BASIC CONCEPTS 5.NBT.3
Reading and Writing Mixed Decimals
Purpose:
To read and write mixed decimals and illustrate place value
Materials:
Decimal Squares, Mixed Decimals Place Value Tables (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Writing mixed decimals and their names
Decimal
Squares
pencils
and paper
1a. Select any green square and use the backs of three other
green squares to model a mixed decimal. For the decimal
.45, the mixed decimal here is 3.45 and its name is "three
and forty-five hundredths." It is called a mixed decimal
because it has a whole number part and a decimal part.
b. Ask a few students to describe the decimal part of their
mixed decimal and give the name of their mixed decimal.
3.45
2. Select any red square and use the backs of two
red squares to model a mixed decimal. Ask a few
students to write their mixed decimal and give its
name. ("two and seven tenths" in this example.)
2.7
3. Repeat this activity by selecting any thousandths square and using the back of one
yellow square to represent a mixed decimal. Ask a few students to describe their mixed
decimals.
4. Select one of the following mixed decimals, represent it with the front and backs of
squares, and write its name. Discuss the informal names for mixed decimals. For example,
sometimes we call 4.725 by the name "four point seven two five" but its official name is
"four and seven hundred twenty-five thousandths."
a. 4.8
b. 1.025
c. 2.75
d. 3.05
e. 1.3
f. 2.925
5. Show students the diagram below.
 What similarity is there between the name of the whole number part of this mixed
decimal and the name of the decimal part? (The first part is read as a whole
number, "four thousand two hundred eight" and the decimal part is also read as a
whole number after which the name of the place value of the last digit is read, "six
hundred thirty-five thousandths")
4208.635
four thousand two hundred eight and six hundred thirty-five thousandths
Activity 2 Place value for mixed decimals
Mixed
Decimal
Place Value
Tables
pencils
and paper
1. Distribute sheets or two rows of Mixed Decimal Place Value Tables. Complete a place
value table for each mixed decimal: a. 5704.239 b. 723.196 c. 406.37
 What patterns do you see in the place value table? (To the immediate left and right of
the ones digit is the tens digit and the tenths digit; then moving one place left and
right is the hundreds digit and the hundredths digit; moving one more place to the
left and right is the thousands digit and the thousandths digit.
 The place values to the left of the ones place are increasing powers of 10. List
these powers of 10. (101 102 and 103) The place values to the right of the ones
place can be written as the fractions 1/10, 1/100, and 1/1000 whose
denominators are powers of 10. (Note: These fractions can also be written as
powers of 10 with negative exponents, 10-1, 10-2, 10-3)
2. The powers of 10 can be used to write a mixed decimal in expanded form. For example:
5(103) + 7(102) + 0(101) + 4(1) + 2(
1
10
) + 3(
1
100
) + 9(
1
1000
)
 Write each mixed decimal in expanded form: a. 402.189 b. 2476.445 c. 38.307
3. The place value table shows the place value for each digit. For example, in the mixed
decimal 5704.239. the place value of the digit "7" is hundreds, and the place value for
the digit "2" is tenths.
 Write the place value for each digit in 9473.286. (9 is in the thousands place; 4 is in
the hundreds place; 7 is in the tens place; 3 is in the ones place or units place; 2 is in
the tenths place; 8 is in the hundredths place; and 6 is in the thousandths place.)
4. What is the value of each digit marked by an arrow?
a. 47.38
b. 3347.892
(a. eight hundredths
c. 2.007
b. three hundred
d. 14.726
c. zero tenths
d. six thousandths)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NBT.3 #5 and #6
decimalsquares.com Place Value
Strategy (Each player tries to form the
greater decimal by placing numbers
from the spinner into the table. The
player with the greater decimal wins
the round. The first player to win two
rounds wins the game.
Mixed Decimal Place Value Tables Name:
Date:
.