/*! 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 47 Round the following decimals to ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 47

Round the following decimals to the nearest thousandth. 0.5673 ______

Short Answer

Expert verified
0.567

Step by step solution

01

Identify the Thousandths Place

In the number 0.5673, the thousandths place is the third digit to the right of the decimal point. In this case, it's the number 7.
02

Identify the Digit for Rounding

Look at the digit to the right of the thousandths place to decide whether to round up or stay the same. In 0.5673, the digit in the ten-thousandths place is 3.
03

Apply Rounding Rule

Since the digit after the thousandths place is 3 (which is less than 5), we round down, meaning the digit in the thousandths place stays the same.
04

Write the Final Rounded Number

Since we did not need to round up, the final rounded number is 0.567.

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.

Understanding the Thousandths Place
When dealing with decimals, understanding place value is crucial. Each digit has a specific spot that determines its value. After the decimal point, the first digit represents the tenths place, the second digit the hundredths, and the third digit represents the thousandths place. For the decimal 0.5673, the digit '7' is in the thousandths place. This means 7 is multiplied by \(0.001\) or \(\frac{1}{1000}\). Knowing which digit is in the thousandths place helps you decide how to round your decimal accurately. Remember, the thousandths place is three digits to the right of the decimal point. Keeping this in mind makes rounding much easier and more precise.
Applying Decimal Rounding Rules
Rounding decimals involves specific rules that determine whether you 'round up' or 'round down'. Here are the steps:
  • Identify the digit in the place you are rounding to; in our case, it's the thousandths place.
  • Look at the digit immediately to the right of this place (the ten-thousandths place).
  • If the digit in the ten-thousandths place is 5 or greater, increase the digit in the thousandths place by 1 (round up).
  • If it is less than 5, leave the digit in the thousandths place as it is (round down).
In the example 0.5673, the digit in the ten-thousandths place is 3, so the thousandths place remains 7. Knowing these rules ensures your rounding is both quick and correct.
Exploring the Place Value System
The place value system is fundamental to understanding why each digit in a number decreases in value as you move from left to right. Each position represents a power of ten, and as you move right past the decimal point, you are dividing by 10 each time. Here's how it works:
  • Tenths (\(10^{-1}\)
  • Hundredths (\(10^{-2}\)
  • Thousandths (\(10^{-3}\)
This hierarchy means decimal numbers can seem complex, but it ensures precision. Knowing the place value system helps in rounding decimals because it clarifies how changing one digit impacts the entire number. For example, even a small change like rounding can significantly alter the value represented by a longer decimal.

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

A client weighed 85.4 kilograms (kg) in January. In February, the client gained \(1.8 \mathrm{~kg}\). In March, the client gained \(2.3 \mathrm{~kg}\). How much did the client weigh in March? ______

A client weighed 186.4 lb before getting sick. After a lengthy recovery period, the client weighed 167.6 lb. How much weight did the client lose? ______

Express the following decimals to the nearest hundredth. 0.147 ______

Identify the decimal with the largest value in the following sets. 0.1,0.05,0.2 ______

Divide the following numbers, and round to the nearest hundredth. \(5 \div 14.3=\)
See all solutions

Recommended explanations on Biology Textbooks

Microbiology

Read Explanation

Biological Molecules

Read Explanation

Cell Cycle

Read Explanation

Substance Exchange

Read Explanation

Organ Systems

Read Explanation

Reproduction

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.