Decimals

What are Decimals?

Decimals contain a whole number and a fractional part that is separated by a dot, or a decimal point. For example, in \(76.5\), \(76\) is the whole number and \(5\) is the fractional part.

In this article, the lesson objectives are:

1. Express tenths as decimals
2. Express hundredths as decimals
3. Express thousandths as decimals
    

Watch our video lesson!

1. Express Tenths As Decimals

Express Tenths As Decimals

The square is divided into \(10\) equal parts. 

Each part represents one tenth. 
One tenth\(\begin{align}​​\\[2ex] &= \frac{1}{10} \\[2ex] &=0.1 \end{align}\)

We read \(0.1\) as zero point one.

Express Tenths On A Number Line

We can also write decimals on a place-value chart. 

For Example:

10 tenths\(\begin{align}​​\\[2ex] &= \frac{10}{10} \\[2ex] &=1.0 \end{align}\)

Question 1: 

Express 8 tenths as a decimal.

Solution:

8 tenths\(\begin{align}​​\\[2ex] &= \frac{8}{10} \\[2ex] &=0.8 \end{align}\)

Answer:

0.8

Question 2: 

Express 68 tenths as a decimal.

Solution:

68 tenths\(\begin{align}​​\\[2ex] &= \frac{68}{10} \\[2ex] &=6.8 \end{align}\)  

Answer:

6.8       

Question 3: 

Express 27 tenths as a decimal.

Solution:

27 tenths\(\begin{align}​​\\[2ex] &= \frac{27}{10} \\[2ex] &=2.7 \end{align}\)

Answer:

2.7

2. Express Hundredths As Decimals

The square is now divided into \(100\) equal parts. 

Each part represents one hundredth. 
One hundredth\(\begin{align}​​\\[2ex] &= \frac{1}{100} \\[2ex] &=0.01 \end{align}\)

We read 0.01 as zero point zero one.

Express Hundredths On A Number Line

We can also write decimals on a place-value chart. 

For example:
10 hundredths\(\begin{align}​​\\[2ex] &= \frac{10}{100} \\[2ex] &=0.10 \end{align}\)

Question 1: 

Express 7 hundredths as a decimal.

Solution:

7 hundredths\(\begin{align}​​\\[2ex] &= \frac{71}{100} \\[2ex] &=0.07 \end{align}\)

Answer:

0.07

Question 2: 

Express \(79\) hundredths as a decimal.

79 hundredths \(=\) __________

Solution: 

79 hundredths\(\begin{align}​​\\[2ex] &= \frac{79}{100} \\[2ex] &=0.79 \end{align}\)

Answer:

0.79

Question 3: 

Express 245 hundredths as a decimal.

245 hundredths = __________

Solution:

245 hundredths\(\begin{align}​​\\[2ex] &= \frac{245}{100} \\[2ex] &=2.45 \end{align}\)

Answer:

2.45

3. Express Thousandths As Decimals

Similarly to tenths and hundredths, if a square is divided into 1000 equal parts, each part represents one thousandth.
One thousandth\(\begin{align}​​\\[2ex] &= \frac{1}{1000} \\[2ex] &=0.001 \end{align}\)

We read \(0.001\) as zero point zero zero one. 

Express Thousandths On A Number Line

We can also write decimals on a place-value chart. 

For Example:
10 thousandths\(\begin{align}​​\\[2ex] &= \frac{10}{1000} \\[2ex] &=0.010 \end{align}\)

Question 1: 

Express 8 thousandths as a decimal.

Solution:

8 thousandths\(\begin{align}​​\\[2ex] &= \frac{8}{1000} \\[2ex] &=0.008 \end{align}\)

Answer:

0.008

Question 2: 

Express 28 thousandths as a decimal.

Solution:

28 thousandths\(\begin{align}​​\\[2ex] &= \frac{28}{1000} \\[2ex] &=0.028 \end{align}\)

Answer:

0.028

Question 3: 

Express 8146 thousandths as a decimal.

Solution:

8146 thousandths\(\begin{align}​​\\[2ex] &= \frac{8146}{1000} \\[2ex] &=8.146 \end{align}\)

Answer:

8.146

Identify Values And Place Values

\(2.534 = 2 + 0.5 + 0.03 + 0.004\)

The value of the digit 4 is 0.004. The digit 4 is in the thousandths place.

The value of the digit 3 is 0.03. The digit 3 is in the hundredths place.

The value of the digit 5 is 0.5. The digit 5 is in the tenths place.

The value of the digit 2 is 2. The digit 2 is in the ones place.

Question 1: 

In 25.49, the digit 4 is in the __________ place.

Solution:

Answer:

tenths

Question 2: 

In 13.074, the digit 7 is in the __________ place.

Solution: 

Answer:

hundredths

Question 3: 

In 18.093, which digit is in the hundredths place? 

Solution:

Answer:

9 

Question 4: 

In 542.603, which digit is in the tenths place? 

Solution: 

Answer:

6 

Question 5: 

What is the value of the point marked X?

The point marked X is __________.

1. 0.44
2. 0.452
3. 0.454
4. 0.47

Solution: 

Answer:

(4) 0.47

Question 6:

What is the value of the point marked X?

The point marked X is __________. 

1. 0.2
2. 0.7
3. 2
4. 7

Answer:

(2) 0.7

Question 7: 

What is the value of the point marked X?

Answer:

1.4

Question 8: 

What is the value of the point marked X? 

Answer:

0.001

Question 9:

What is the value of the point marked X? 

Answer:

0.022

Question 10: 

What is the value of the point marked X? 

Answer:

0.014