show the calculator answer, significant digits answer and identify the number of significant digits. show all work.

Question

43.2 x 30.3 x 17.0=
43.30 x 0045 x 99
make it more clear.

Answer 1

Let's solve each multiplication step by step, showing the calculator answers, significant digits answers, and identifying the number of significant digits for each of the calculations.

Problem 1: \( 43.2 \times 30.3 \times 17.0 \)

Step 1: Numbers and Significant Digits

• 43.2 has 3 significant digits.
• 30.3 has 3 significant digits.
• 17.0 has 3 significant digits.

Step 2: Perform the calculation

1. Calculate \( 43.2 \times 30.3 = 1300.96 \)
2. Now use that result: \( 1300.96 \times 17.0 = 22116.32 \)

Step 3: Determine the significant digits in the final result

• The result (22116.32) must be rounded to the least number of significant digits from the calculations, which is 3 (from the numbers we multiplied).

So, we round 22116.32 to 3 significant digits:

• The first three significant digits are 2, 2, and 1 (221). The next digit is "1", which means we round up.
• The final answer will be 22,100.

Summary of Problem 1:

• Calculator Answer: 22116.32
• Significant Digits Answer: 22,100
• Number of Significant Digits in Final Answer: 3

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Problem 2: \( 43.30 \times 0045 \times 99 \)

Step 1: Numbers and Significant Digits

• 43.30 has 4 significant digits.
• 0045 (or 45 with leading zeros removed) has 2 significant digits.
• 99 has 2 significant digits.

Step 2: Perform the Calculation

1. Calculate \( 43.30 \times 0045 = 1,948.5 \)
2. Use that result: \( 1948.5 \times 99 = 192853.5 \)

Step 3: Determine the significant digits in the final result

• The number that limits us is 2 significant digits (from both 0045 and 99).

So we round 192853.5 to 2 significant digits:

• The first two significant digits are "19", and the next digit is "2", which means we round down.
• The final answer will be 190,000.

Summary of Problem 2:

• Calculator Answer: 192853.5
• Significant Digits Answer: 190,000
• Number of Significant Digits in Final Answer: 2

Final Summary:

1. Problem 1:

   • Calculator Answer: 22116.32
   • Significant Digits Answer: 22,100
   • Number of Significant Digits: 3

2. Problem 2:

   • Calculator Answer: 192853.5
   • Significant Digits Answer: 190,000
   • Number of Significant Digits: 2