Problem 19 - Prealgebra

Question

Write each decimal as a fraction or mixed number in simplest form. $$0.09$$

Step-by-Step Solution

Answer

0.09 as a fraction is \(\frac{9}{100}\).

Step 1: Understand the Decimal

The decimal given is 0.09. It represents nine hundredths.

Step 2: Convert Decimal to Fraction

Write 0.09 as a fraction by placing 9 over 100, because 0.09 is 9 out of 100. This is expressed as \( \frac{9}{100} \).

Step 3: Simplify the Fraction

Check if \( \frac{9}{100} \) can be simplified. Since 9 and 100 have no common factors other than 1, \( \frac{9}{100} \) is already in its simplest form.

Key Concepts

Decimals to Fractions

Converting decimals to fractions is a useful skill in prealgebra. It helps in understanding numbers better and comparing them easily. To convert a decimal like 0.09 into a fraction, think about what the decimal really represents. The number 0.09 is the same as nine hundredths.
To express this as a fraction, take the digits of the decimal (09, or just 9) and place them over the base 10 power that matches the decimal's position. Since 0.09 has two decimal places, you use 100 as the denominator, resulting in the fraction \( \frac{9}{100} \). Always remember:

• Count the number of decimal places in the original decimal.
• Use a denominator of 1 followed by as many zeros as there are decimal places.

This method can be applied to any decimal number, making it easier to represent them as fractions or mixed numbers.

Simplifying Fractions

Once you've converted a decimal into a fraction, the next step often involves simplifying it. Simplifying a fraction means rewriting it in its most concise form without changing its value.
The fraction \( \frac{9}{100} \) is our result for converting 0.09. To simplify, find the greatest common factor (GCF) of the numerator and the denominator. The GCF is the largest number that evenly divides both. In this case, 9 and 100 have no factors in common except for 1.
When both numbers have no common factors other than 1, the fraction is already simplified. That's why \( \frac{9}{100} \) can't be reduced further. To ensure you've simplified correctly, always check:

• Identify any common factors in the numerator and denominator.
• Divide both terms by their GCF, if applicable.
• Rewrite the fraction with these new values.

A simplified fraction is crucial for clarity and ease when using fractions in equations or comparing them with others.

Prealgebra

Prealgebra is an essential foundation for more advanced math topics. It covers the basic arithmetic skills necessary for understanding algebra and beyond.
Decimals and fractions are key components of prealgebra because they often appear in everyday math problems and academic exercises. By mastering the conversion of decimals to fractions and simplifying them, you strengthen your overall math skills.
Here are some of the core areas covered in prealgebra:

• Understanding and working with whole numbers, fractions, and decimals.
• Identifying and calculating with factors and multiples.
• Grasping the concepts of ratios, percentages, and basic algebraic expressions.

The skills gained in prealgebra, such as converting decimals to fractions and simplifying them, will help you tackle more complex problems in subjects such as algebra, geometry, and beyond. They also hone critical thinking skills, which are valuable in real-life problem-solving scenarios.