Certainly! Let's analyze each expression and determine the number of significant figures.
1. Expression: [tex]$55 + 7.1$[/tex]
- When adding or subtracting numbers, the result should be rounded to the least number of decimal places of any number in the operation.
- Here, [tex]$55$[/tex] has 2 significant figures, and [tex]$7.1$[/tex] has 2 significant figures.
- Therefore, the result of the addition should be rounded to 2 significant figures.
Number of significant figures: 2
2. Expression: [tex]$0.06$[/tex]
- In the number [tex]$0.06$[/tex], the zeros before the 6 are not significant. Only the digit 6 is significant.
- Hence, [tex]$0.06$[/tex] has 1 significant figure.
Number of significant figures: 1
3. Expression: [tex]$1,760$[/tex]
- For the number [tex]$1,760$[/tex], it's ambiguous if the trailing zero is significant or not.
- If we assume it to have 3 significant figures, then this number has 3 significant figures.
Number of significant figures: 3
4. Expression: [tex]$3$[/tex]
- In the number [tex]$3$[/tex], there is only one digit, which is significant.
- Hence, [tex]$3$[/tex] contains 1 significant figure.
Number of significant figures: 1
5. Expression: [tex]$185.3$[/tex]
- In the number [tex]$185.3$[/tex], all the digits (1, 8, 5, and 3) are significant.
- Therefore, [tex]$185.3$[/tex] has 4 significant figures.
Number of significant figures: 4
Let's summarize the number of significant figures for each expression:
1. [tex]$55 + 7.1$[/tex] has 2 significant figures.
2. 0.06 has 1 significant figure.
3. 1,760 has 3 significant figures.
4. 3 has 1 significant figure.
5. 185.3 has 4 significant figures.
Thus, the final match-up of expressions to significant figures is:
- [tex]$55+7.1$[/tex]: 2 significant figures
- 0.06: 1 significant figure
- 1,760: 3 significant figures
- 3: 1 significant figure
- 185.3: 4 significant figures
