ercise 3: Round off the following numbers to the specified number of decimal places: (Theo a) $$ 5,235865845 \quad $$ ( 2 decimal places) d) $$ \sqrt{5} $$ (2 decimal places) b) 0,256862554 ( 4 decimal places) e) $$ (3,35)^{2} \div 2,6 $$ (4 decimal places) c) 28,56988712 ( 3 decimal places) f) $$ \pi+\sqrt{14} $$ (3 decimal places) Solutions to Excicise 3 aro on poge 235

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Sure, let's solve each part of Exercise 3 by rounding the given numbers to the specified number of decimal places.

### a) $$ 5.235865845 $$ (2 decimal places)

**Steps:**
1. Identify the second decimal place (3) and the third decimal place (5).
2. Since the third decimal place is 5 or greater, round up the second decimal place.

**Solution:**
$$ 5.235865845 \approx 5.24 $$

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### b) $$ 0.256862554 $$ (4 decimal places)

**Steps:**
1. Identify the fourth decimal place (8) and the fifth decimal place (6).
2. Since the fifth decimal place is 5 or greater, round up the fourth decimal place.

**Solution:**
$$ 0.256862554 \approx 0.2569 $$

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### c) $$ 28.56988712 $$ (3 decimal places)

**Steps:**
1. Identify the third decimal place (9) and the fourth decimal place (8).
2. Since the fourth decimal place is 5 or greater, round up the third decimal place.

**Solution:**
$$ 28.56988712 \approx 28.570 $$

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### d) $$ \sqrt{5} $$ (2 decimal places)

**Steps:**
1. Calculate $$ \sqrt{5} \approx 2.2360679775 $$.
2. Identify the second decimal place (3) and the third decimal place (6).
3. Since the third decimal place is 5 or greater, round up the second decimal place.

**Solution:**
$$ \sqrt{5} \approx 2.24 $$

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### e) $$ \frac{(3.35)^2}{2.6} $$ (4 decimal places)

**Steps:**
1. Calculate $$ (3.35)^2 = 11.2225 $$.
2. Divide by 2.6: $$ \frac{11.2225}{2.6} \approx 4.3163461538 $$.
3. Identify the fourth decimal place (3) and the fifth decimal place (4).
4. Since the fifth decimal place is less than 5, do not round up the fourth decimal place.

**Solution:**
$$ \frac{(3.35)^2}{2.6} \approx 4.3163 $$

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### f) $$ \pi + \sqrt{14} $$ (3 decimal places)

**Steps:**
1. Calculate $$ \pi \approx 3.141592654 $$ and $$ \sqrt{14} \approx 3.741657387 $$.
2. Sum them: $$ 3.141592654 + 3.741657387 \approx 6.883250041 $$.
3. Identify the third decimal place (3) and the fourth decimal place (2).
4. Since the fourth decimal place is less than 5, do not round up the third decimal place.

**Solution:**
$$ \pi + \sqrt{14} \approx 6.883 $$

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### **Summary of Solutions:**

a) $$ 5.24 $$  
b) $$ 0.2569 $$  
c) $$ 28.570 $$  
d) $$ 2.24 $$  
e) $$ 4.3163 $$  
f) $$ 6.883 $$  
a) 5.24 b) 0.2569 c) 28.570 d) 2.24 e) 4.3163 f) 6.883

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