converting decimals

Introduction to Conversions

• The lesson begins with a contextual scenario regarding shopping:

  • New boots are on sale with a discount of 40% off the original price of $129.

  • The question posed is whether one has enough money ($75) to purchase the boots at the discounted price.

  • Key to answering the question is converting the percentage (40%) into a decimal.

Importance of Conversion Skills

• This lesson highlights the importance of converting between various mathematical forms:

  • Fractions to Decimals

  • Fractions to Percents

  • Decimals to Fractions

  • Decimals to Percents

  • Percents to Decimals

  • Percents to Fractions

• Proficiency in these conversions enables:

  • Accurate price calculations of sale items.

  • Efficient tip calculations.

  • Various other daily mathematical tasks.

• At the conclusion of the lesson, students should be able to correctly convert between fractions, decimals, and percentages.

Converting Decimals to Fractions

Basic Method

• To convert a decimal to a fraction, follow these steps:

  1. Identifying the Numerator:

  • Use the digits of the decimal without the decimal point.

  1. Creating the Denominator:

  • Count the number of decimal places to the right.

  • For each decimal place, add a zero to the denominator.

  • Place a one in front of the zeros.

• Example:

  • The decimal 0.35 (35 hundredths) translates to:

  • Numerator = 35

  • Denominator = 100

  • Resulting Fraction: $\frac{35}{100}$

  • Reduce to lowest terms: $\frac{7}{20}$

Converting Decimals with Whole Numbers

• When a decimal includes a whole number:

  1. Use the entire number (without the decimal) as the numerator.

  2. Follow the same method to determine the denominator based on decimal places.

• Example:

  • The decimal 1.125 (one and one hundred twenty-five thousandths) translates to:

  • Numerator = 1125

  • Denominator = 1000

  • Resulting Fraction: $\frac{1125}{1000}$

  • This is an improper fraction, and simplifying it yields a mixed number: 1 $\frac{1}{8}$

Handling Zeros in Decimals

• If the decimal to be converted has zeros immediately to the right of the decimal point:

  • Do not include these zeros in the numerator.

  • However, these zeros must be counted when preparing the denominator.

• Example:

  • The decimal 0.023 (23 thousandths) translates directly to:

  • Numerator = 23

  • Denominator = 1000 (because there are three decimal places)

  • Resulting Fraction: $\frac{23}{1000}$

Personal Reflection

• The lesson ends with a personal note about attempting to improve a marriage, showing that conversions and mathematical processes can also relate to real-life experiences and challenges.