Converting Simple Decimals to Fractions and Vice Versa

Converting Simple Decimals to Fractions and Vice Versa

Today’s Learning Goals § We will continue to link our understanding of fractions with decimals. § We will continue to develop our understanding of place value when determining the fraction equivalence of decimals.

Representing Decimals n n Recently, we have seen how to represent a decimal number to the hundredths using a rectangle cut up into 100 parts. For example, how would we represent the number 2. 34 if we let the large rectangle below represent 1 whole? Good…we need 2 wholes and 34 hundredths.

Decimals to Fractions n n The number 2. 34 and the representation above show different ways to write the number as a fraction. First, you could write the decimal out in expanded form. Expanded form shows the value of each place. 3 4 on huetes nd nt re hs dt hs 2 n How would we write 2. 34 in expanded form? Nice…

Decimals to Fractions n When writing a decimal as a mixed fraction, we must state how many wholes there and then what part of another whole by combining everything to the right of the decimal place. n How would we write 2. 34 as 2 3 4 a mixed fraction? on huetes nd nt re hs dt hs n Another way to write a decimal is as a mixed fraction. Good…

Decimals to Fractions n n A third way to write a decimal is just as a single fraction. When writing a decimal as a single fraction, we must combine all place values together. 3 4 on huetes nd nt re hs dt hs 2 n How would we write 2. 34 as a single fraction? Good…

Fractions to Decimals n n a) d) As we have discussed, all decimal numbers are fractions with a denominator that is a power of 10 (e. g. tenths, hundredths). Consider the following fractions. How would you write the following as decimals? = 0. 3 = 2. 6 b) e) = 0. 06 = 35. 24 c) = 0. 52 f) = 1. 07

Fractions to Decimals Suppose the fraction was. This fraction is not in tenths or hundredths. What could we do to write this fraction as a decimal? Excellent…we could get an equivalent fraction for 2/5. n n Now that we have 2/5 written with a base-10 denominator, how could we write 2/5 as a decimal? Awesome… = 0. 4

Fractions to Decimals n a) Consider the following fractions. How would you write the following as decimals? b) c)

Partner Work n You have 20 minutes to work on the following problems with your partner.

For those that finish early What number does each letter represent? A 0 C B 0. 05 0. 1 E D 0. 15 0. 25

Big Idea from Today’s Lesson n We can represent the same decimal number in many different ways. n n In expanded form, mixed fraction form, or as a single fraction. One way to go from a fraction to a decimal is to get the fraction to have a denominator that is a power of 10.

Homework n n Complete Homework Worksheet. Pg. 155 (2, 3, 15, 17, 18)