Changing Form Fractions and Decimals

Suppose you share a pan of brownies among four friends plus yourself. 1a) How many people are sharing the brownies? b) Draw a diagram to show how you would divide the pan of brownies. c) What fraction of the pan does each person receive?

d) Draw another diagram to show what part of the pan each person would get if it were divided into 10 equal parts. e) Write the fraction. f) Compare the diagrams. g) Write a decimal to represent each person’s share of the pan of brownies.

Suppose one of your friends does not like brownies. 2a) How many people are sharing the brownies? b) Draw a diagram to show how you would divide the pan of brownies. c) Write the fraction as an equivalent fraction with a denominator of 100. d) Write a decimal to represent each person’s share.

3a) What is as a decimal? b) What is as a decimal?

4a) Compare your answers to question 3 to the decimals you calculated in questions 1 and 2. b) How could we use a calculator to find the decimal equivalent of a fraction?

Example 1 Each pan of brownies requires 1 ¼ cups of sugar. Write 1 ¼ as a decimal. Solution Write ¼ as an equivalent fraction with a denominator of 10, 100, or 1000.

Combine the whole cup and the part to express the complete number in decimal form =

Example 2 Lynette and her sister together ate 0.6 of a pan of brownies. What fraction on the brownies did they eat? 0.6 means 6 tenths or 6/10. You can express this fraction in a simpler form by dividing the denominator and the numerator by the same number.

Definition Terminating Decimal A decimal number whose digits end Examples: 1.56, 1.023, 0.6

One of your friends had a big lunch and does not want any brownies. That leaves just three of you. How can you write each person’s share as a decimal? 1)Write the fraction of the brownies that each of you will have.

2) Convert 1/3 to a decimal number by dividing the numerator by the denominator. 3) How does the decimal number differ from the decimals 0.2 and 0.25? 4) Predict the decimal equivalent of 2/3. 5) Calculate the decimal equivalent of 2/3. 6) What do you notice about the last digit?

Definition Repeating Decimal A decimal number that has one or more digits that repeat without end. Examples:, 1.023, Period The sequence of repeating digits Example: in the decimal the period is 867

Definitions Length of the Period The number of digits in the repeating sequence Example: in the decimal … the length of the period is 3

Use a calculator to convert each fraction to a decimal. Fill in the table: FractionDecimal (Calculator Output) PeriodLength of Period Decimal (Repeating Notation)

1a) Use a calculator to express each fraction as a repeating decimal. b) Predict the decimal form of c) Use the pattern to write a fraction for: i) ii)

d) Write two equivalent fractions for. e) Write as a fraction. What is this fraction equal to?