In which of the following pairs do both numbers contain the same number of significant figures?
Check all that apply.
The pairs of numbers that contain the same number of significant figures are:
1. 12.45 and 0.003
2. 3.00 and 300
3. 0.012 and 0.00023
To determine which pairs have the same number of significant figures, we need to understand the concept of significant figures.
Significant figures are the digits in a number that carry meaning in terms of precision. The rules for determining significant figures are as follows:
1. Non-zero digits are always significant. For example, in the number 345, all three digits are significant.
2. Zeroes between non-zero digits are always significant. For example, in the number 203, both zeroes are significant.
3. Leading zeroes (those to the left of non-zero digits) are not significant; they only indicate the position of the decimal point. For example, in the number 0.0032, the zeroes before the 3 are not significant.
4. Trailing zeroes (those to the right of non-zero digits) are significant if they are after the decimal point. For example, in the number 56.00, both zeroes are significant.
Based on these rules, we can now check the pairs to see if they have the same number of significant figures.
Pair 1: 5.1 and 0.910
- 5.1 has two significant figures (5 and 1).
- 0.910 has three significant figures (9, 1, and 0).
- These numbers do not have the same number of significant figures.
Pair 2: 100 and 0.001
- 100 has three significant figures (1, 0, and 0).
- 0.001 has one significant figure (1).
- These numbers do not have the same number of significant figures.
Pair 3: 0.0053 and 0.100
- 0.0053 has two significant figures (5 and 3).
- 0.100 has three significant figures (1, 0, and 0).
- These numbers do not have the same number of significant figures.
Pair 4: 5.30 and 0.086
- 5.30 has three significant figures (5, 3, and 0).
- 0.086 has two significant figures (8 and 6).
- These numbers do not have the same number of significant figures.
Therefore, none of the given pairs have the same number of significant figures.