Problem 43 - Prealgebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \( 1.23 \div 2 \).

Step 2: 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.

Step 3: 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.

Step 4: 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.

Step 5: 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.

Step 6: 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.

Step 7: Write the Decimal Result

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

Key Concepts

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.