Question

directions: calculate the following expressions with significant figures.list the significant figures of the final answer.

	sum/difference or product/quotient?	decimal or sig fig?	whats the least amount?	final answer?
8563.5 - 130 =
50. × 200. =
35 ÷ 6.3 =

Explanation:

1. For \( 1.50 + 1.7 \)

Step1: Identify operation and rule

Operation: Sum (addition). For addition/subtraction, we go by decimal places. \( 1.50 \) has 2 decimal places, \( 1.7 \) has 1 decimal place. The least number of decimal places is 1.

Step2: Perform the addition

\( 1.50 + 1.7 = 3.20 \). Now, round to 1 decimal place.

Step3: Round the result

\( 3.20 \) rounded to 1 decimal place is \( 3.2 \). The significant figures in \( 3.2 \) are 3 and 2 (2 significant figures? Wait, no: \( 3.2 \) has two significant figures? Wait, \( 1.50 \) has 3 sig figs, \( 1.7 \) has 2. Wait, no, for addition, it's about decimal places. Wait, \( 1.50 \) is to the hundredth place, \( 1.7 \) to the tenth. So the result should be to the tenth place. So \( 1.50 + 1.7 = 3.20 \), which we round to \( 3.2 \) (tenth place). The significant figures in \( 3.2 \) are 3 and 2 (two significant figures? Wait, no: \( 3.2 \) has two significant figures? Wait, \( 1.50 \) has 3, \( 1.7 \) has 2. But for addition, the rule is decimal places. So the least number of decimal places is 1 (from \( 1.7 \)). So the result should have 1 decimal place. So \( 3.2 \), which has two significant figures? Wait, no: \( 3.2 \) has two significant figures? Wait, \( 3.2 \): the 3 is significant, the 2 is significant. So two? Wait, no, \( 1.50 \) is 1.50 (three sig figs), \( 1.7 \) is 1.7 (two sig figs). But addition is about decimal places. So the sum is \( 3.20 \), which we round to \( 3.2 \) (one decimal place). So the significant figures in \( 3.2 \) are 3 and 2 (two significant figures? Wait, no, \( 3.2 \) has two significant figures? Wait, \( 3.2 \): the 3 is a non - zero digit, the 2 is a non - zero digit. So two significant figures. But wait, maybe I made a mistake. Let's re - calculate: \( 1.50+1.7 = 3.20 \). The number of decimal places in the least precise measurement (\( 1.7 \)) is 1. So we round \( 3.20 \) to one decimal place, getting \( 3.2 \). The significant figures in \( 3.2 \) are 3 and 2 (two significant figures? Wait, no, \( 3.2 \) has two significant figures? Wait, \( 3.2 \): the 3 is significant, the 2 is significant. So two. But maybe the question is just to calculate the sum with sig figs and list the sig figs of the final answer. So final answer is \( 3.2 \), sig figs are 3 and 2.

Filling the table:

• Sum/Difference or Product/Quotient?: Sum
• Decimal or Sig Fig?: Decimal (since it's addition, we use decimal places rule)
• What's the least amount?: 1 decimal place (from \( 1.7 \))
• Final Answer?: \( 3.2 \) (significant figures: 3, 2)

2. For \( 8563.5−130 \)

Step1: Identify operation and rule

Operation: Difference (subtraction). For subtraction, we use decimal places. \( 8563.5 \) has 1 decimal place, \( 130 \) has 0 decimal places (it can be considered as \( 130. \) with 0 decimal places). The least number of decimal places is 0.

Step2: Perform the subtraction

\( 8563.5−130 = 8433.5 \)

Step3: Round the result

We need to round to 0 decimal places (whole number). So \( 8433.5 \) rounded to the nearest whole number is \( 8434 \)? Wait, no. Wait, \( 130 \) has two significant figures? Wait, no, \( 130 \): if it's written as \( 130 \) without a decimal, the trailing zero may be ambiguous, but in the context of subtraction with \( 8563.5 \) (which has 5 significant figures), \( 130 \) can be considered as having two significant figures? Wait, no, the rule for addition/subtraction is decimal places. \( 8563.5 \) has 1 decimal place, \( 130 \) has 0 decimal places. So the result should have 0 decimal places. So \( 8563.5 - 130=8433.5 \), which we round to \( 8434 \)? Wait, no, \( 8433.5 \) rounded to the nearest whole number is \( 8434 \)? Wait, no, \( 8433.5 \) is halfway between \( 8433 \) and \( 8434 \), but in significant figures for subtraction, we look at decimal places. Wait, \( 130 \) is \( 1.3\times10^{2} \), \( 8563.5 \) is \( 8.5635\times10^{3} \). The difference is \( 8563.5 - 130 = 8433.5 \). Since \( 130 \) has its last significant digit in the tens place (if we consider \( 130 \) as two significant figures: 1 and 3, with the zero as a placeholder), then the result should be rounded to the tens place. Wait, maybe I confused the rule. Let's re - state: for addition and subtraction, the result should have the same number of decimal places as the measurement with the least number of decimal places. \( 8563.5 \) has 1 decimal place, \( 130 \) has 0 decimal places. So the result should have 0 decimal places. So \( 8433.5 \) rounded to 0 decimal places is \( 8434 \)? Wait, no, \( 8433.5 \) rounded to the nearest whole number is \( 8434 \), but \( 130 \) has two significant figures? Wait, maybe the problem is simpler. Let's just do the subtraction: \( 8563.5-130 = 8433.5 \). Now, since \( 130 \) has no decimal places, we round \( 8433.5 \) to the nearest whole number, which is \( 8434 \). The significant figures in \( 8434 \) are 8, 4, 3, 4 (four significant figures? Wait, \( 8434 \): all digits are non - zero (except maybe the last, but 4 is non - zero). So four significant figures.

Filling the table:

• Sum/Difference or Product/Quotient?: Difference
• Decimal or Sig Fig?: Decimal (subtraction, use decimal places rule)
• What's the least amount?: 0 decimal places (from \( 130 \))
• Final Answer?: \( 8434 \) (significant figures: 8, 4, 3, 4)

3. For \( 50.\times200. \)

Step1: Identify operation and rule

Operation: Product (multiplication). For multiplication/division, we use significant figures. \( 50. \) has 2 significant figures (the decimal shows that the zero is significant), \( 200. \) has 3 significant figures (the decimal shows the trailing zeros are significant). The least number of significant figures is 2.

Step2: Perform the multiplication

\( 50.\times200. = 10000. \)

Step3: Round the result

We need to round to 2 significant figures. \( 10000. \) in scientific notation is \( 1.0\times10^{4} \) (which has 2 significant figures).

Filling the table:

• Sum/Difference or Product/Quotient?: Product
• Decimal or Sig Fig?: Sig Fig (multiplication, use significant figures rule)
• What's the least amount?: 2 significant figures (from \( 50. \))
• Final Answer?: \( 1.0\times10^{4} \) (significant figures: 1, 0)

4. For \( 35\div6.3 \)

Answer:

Step1: Identify operation and rule

Operation: Quotient (division). For division, we use significant figures. \( 35 \) has 2 significant figures, \( 6.3 \) has 2 significant figures. The least number of significant figures is 2.

Step2: Perform the division

\( 35\div6.3\approx5.555\cdots \)

Step3: Round the result

We round to 2 significant figures. \( 5.555\cdots \) rounded to 2 significant figures is \( 5.6 \).

Filling the table:

• Sum/Difference or Product/Quotient?: Quotient
• Decimal or Sig Fig?: Sig Fig (division, use significant figures rule)
• What's the least amount?: 2 significant figures (from both \( 35 \) and \( 6.3 \))
• Final Answer?: \( 5.6 \) (significant figures: 5, 6)

Final Table Filling (Summarized)

Expression	Sum/Difference or Product/Quotient?	Decimal or Sig Fig?	What's the least amount?	Final Answer?
\( 8563.5 - 130 \)	Difference	Decimal	0 decimal places	\( 8434 \) (sig figs: 8, 4, 3, 4)
\( 50. \times 200. \)	Product	Sig Fig	2 sig figs	\( 1.0\times10^{4} \) (sig figs: 1, 0)
\( 35\div6.3 \)	Quotient	Sig Fig	2 sig figs	\( 5.6 \) (sig figs: 5, 6)