Problem 29 - Elementary Algebra

Question

$$ \text { Round } 0.2394 \text { to the nearest hundredth. } $$

Step-by-Step Solution

Answer

0.24

Step 1 - Identify the digit at the hundredth place

Locate the hundredth place in the number 0.2394. The digit at the hundredth place is 3.

Step 2 - Identify the digit to the right of the hundredth place

Look at the digit immediately to the right of the hundredth place, which is the thousandth place. The digit here is 9.

Step 3 - Apply rounding rules

If the digit at the thousandth place (9) is 5 or higher, round the hundredth place digit (3) up by one. Otherwise, leave the hundredth place digit unchanged.

Step 4 - Perform the rounding

Since 9 is greater than 5, add 1 to the hundredth place digit. Therefore, 3 becomes 4, and the number 0.2394 rounded to the nearest hundredth is 0.24.

Key Concepts

nearest hundredth

When rounding a number to the nearest hundredth, we are looking at the second decimal place value. This is crucial for understanding how precise our results will be, especially in scientific and financial contexts.
For example, in the number 0.2394, the digit located in the hundredth place is 3. We focus on this place because it determines how we will round the number.
This step helps us get ready to make a rounding decision. It ensures that our rounded number is as close as possible to the original value within the specified precision.

rounding rules

Rounding numbers follows a set of specific rules which make sure our results are consistent and easy to understand. Here's a quick guide to follow:

• If the digit immediately to the right of the rounding place (in this case, the thousandth place) is 5 or higher, round up the target digit.
• If the digit immediately to the right is 4 or lower, round down, which means leaving the target digit as is.

Applying these rounding rules ensures that the adjustments are minimal but accurate enough to be useful in calculations. In the step-by-step solution of our problem, 0.2394, the digit at the thousandth place is 9. Since 9 is greater than 5, we add 1 to the hundredth place digit (3), resulting in 0.24.

decimal place values

Understanding decimal places is essential for rounding correctly. Decimal place values are the positions of digits to the right of the decimal point. Each position represents a fraction of ten:

• The first position is the tenths place (0.1)
• The second is the hundredths place (0.01)
• The third is the thousandths place (0.001)

In our example, 0.2394:

• The tenths place holds the digit 2.
• The hundredths place holds the digit 3.
• The thousandths place holds the digit 9.
• And the ten-thousandths place (fourth position) holds the digit 4.

Knowing these places helps us pinpoint exactly which numbers we're adjusting and why, making rounding to the nearest hundredth straightforward and accurate.