Question

Round 2745.2158 (a) Rounding to the nearest hundredth:

Option 1: 2745.22
Option 2: 2745.21
Option 3: 2745.23
Option 4: 2745.24

(b) Rounding to the nearest hundred:

Option 1: 2700
Option 2: 2600
Option 3: 2800
Option 4: 2900

Answer 1

(a) Rounding 2745.2158 to the nearest hundredth, the digit in the thousandth place (5) triggers rounding up, resulting in 2745.22. So the correct option is Option 1: 2745.22

(b) Rounding to the nearest hundred, since the digit in the tenth place (4) is less than 5, the hundredth place remains unchanged, yielding 2700. So the correct option is Option 1: 2700

Explanation

(a), rounding to the nearest hundredth means looking at the digit in the thousandth place (5 in this case). Since 5 is equal to or greater than 5, the digit in the hundredth place (4) is rounded up to 5. Therefore, the correct answer is Option 1: 2745.22.

(b), rounding to the nearest hundred involves looking at the digit in the tenth place (4 in this case). Since 4 is less than 5, the digit in the hundredth place remains the same. Therefore, the correct answer is Option 1: 2700.

Now, let's delve into the explanation. Rounding involves determining the appropriate value based on the specified decimal place. For (a), rounding to the nearest hundredth, we considered the digit in the thousandth place to make the decision.

In (b), rounding to the nearest hundred, we looked at the digit in the tenth place. Understanding the rules of rounding is crucial to ensure accuracy in representing numbers. In both cases, the final answer is determined by the specific rules applied to the given decimal places.So the correct option is Option 1: 2700

Answer 2

(a) Option 1: 2745.22

(b) Option 3: 2700

Step-by-step explanation:

Rounding to the nearest hundredth in option (a) involves looking at the digit in the thousandth place, which is 5. Since 5 is equal to or greater than 5, we round the hundredth place up by 1. Thus, the final answer is 2745.22.

For rounding to the nearest hundred in option (b), we examine the digit in the tens place, which is 4. Since 4 is less than 5, we keep the hundredth place as it is. Therefore, the final rounded value is 2700.

In mathematical terms, for rounding to the nearest hundredth, we can express it as follows:

`\[2745.2158 \approx 2745.22.\]`

And for rounding to the nearest hundred:

`\[2745.2158 \approx 2700.\]`

These rounding methods are essential in real-world applications where precise values are not necessary, and rounding helps simplify calculations and improve readability.