/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Approximate each number (a) roun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 33

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

Short Answer

Expert verified
0.063 (rounded), 0.062 (truncated).

Step by step solution

01

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.
02

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.
03

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.
04

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression. (a) \(x=0\) (b) \(x=1\) (c) \(x=0\) (d) \(x=-1\) \(\frac{x^{3}}{x^{2}-1}\)

In Problems 113-120, use a calculator to evaluate each expression. Round your answer to three decimal places. \((8.2)^{6}\)

When dividing a polynomial by \(x-c,\) do you prefer to use long division or synthetic division? Does the value of \(c\) make a difference to you in choosing? Give reasons.

The final velocity \(v\) of an object in feet per second (ft/s) after it slides down a frictionless inclined plane of height \(h\) feet is $$v=\sqrt{64 h+v_{0}^{2}}$$ where \(v_{0}\) is the initial velocity (in \(\mathrm{ft} / \mathrm{s}\) ) of the object. (a) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 4 feet? Assume that the initial velocity is \(0 .\) (b) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 16 feet? Assume that the initial velocity is \(0 .\) (c) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of \(4 \mathrm{ft} / \mathrm{s} ?\)

Explain to a friend how the Distributive Property is used to justify the fact that \(2 x+3 x=5 x\).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.