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Chapter 0: Problem 34

Approximate each number (a) rounded and (b) truncated to three decimal places. $$ 0.05388 $$

Short Answer

Expert verified
Rounded: 0.054, Truncated: 0.053

Step by step solution

01

Understand Rounding and Truncating

Rounding a number involves looking at the digit to the right of the desired decimal place and adjusting the last kept digit accordingly. Truncating means cutting off all digits beyond the desired decimal place without rounding.
02

Round to Three Decimal Places

First, identify the third decimal place in the number 0.05388. The third decimal place is 3. Look at the digit immediately to its right (the fourth decimal place), which is 8. Since 8 is greater than or equal to 5, round the third decimal place up from 3 to 4. Thus, 0.05388 rounded to three decimal places is 0.054.
03

Truncate to Three Decimal Places

To truncate 0.05388 to three decimal places, simply remove all digits after the third decimal place without rounding. This leaves us with 0.053.

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Key Concepts

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

Rounding Numbers
Rounding numbers is an essential skill in mathematics, ensuring values are easier to work with. The process involves looking at the specific decimal place you need and deciding if it should stay the same or increase by one.
For example, if you need to round the number 0.05388 to three decimal places, you look at the third decimal place, which is 3, and then check the number right after it (4th place), which is 8.
If the number after your target place is 5 or higher, you round up. Otherwise, you keep it the same. So, in this case, the 8 is greater than 5, and we round the 3 up to 4, making the rounded number 0.054.
This process helps to simplify numbers without losing too much precision.
Truncating Decimals
Truncating decimals is another way to simplify numbers, but it works a bit differently from rounding. Truncation means cutting off digits beyond a certain decimal place without worrying about rounding up or down.
So, for the number 0.05388, if you truncate to three decimal places, you simply cut off everything after the third digit. You don鈥檛 check the next digit like you do when rounding. This leaves you with 0.053.
Truncating is often used in computer science and programming, where precision is critical and rounding up or down might introduce errors. It's a straightforward method that keeps numbers neat and just as needed.
Decimal Places
Understanding decimal places is crucial for both rounding and truncating numbers. A decimal place refers to the position of a number to the right of the decimal point. Each place has a specific value based on its distance from the decimal point.
The first place represents tenths, the second hundredths, and the third thousandths, and so on.
In the number 0.05388, the digit 5 is in the hundredths place, 3 is in the thousandths place, and so on. When asked to round or truncate to three decimal places, you're focusing on digits up to the thousandths place.
Knowing which decimal place to work with helps ensure accuracy in rounding or truncating, and it is a fundamental skill in handling both simple and complex mathematical tasks.

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Most popular questions from this chapter

Rationalize the numerator of each expression. Assume that all variables are positive when they appear. $$\frac{\sqrt{11}+1}{2}$$

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