/*! 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 43 The following problems review ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 43

The following problems review material from a previous section. Reviewing these problems will help you with the next section. Write as a decimal. $$\frac{1.23}{2}$$

Short Answer

Expert verified
The decimal equivalent of \( \frac{1.23}{2} \) is 0.615.

Step by step solution

01

Understand the Fraction

The problem asks you to write the fraction \( \frac{1.23}{2} \) as a decimal. To do this, you need to perform the division \( 1.23 \div 2 \).
02

Set Up the Division

Place 1.23 under the division bar, with 2 outside the division bar as the divisor. This shows that 1.23 is being divided by 2.
03

Divide the Whole Number Part

First, divide the whole number part, which is 1 in this case. 2 goes into 1 zero times, so the initial quotient digit is 0. Bring down the 2 from the decimal 1.23.
04

Divide Including Decimal

Now consider 12 (from 1.23). 2 divides into 12 six times. Write 6 in the quotient and subtract. Now bring down the next digit, which is 3.
05

Divide the Decimal with Remainder

Now you have 3 as a remainder. 2 goes into 3 once. Write 1 in the quotient, and the remainder is 1. You can add another zero to bring it to a complete division.
06

Complete the Division Process

With a remainder of 1 from 1.23, bring down a zero to make it 10. 2 divides into 10 five times evenly with no remainder, adding 5 to the quotient.
07

Write the Decimal Result

The full division results in 0.615. Hence, \( \frac{1.23}{2} \) as a decimal is 0.615.

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.

Fraction Division
To convert a fraction into a decimal, division of the numerator by the denominator is required. In our exercise, the fraction is \( \frac{1.23}{2} \). Here, 1.23 is the numerator, and 2 is the denominator.
Performing the division \( 1.23 \div 2 \) will allow us to find the decimal equivalent.
  • Start with the whole number in the numerator and see how many times the denominator fits into it.
  • Move through the digits, adjusting as necessary until you've achieved a fully precise decimal.
Understanding fraction division is crucial, as it's the bridge that transforms fractions into decimals. It rounds out our comprehension of both mathematical constructs.
Decimal Notation
Decimal notation is a way of expressing numbers using a base-10 system, which is crucial for understanding our exercised solution.
This system uses digits 0 through 9, applying place value to determine each digit's worth.
Consider the example of converting \( \frac{1.23}{2} \). With completion of division, we yield 0.615 in decimal notation.
  • Decimal points separate whole numbers from fractional parts.
  • Each position to the right of the decimal represents tenths, hundredths, thousandths, etc. Each step delves deeper into finer divisions.
Grasping decimal notation enhances our ease in reading and working with numbers commonly seen in everyday life and mathematical tasks.
Long Division
Long division is a structured method of resolving division, especially useful for decimals as seen in our exercise. It takes the problem step-by-step:
  • Write the dividend (1.23) beneath the division bar with each digit appropriately spaced.
  • Place the divisor (2) to the left of the bar.
  • Calculate how many times the divisor fits into parts of the dividend.
Use subtraction step-by-step to manage remainders and bring down available digits until completion. This methodical approach is particularly helpful for maintaining accuracy when calculating precise decimal answers from fractions.
Through each of these iterative steps, you'll smoothly convert any complex fraction into a straightforward 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

Divide. Find the sum of \(2 \frac{2}{3}\) and \(1 \frac{1}{2}\).

Multiply and divide as indicated. $$\frac{165}{84} \cdot \frac{24}{195}$$

Write each of the following ratios as a fraction in lowest terms. None of the answers should contain decimals. $$36 \quad to\quad 18$$

Add and subtract as indicated. $$\frac{1}{2}+\frac{3}{8}$$

Write each of the following ratios as a fraction in lowest terms. None of the answers should contain decimals. $$\frac{6}{5} \text { to } \frac{6}{7}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.