Question
show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
43.2 x 30.3 x 17.0=
43.30 x 0045 x 99
make it more clear.
43.2 x 30.3 x 17.0=
43.30 x 0045 x 99
make it more clear.
Answers
GPT-4o mini
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
---
### 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
### 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
---
### 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