Problem 35 - Elementary Algebra

Question

$$ \text { Round } 0.0084 \text { to the nearest thousandth. } $$

Step-by-Step Solution

Answer

0.008

Step 1: Identify the Place Value

The thousandth place is three places to the right of the decimal point. Here, in 0.0084, the digit in the thousandth place is 8.

Step 2: Look at the Next Digit

Look at the digit to the right of the thousandth place, which is the digit in the ten-thousandth place. In this case, it is 4.

Step 3: Determine Rounding Action

If the digit in the ten-thousandth place is 5 or greater, round up. If it is less than 5, round down. Here, 4 is less than 5, so round down.

Step 4: Apply Rounding

Since we are rounding down, the digit in the thousandth place remains the same. So, 0.0084 rounded to the nearest thousandth is 0.008.

Key Concepts

Place Value

Place value is a fundamental concept in mathematics. It tells us the value of a digit based on its position in a number.
Each position represents a specific value, increasing or decreasing by powers of ten.
Understanding place value is essential for rounding numbers accurately. For instance, in the number 0.0084, we have:
- The 0 before the decimal point representing units.
- The first digit after the decimal, 0, representing tenths.
- The second digit after the decimal, 0, representing hundredths.
- The third digit after the decimal, 8, representing thousandths.
Determining place value helps you pinpoint exactly which digit you need to round.

Nearest Thousandth

When rounding to the nearest thousandth, you focus on the digit that is three places to the right of the decimal point.
This is known as the thousandths place. In our example, with the number 0.0084, the thousandth place is occupied by the digit 8.
Identifying this digit is the first step in the rounding process, before considering the next digit.

Rounding Rules

Rounding rules help you decide whether to round a number up or down.
These rules are simple:

- If the digit immediately to the right of your rounding place (the next digit) is 5 or greater, you round up.
- If it is less than 5, you round down.
In the example of 0.0084, the digit in the thousandths place is 8, and the next place (the ten-thousandths place) is 4.
Since 4 is less than 5, we round down. Therefore, we round 0.0084 to 0.008 when rounding to the nearest thousandth.

Decimal Places

Decimal places refer to the number of digits to the right of the decimal point.
They are crucial for precision in mathematics and various fields like science, engineering, and finance.
For example:

- The number 0.5 has one decimal place.
- The number 0.75 has two decimal places.
- The number 0.0084 has four decimal places.
When rounding, you often reduce the number of decimal places to make the number simpler.
Rounding 0.0084 to the nearest thousandth means expressing it with three decimal places, which results in 0.008.
This makes numbers more manageable without significantly losing accuracy.