 Find the absolute error if the number X = 0.00000545828 is truncated to three decimal digits: (i) rounded off to three decimal digits.


We need to calculate the **absolute error** when the number \( X = 0.00000545828 \) is truncated and rounded off to three decimal places.

### (i) Truncated to three decimal digits:
Truncating a number means cutting off digits beyond the required precision without rounding.

Since \( X = 0.00000545828 \), we truncate it to three decimal digits (after the decimal point), which gives:

\[
X_{\text{truncated}} = 0.000
\]

The **absolute error** is the difference between the original number and the truncated number:

\[
\text{Absolute Error (truncated)} = |X - X_{\text{truncated}}| = |0.00000545828 - 0.000| = 0.00000545828
\]

Thus, the absolute error when truncated to three decimal digits is:

\[
\boxed{0.00000545828}
\]

### (ii) Rounded off to three decimal digits:
Rounding involves adjusting the number based on the next digit after the desired precision. Since \( X = 0.00000545828 \), we look at the fourth decimal place, which is \( 5 \). According to rounding rules, if the next digit is 5 or more, we round up the last digit of the desired precision.

So, rounding \( 0.00000545828 \) to

Find the absolute error if the number X = 0.00000545828 is truncated to three decimal digits: (i) rounded off to three decimal digits.

Learn how to calculate the absolute error when the number X = 0.00000545828 is truncated or rounded off to three decimal digits. This guide explains the steps for truncation and rounding, and the absolute error formula. Suitable for high school students in Grades 10-12.

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