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.
10. x 300.

make it more clear.

GPT-4o mini · Answer

To solve the expression $ 10 \times 300 $ and analyze it for significant digits, let's go through the steps one by one. ### Step 1: Calculate the Result Perform the multiplication: $$ 10 \times 300 = 3000 $$ ### Step 2: Determine Significant Digits Next, we need to determine the number of significant digits in each of the two numbers involved in the multiplication. 1. **Number: 10** - As typically written, "10" has 2 significant digits (the "1" and the "0" are both considered significant in this context). 2. **Number: 300** - The number "300" can be ambiguous in terms of significant figures. If it is written without a decimal point (as "300"), it typically has **1 significant digit** (the "3") because trailing zeros in a whole number without a decimal point are not counted as significant. - If "300" were written as "300." (with a decimal), it would have 3 significant digits, but since that is not the case here, we will consider it to have **1 significant digit**. ### Step 3: Rules for Significant Figures in Multiplication When multiplying numbers, the result should have the same number of significant digits as the factor with the least number of significant digits. In this case: - **10** has **2 significant digits**. - **300** has **1 significant digit**. The limiting factor is the number with **1 significant digit** (indicated by the number "300"). ### Step 4: Determine the Final Answer with Correct Significant Digits Since $ 3000 $ (the raw result) has 4 digits, we round it to the appropriate number of significant figures (which is 1 significant digit). Rounding $ 3000 $ to **1 significant digit**: - The first significant digit is "3". - We keep it as "3000" but only indicate **1 significant digit**. ### Final Summary - **Calculator Answer**: $ 3000 $ - **Significant Digits Answer**: $ 3000 $ (but presented as "3" with 1 significant digit) - **Number of Significant Digits**: 1 (from the number $ 300 $) ### Final Answer **Result**: $ 3000 $ (rounded to **1 significant digit** -> treated as $ 3 \times 10^3 $ or simply **3000** with an indication of significant digits, confirming its precision based on the least precise factor in the multiplication).