Question

Approximate each number (a) rounded and (b) truncated to three decimal places. $$ 0.06291 $$

Short answer

0.063 (rounded), 0.062 (truncated).

Step-by-step solution

Understand Rounding

Rounding a number to three decimal places means looking at the fourth decimal place and using it to determine whether the third decimal place stays the same or increases by one. If the fourth decimal place is 5 or higher, the third decimal place is increased by one. Otherwise, it stays the same.

Apply Rounding to the Given Number

The given number is 0.06291. The fourth decimal place is 9, which is greater than 5. Therefore, round up the third decimal place: Thus, 0.06291 rounded to three decimal places is 0.063.

Understand Truncation

Truncating a number to three decimal places means simply cutting off the number after the third decimal place without rounding. Only the first three decimal places are kept, and the rest are discarded.

Apply Truncation to the Given Number

Using the same number, 0.06291, we truncate after the third decimal place: Thus, 0.06291 truncated to three decimal places is 0.062.

Key concepts

decimal places

When working with numbers, decimal places are the digits that appear after the decimal point. In the number 0.06291, the digits 6, 2, 9, and 1 are the decimal places. Each position after the decimal point has a specific value: the first place is tenths, the second is hundredths, the third is thousandths, and so on. Understanding decimal places is crucial for accurately performing rounding and truncation procedures. For instance, if you need to round or truncate to three decimal places, you focus on the digits in the thousandths place.

rounding rules

Rounding is a technique used to approximate a number to a certain number of decimal places by following a set of rules. Here are the key steps:
1. Identify the decimal place to which you want to round.
2. Look at the digit immediately to the right of this place (the 'rounding digit').
3. If the rounding digit is 5 or higher, increase the last retained digit by one.
4. If the rounding digit is less than 5, leave the last retained digit unchanged.
For example, rounding 0.06291 to three decimal places involves looking at the fourth decimal place, which is 9 in this case. Since 9 is greater than 5, the value at the third decimal place is increased by one, changing 0.06291 to 0.063.

truncation method

The truncation method is a straightforward approach to approximating numbers by cutting off all digits beyond a specified decimal place without any rounding.
Here's how truncation is done:
1. Determine the decimal place to which you want to truncate.
2. Simply discard all digits beyond this place.
For example, truncating 0.06291 to three decimal places involves keeping only the digits up to the thousandths place. The resulting number is 0.062, because the digits beyond the third decimal place (the 9 and 1) are removed without any rounding adjustment.
The truncation method is often used when an exact cut-off is needed, without rounding the numbers.