Math with Mr. J: Converting Between Fractions, Decimals, and Percents

Overview of Course

• A mini-course on converting fractions, decimals, and percents.
• Covered conversions:
  • Decimals to Fractions
  • Decimals to Percents
  • Fractions to Decimals
  • Fractions to Percents
  • Percents to Fractions
  • Percents to Decimals
• The course is divided into chapters with timestamps for easy navigation.

Converting Decimals to Fractions

1. Understanding Decimal Places

   • Determine the place value where the decimal ends (tenths, hundredths, thousandths, etc.).
   • This place value becomes the denominator.
   • The digits to the right of the decimal become the numerator.

2. Examples

   • 0.9: Ends in tenths place – Fraction: (\frac{9}{10}). Simplified: Already in simplest form.
   • 0.09: Ends in hundredths place – Fraction: (\frac{9}{100}). Simplified: Already in simplest form.
   • 0.2: Ends in tenths place – Fraction: (\frac{2}{10}). Simplified: (\frac{1}{5}).
   • 0.75: Ends in hundredths place – Fraction: (\frac{75}{100}). Simplified: (\frac{3}{4}).
   • 0.014: Ends in thousandths place – Fraction: (\frac{14}{1000}). Simplified: (\frac{7}{500}).
   • 3.36: Whole number 3 with decimal 0.36 – Fraction: 3 (\frac{36}{100}). Simplified: 3 (\frac{9}{25}).

Converting Decimals to Percents

1. Method

   • Multiply the decimal by 100.
   • Quick method: Move the decimal point two places to the right.

2. Examples

   • 0.52: 52%
   • 0.01: 1%
   • 0.9: 90%
   • 0.436: 43.6%

Converting Fractions to Decimals

1. Method

   • Divide the numerator by the denominator.
   • Use long division or a calculator.

2. Examples

   • (\frac{1}{8}): 0.125
   • (\frac{5}{12}): 0.4166... (repeating)
     • Can be rounded off as needed.
   • (\frac{9}{16}): 0.5625
   • (\frac{30}{35}): 0.857142 (repeating)

Converting Fractions to Percents

1. Method

   • Convert fraction to decimal.
   • Multiply the decimal by 100.

2. Examples

   • (\frac{3}{4}): 75%
   • (\frac{7}{15}): 46.6...% (repeating); can round to 47%
   • (\frac{24}{30}): 80%
   • (\frac{3}{16}): 18.75%

Converting Percents to Fractions

1. Method

   • Rewrite the percent as a fraction over 100.
   • Simplify if possible.

2. Examples

   • 23%: (\frac{23}{100})
   • 10%: (\frac{1}{10}) (simplified)
   • 94%: (\frac{47}{50}) (simplified)
   • 65%: (\frac{13}{20}) (simplified)

Converting Percents to Decimals

1. Method

   • Divide the percent by 100.
   • Move the decimal point two places to the left.

2. Examples

   • 85%: 0.85
   • 2%: 0.02
   • 70%: 0.7
   • 39.4%: 0.394

Conclusion

• A comprehensive guide to converting between fractions, decimals, and percents.
• Useful for understanding relationships and simplifying mathematical expressions.
• Simplifying fractions and understanding repeating decimals are key aspects.

• Study Tip: Practice converting back and forth to solidify understanding and speed. Use a calculator for more complex divisions to familiarize with decimal conversions.