Problem 95 - Prealgebra

Question

Write as a decimal. $$\frac{1}{16}$$

Step-by-Step Solution

Answer

The decimal of \( \frac{1}{16} \) is 0.0625.

Step 1: Understand the Fraction

The fraction given is \( \frac{1}{16} \). This means we have 1 part out of 16 parts of a whole. Our task is to convert this fraction into its decimal form.

Step 2: Divide the Numerator by the Denominator

To convert \( \frac{1}{16} \) to a decimal, divide the numerator (1) by the denominator (16). Set up the division: 1 divided by 16.

Step 3: Perform the Division

Perform the long division of 1 divided by 16. Since 1 is smaller than 16, add a decimal point and zeros to 1 to make it 10, 100, etc. Start by dividing 1.000000 by 16. This gives 0.0625.

Step 4: Confirm the Decimal

After performing the division, we find that \( \frac{1}{16} = 0.0625 \). Double-check by multiplying the decimal back by 16 to see if you get 1, confirming the division was correct.

Key Concepts

Fraction to Decimal

Converting a fraction into a decimal is a fundamental skill in mathematics. It's quite simple once you understand the core concept. You start with a fraction in the form of \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator. The goal is to express this fraction as a decimal number.

The process involves dividing the numerator by the denominator. Essentially, you are asking, "How many times does \( b \) fit into \( a \)?" For example, to convert the fraction \( \frac{1}{16} \) into a decimal, you perform the division 1 divided by 16. This results in a decimal value.

Fractions and decimals are two ways of representing the same thing: parts of a whole. Decimals, being more ubiquitous in digital devices and everyday transactions, make calculations smoother and often more intuitive.

Long Division

Long division is a method that simplifies breaking down complex division problems into manageable steps. It's especially useful when converting fractions to decimals. The long division process helps determine how many times the denominator fits into the numerator, beyond just whole numbers.

Here's a simplified step-by-step of the method:

• Set Up the Division: Write down the numerator (the number you're dividing) inside the division bracket and the denominator outside it.
• Attach Decimals: If the numerator is smaller than the denominator, append decimal zeros to aid the division.
• Divide: Carry out the division as you would with whole numbers. Identify how many times the denominator fits into the current number.
• Continue Until Satisfactorily Simple: Keep going with adding zeros and dividing until you derive a satisfactory decimal answer or recognize a repeating pattern.

Practicing long division not only helps with fractions but improves general arithmetic skills. It allows you also to double-check your work by reversing the operation (multiplying the decimal result by the original denominator) to see if you revert back to the original numerator.

Mathematics Education

Mathematics education plays a pivotal role in laying the foundation for critical thinking and problem-solving. Converting fractions to decimals, understanding long division, and comprehending mathematics concepts help students build logical reasoning skills. These skills aren't just for examinations but are applicable in everyday life and many professions.

Teaching these concepts allows students to develop an appreciation for numbers and patterns.

• Improves Problem-Solving Abilities: Students learn how to deconstruct problems, analyze them step by step, and find solutions.
• Enhances Logical Reasoning: Students are encouraged to look for patterns and establish strategies that make solving mathematical problems more systematic.
• Practical Applications: From budgeting to splitting bills and understanding interest rates, mathematics is an integral part of everyday financial decision-making.

Education systems aim to provide students with the tools they need to not only handle academic tasks but also apply mathematical reasoning in real-world contexts.