Problem 30 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ -\frac{5}{12} $$

Step-by-Step Solution

Answer

-0.4167

Step 1: Understand the Problem

The task is to convert the fraction \( -\frac{5}{12} \) into its decimal notation.

Step 2: Set Up the Division

A fraction can be converted to decimal by dividing the numerator by the denominator. Set up the division of 5 by 12.

Step 3: Perform the Division

Divide 5 by 12 to find its decimal form. This might require long division: \( 5 \div 12 \approx 0.416666... \)

Step 4: Apply the Sign

Don't forget the negative sign from the original fraction. Therefore, the decimal notation of \( -\frac{5}{12} \) is \ -0.416666... \ or \ -0.4167 \ (rounded to four decimal places).

Key Concepts

fractions to decimals

Converting fractions to decimals is a useful skill in math. It helps in various situations like measurements, finances, and calculations. To convert a fraction like \(-\frac{5}{12}\) into a decimal, you divide the numerator (the top number) by the denominator (the bottom number). The numerator here is \(5\), and the denominator is \(12\). This process involves division, which can be performed using long division. Let's dive deeper into how this works.

long division

Long division is a step-by-step method of dividing two numbers. Here’s how you can use long division to convert the fraction \(-\frac{5}{12}\) into a decimal:
1. Set up the division problem: Write the numerator (5) inside the division bracket and the denominator (12) outside.
2. Divide the numerator by the denominator: How many times does 12 go into 5? It doesn't, so place a zero (0) and a decimal point to the right of the 5 to make it 5.0.
3. Now, think of it as 50. How many times does 12 go into 50? The answer is 4 times, as \(12 \times 4 = 48\). Write 4 next to the decimal point.
4. Subtract \(48\) from \(50\) (50 - 48 = 2).
5. Bring down a zero, making it 20. How many times does 12 go into 20? The answer is 1 time, as \(12 \times 1 = 12\). Write 1 next to 4, making it 0.41.
6. Subtract \(12\) from \(20\) (20 - 12 = 8).
7. Bring down another zero, making it 80. Continue this process to get more precision. The decimal for \(-\frac{5}{12}\) keeps repeating: \(-0.4166...\).

rounding decimals

Rounding decimals is a way to simplify a number while keeping its value close to what it originally was. It’s especially useful when dealing with repeating decimals or when you need a certain level of precision.
When we convert \(-\frac{5}{12}\) into a decimal, we get \-0.416666...\.
To round a decimal:
1. Look at the digit right after the place value you are rounding to. For example, if rounding to four decimal places, check the fifth digit.
2. If that digit is 5 or more, round the previous digit up by one.
3. If that digit is less than 5, keep the previous digit the same.
So, rounding \-0.416666...\ to four decimal places gives us \-0.4167\.