MULTIPLICATION 5.NBT.2
Multiplying Whole Numbers and Decimals by Powers of Ten
Purpose:
To illustrate the placement of decimal points when multiplying by powers of 10
Materials:
Blank Decimal Squares - Multiplying by Powers of 10 (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Blank
Decimal
Squares
pencils
or colored
markers
1. Distribute Blank Decimal Squares "Multiplying by Powers of 10" to students.
a. Shade the top blank square in #1a on your sheet for .2 and the lower two squares to show
10 × .2. Complete the equation for this product. (10 × .2 = 2.0) Discuss that the square for
.2 has 2 shaded parts and 10 × 2 = 20 shaded parts. Since there are 10 equal parts in a whole
square, 20 shaded parts is 2 whole squares.
b. Shade the top blank square in #1b on your sheet for .14 and the lower two squares to
show 10 × .14. What is the equation for this product? (10 × .14 = 1.4) Discuss that the
square for .14 has 14 shaded parts and 10 × 14 = 140 shaded parts. Since there are 100
parts in a whole square, 140 shaded parts is 1 whole square and 40 parts out of 100.
× 10
10 × .2 = 2.0
× 10
10 × .14 = 1.4
c. What patterns do you see in computing these products? (The decimal in the number
being multiplied by 10 is moved one place to the right; and to multiply a whole number
by 10, a zero is placed at the right end of the number.)
2a. Shade the top blank square in #2a for .01 and the
lower square to show 100 × .01. Complete the equation
for this product. (100 × .01 = 1.0) Discuss that 100 times
one shaded part is 100 shaded parts and for a square with
100 equal parts, this is one whole square.
× 100
100 × .01 = 1.0
b. Shade the top square in #2b for .02
and the lower two squares to show 100 × .02.
What is the equation for this product?
(100 × .02 = 2.0) Discuss that the square for
.02 has 2 shaded parts and 100 × 2 = 200 shaded
parts. Since there are 100 equal parts in a whole
square, 200 shaded parts is 2 whole squares.
× 100
100 × .02 = 2.0
c. What patterns do you see in computing these products? (The decimal in the number
being multiplied by 100 is moved two places to the right; and to multiply a whole number
by 100, two zeros are placed at the right end of the number.)
3a. Shade the top square in #3a for .001 (one part out of 1000) and the lower square to
show 1000 × .001. Complete the equation for this product. (1000 × .001 = 1.0) Discuss that
1000 times one shaded part is 1000 shaded parts or one whole square.
× 1000
1000 × .001 = 1.0
b. Repeat this activity for 3b on your sheet to illustrate 1000 × .002 and complete the equation.
c. What patterns do you see in computing these products? (The decimal in the number being
multiplied by 1000 is moved three places to the right; and to multiply a whole number by
1000, three zeros are placed at the right end of the number.)
3
4. The whole number 1000 is called the "third power of 10" because 1000 = 10 . Similarly,
100 is called the "second power of 10" and 10 is called the "first power of 10."
What patterns can you see when numbers are multiplied by powers of 10? (If the number is a
decimal, the decimal point is moved to the right, and the number of places it is moved is the
power of 10. When multiplying a whole number by a power of 10, zeros are placed at the
right end of the number and the number of zeros is also the power of 10.)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheet 5.NBT.2 #1