scientific notation, so only use the mantissa.
As per the first rule, all non-zero digits are signficant, so this number has 3 significant figures.
(l) 0.0000242 mg: 3 significant figures
The four zeros before 242 are just place holders, so as per the fourth rule, they are not signficant, and this number has 3 significant numbers (the three non-zero digits).
