Writing Decimals as Fractions What is the fraction

Writing Decimals as Fractions

What is the fraction representation of each decimal? 0. 3 = 3/10 0. 27 = 27/100 0. 493 = 493/1000

REMINDER!! • ALWAYS WRITE FRACTIONS IN SIMPLEST FORM. • Example: • 0. 45 = 45/100 = 9/20 • 2. 6 = 2 6/10 = 2 3/5

0. 3333…. What is the fraction representation of this decimal?

0. 454545…. . How could you write this decimal as a fraction?

45/100 = 0. 45 Making the denominator greater does what to a fraction? It makes the fraction smaller. Make the denominator a bit greater. 45/101 = 0. 4455… You will discover that the fraction is even less.

Today’s problems will involve looking for patterns to help write repeating decimals as fractions. Assignment: 1. Complete handout 5. 3 2. Class discussion 3. Complete “Follow Up” problems 5. 3

SUMMARY • What is the decimal representation for these fractions? 19/9 = 2. 11111… 20/9 = 2. 22222…

• What is the decimal representation for these fractions? 50/99 100/99 = = 0. 505050… 1. 010101…

What fraction is equivalent to 4. 111111… 0. 353535… Answers: 4 1/9 or 37/9 35/99

Can you predict the decimal representations for fractions with denominators of 999 and 9999? If there are 3 digits repeating the denominator will be 3 nines. If there are 4 digits repeating the denominator will be 4 nines.

Exploration Another method to change repeating decimals to fractions. Change 0. 454545… to a fraction Call the unknown fraction N. N = 0. 454545…. . Multiply both sides of the equation by 100 N = 45. 454545… Subtract the first equation from the second: 100 N = 45. 454545… - N = 0. 454545… 99 N = 45 Therefore: N = 45/99 or 5/11