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

Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
65 000(0.08 x 200 x 0.004) / (800 x 300)

make it more clear.

GPT-4o mini · Answer

To solve the expression $ \frac{65,000 \times (0.08 \times 200 \times 0.004)}{800 \times 300} $ and determine the significant figures, we will go through each step carefully. ### Step 1: Calculate the expression 1. Calculate the numerator: $ 0.08 \times 200 \times 0.004 $. - $ 0.08 $ has **1 significant digit**. - $ 200 $ has **1 significant digit** (as it can be considered as $ 2 \times 10^{2} $). - $ 0.004 $ has **1 significant digit**. Now, let's calculate it: $$ 0.08 \times 200 = 16 \quad (\text{1 significant digit carries over to } 0.004) $$ $$ 16 \times 0.004 = 0.064 $$ The significant figures for $ 0.064 $: **2 significant digits** (the digits 6 and 4). 2. Now calculate $ 65,000 \times 0.064 $: - $ 65,000 $ has **2 significant digits** (the digits 6 and 5; the trailing zeros do not count unless specified). - Using $ 0.064 $ with **2 significant digits**. Now let's calculate: $$ 65,000 \times 0.064 = 4,160 \quad (\text{The answer ends up being 4160}) $$ The result here has **3 significant digits** (the digits 4, 1, and 6). 3. Calculate the denominator: $ 800 \times 300 $. - $ 800 $ has **1 significant digit** (considered as $ 8 \times 10^{2} $). - $ 300 $ has **1 significant digit**. So: $$ 800 \times 300 = 240,000 $$ The result here has **2 significant digits** (the digits 2 and 4; the trailing zeros do not count unless specified). ### Step 2: Now divide the numerator by the denominator $$ \frac{4,160}{240,000} $$ Now performing the division: $$ 4,160 \div 240,000 = 0.0173333\ldots $$ ### Step 3: Apply significant figures to the answer The result must be rounded based on the significant figures from the numerator and denominator: - **Numerator** (4,160): **3 significant digits** - **Denominator** (240,000): **2 significant digits** Since the final result will be based on the lower number of significant figures (which is 2 in this case), we should round $ 0.0173333 $ to **2 significant digits**. ### Final Result $$ \text{Rounded: } 0.017 \quad \text{(2 significant figures)} $$ ### Summary - **Calculator answer:** 0.0173333 - **Rounded answer with significant figures:** 0.017 - **Number of significant digits in the final answer:** 2 significant digits.