# Decimal Place Value — Two Decimal Digits

This is a complete lesson with instruction and varied exercises, explaining decimal place value and expanded form using numbers that have two decimal digits (tenths and hundredths). Students write numbers in expanded form / normal form, and convert decimals to fractions and vice versa. The lesson is meant for 4th or 5th grade.

Look at the different place values in the place value chart.
What would be the next place value after tenths?

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 2 7 0 3. 9 4 thou- sands hund- reds tens ones tenths Let's look at the number 0.27.  First, mark 0.27 on the number line.  Then, look at the chart below.

 We see from the chart that 0.27 has 2 tenths and 7 hundredths, or 2 10 and 7 100 .

But that is two separate fractions. How can 0.27 be written as a single fraction?

 0 . 2 7 ones tenths hund- redths
 To find out, we add 2 10 + 7 100 = 20 100 + 7 100 = 27 100 . So, 0.27 is 27 100 or 27 hundredths.
0.51 is 5 tenths and 1 hundredth, or  0.5 + 0.01. That is its expanded form because it is written as a sum of the different parts that make up the number. Let's write the expanded form using fractions, and add:
 0 . 5 1 ones tenths hund- redths
 0.51 = 5 10 + 1 100 = 50 100 + 1 100 = 51 100 .   So, 0.51 is 51 hundredths.

1. Break each number into ones, tenths and hundredths (this means you write it in expanded form).
Use both fractions and decimals. Then read the number.

 a. 0.78 = 0.7 + 0.08 78 100 = 7 10 + 8 100

(seventy-eight hundredths)

 b. 0.33 = ______ + ______

 c. 0.19 = ______ + ______
 d. 1.25 = 1 + 0.2 + 0.05

 e. 3.97 = ___ + ____ + _____

 f. 4.65 = ___ + ____ + _____

2. Write as a decimal or as a fraction.

Decimal Fraction
a.
 56 10
b.
 2 35 100
c. 0.47
 Decimal Fraction d. 0.06 e. 5.06 f. 7.99
Decimal Fraction
g.
 3 100
h.
 12 20 100
i.
 8 4 10

3. Name the place value that has been underlined in the number.

 a. 209.87   _____________________________ b. 503.49   _____________________________ c. 2,938.5    ____________________________ d. 2,093.40   ____________________________ e. 2,093.40   ____________________________ f. 2,093.40   ____________________________

4. These numbers are written in expanded form. Write them as decimals.

 a. 41 100
 b. 6 + 80 100
 c. 19 + 9 100
 d. 90 + 8 + 1 100
 e. 50 + 12 100
 f. 2,000 + 2 + 2 100
 g. 7,000 + 400 + 50 + 8 + 37 100
 h. 6,000 + 40 + 4 + 6 100

5. Break down the following numbers. Then read the numbers in two different ways.

a.
 456.14 = 400 + 50 + 6 + 14 100
e. 3,203.00
b. 0.06 f. 90.03
c. 44.41 g. 80.8
d. 605.6 h. 0.55

6. Fill in the blanks.

 a.  0.45 = 0.05 + _______ e.  23.08 = 0.08 + 3 + _______ b.  0.78 = 0.7 + ________ f.  101.52 = 1 + 100 + 0.02 + _______ c.  1.43 = 1 + _______ + 0.03 g.  430.21 = 400 + 0.01 + 0.2 +  _______ d.  0.99 = 0.9 + ________ h.  14.05 = 10 + _______ + 0.05

7. Mark these decimals on the number line (approximately): 0.2  0.42  0.58  0.13  1.19  0.81  0.75 8. Study the pictures. Then write
the following fractions as
decimals. = 1 4 = 25 100 =  0.25 = 1 5 = 20 100 =  0.20 = 0.2
 a. 3 4
 b. 2 4
 c.  1 1 4
 d.  1 3 4
 e.  2 1 4
 f.  3 3 4
 g. 2 5
 h. 4 5
 i.  1 1 5
 j.  1 3 5
 k.  2 1 5
 l.  3 4 5

9. Match each expression from
the first column with one from
the second.
 5 14 100
 15 + 4 100
 5 + 4 10
 14 100 + 15
 0.14 + 15 15 + 0.04 0.14 + 5 5 + 0.4

Write each decimal given in expanded form in normal form (two decimal digits)

Write decimals as fractions (1-2 decimal digits) (the numbers are less than 1)

Write decimals as mixed numbers (1-2 decimal digits)

Write fractions as decimals (tenths and hundredths) (the numbers are less than 1)

Write improper fractions as decimals (till hundredths)

This lesson is taken from Maria Miller's book Math Mammoth Decimals 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Decimals 1

A self-teaching worktext for 4th grade that gives a solid foundation for decimals. It covers tenths and hundredths, comparing decimals, adding and subtracting decimals both mentally and in columns, multiplying decimals by whole numbers, rounding, estimating, and money problems.