solve the following . observing significant figure rules 25mtimes 0.05m 1.25m^2 1m^2 1.2500m^2 1.3m^2

To solve the problem while observing significant figure rules, let's carefully analyze the given calculation:<br /><br />### Problem:<br />We are tasked with calculating \( 25 \, \text{m} \times 0.05 \, \text{m} \) and determining the result in terms of significant figures.<br /><br />---<br /><br />### Step 1: Perform the multiplication<br />\[<br />25 \, \text{m} \times 0.05 \, \text{m} = 1.25 \, \text{m}^2<br />\]<br /><br />---<br /><br />### Step 2: Determine the number of significant figures in each value<br />- \( 25 \, \text{m} \): This has **2 significant figures**.<br />- \( 0.05 \, \text{m} \): This has **1 significant figure** (the leading zero is not significant).<br /><br />---<br /><br />### Step 3: Apply the rule for significant figures in multiplication<br />When multiplying or dividing, the result should have the same number of significant figures as the factor with the **fewest significant figures**. In this case, \( 0.05 \, \text{m} \) has only **1 significant figure**, so the result must also be rounded to **1 significant figure**.<br /><br />---<br /><br />### Step 4: Round the result<br />The unrounded result is \( 1.25 \, \text{m}^2 \). Rounding this to **1 significant figure** gives:<br />\[<br />1 \, \text{m}^2<br />\]<br /><br />---<br /><br />### Final Answer:<br />\[<br />\boxed{1 \, \text{m}^2}<br />\]