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Chapter 0: Problem 36

Approximate each number (a) rounded and (b) truncated to three decimal places. $$ 1.0006 $$

Short Answer

Expert verified
(a) 1.001 (b) 1.000

Step by step solution

01

Understanding Rounding

Rounding a number involves looking at the digit immediately after the third decimal place and determining whether to round up or down based on its value.
02

Rounding the Number

Look at the fourth decimal place of 1.0006, which is '6'. Since '6' is greater than or equal to '5', round the third decimal place up by one. Therefore, 1.0006 rounded to three decimal places is 1.001.
03

Understanding Truncating

Truncating a number involves cutting off all digits after the desired decimal place without rounding.
04

Truncating the Number

Simply remove every digit beyond the third decimal place. Therefore, 1.0006 truncated to three decimal places is 1.000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Places
When working with decimals, 'decimal places' refer to the number of digits to the right of the decimal point. For instance, in the number 1.0006, the digits '0', '0', '0', and '6' are all decimal places. The more decimal places a number has, the more precise it is. In many mathematical and real-world applications, only a certain number of decimal places are needed for sufficient accuracy. For example, rounding a number to three decimal places involves looking at the first three digits right after the decimal point.
Rounding Rules
Rounding rules are a set of guidelines that tell us how to round numbers to the desired decimal places. Here's a simple breakdown of rounding rules:
  • If the digit immediately after the desired decimal place is 5 or higher, round up.
  • If the digit is less than 5, round down.
Let's apply these rules to the example number 1.0006 and round it to three decimal places. The fourth decimal place is '6'. Since '6' is greater than '5', we round the third decimal place up. Therefore, 1.0006 rounded to three decimal places becomes 1.001.
Truncation in Mathematics
Truncation is a method used to shorten a number by cutting off digits after a certain decimal place without rounding. Unlike rounding, truncation simply removes the digits without adjusting the last kept digit. To truncate 1.0006 to three decimal places, we remove all digits beyond the third decimal place. This leaves us with 1.000.

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Most popular questions from this chapter

The period \(T\), in seconds, of a pendulum of length \(l,\) in feet, may be approximated using the formula $$T=2 \pi \sqrt{\frac{l}{32}}$$ Express your answer both as a square root and as a decimal approximation. Find the period \(T\) of a pendulum whose length is 16 feet.

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