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 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 The number 2.34 and the representation above show different ways to write the number as a fraction ones tenths hundredths First, you could write the decimal out in expanded form. Expanded form shows the value of each place. How would we write 2.34 in expanded form? Nice…

Decimals to Fractions Another way to write a decimal is as a mixed fraction. When writing a decimal as a mixed fraction, we must state how many wholes there are and then what part of another whole by combining everything to the right of the decimal place ones tenths hundredths How would we write 2.34 as a mixed fraction? Good…

Decimals to Fractions 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. How would we write 2.34 as a single fraction? Good… ones tenths hundredths

Fractions to Decimals 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? a) = 0.3 b) = 0.06 c) = 0.52 d) = 2.6 e) = 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. 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 Consider the following fractions. How would you write the following as decimals? a)b)c)

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

For those that finish early What number does each letter represent? AB CD E

Big Idea from Today’s Lesson We can represent the same decimal number in many different ways. 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 Complete Homework Worksheet. Pg. 155 (2, 3, 15, 17, 18)