Decimals

What are Decimals?

Decimal Numbers 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 : Practice Problems
2. Express hundredths as decimals : Practice Problems
3. Express thousandths as decimals : Practice Problems

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

Practice Problems

Question 1: 

Express $8$ tenths as a decimal.

Solution:

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

Answer:

$\displaystyle{0.8}$

Question 2: 

Express $\displaystyle{68}$ tenths as a decimal.

Solution:

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

Answer:

$\displaystyle{6.8}$       

Question 3: 

Express $\displaystyle{27}$ tenths as a decimal.

Solution:

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

Answer:

$\displaystyle{2.7}$

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 $\displaystyle{0.01}$ as zero point zero one.

Express Hundredths On A Number Line

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

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

Practice Problems

Question 1: 

Express $\displaystyle{7}$ hundredths as a decimal.

Solution:

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

Answer:

$\displaystyle{0.07}$

Question 2: 

Express $79$ hundredths as a decimal.

$\displaystyle{79}$ hundredths $=$ __________

Solution: 

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

Answer:

$\displaystyle{0.79}$

Question 3: 

Express $\displaystyle{245}$ hundredths as a decimal.

$\displaystyle{245}$ hundredths $=$ __________

Solution:

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

Answer:

$\displaystyle{2.45}$

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:
$\displaystyle{10}$ thousandths$\begin{align}​​\\[2ex] &= \frac{10}{1000} \\[2ex] &=0.010 \end{align}$

Practice Problems

Question 1: 

Express $\displaystyle{8}$ thousandths as a decimal.

Solution:

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

Answer:

$\displaystyle{0.008}$

Question 2: 

Express $\displaystyle{28}$ thousandths as a decimal.

Solution:

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

Answer:

$\displaystyle{0.028}$

Question 3: 

Express $\displaystyle{8146}$ thousandths as a decimal.

Solution:

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

Answer:

$\displaystyle{8.146}$

Identify Values And Place Values

$2.534 = 2 + 0.5 + 0.03 + 0.004$

The value of the digit $\displaystyle{4}$ is $\displaystyle{0.004}$. The digit $\displaystyle{4}$ is in the thousandths place.

The value of the digit $\displaystyle{3}$ is $\displaystyle{0.03}$. The digit $\displaystyle{3}$ is in the hundredths place.

The value of the digit $\displaystyle{5}$ is $\displaystyle{0.5}$. The digit $\displaystyle{5}$ is in the tenths place.

The value of the digit $\displaystyle{2}$ is $\displaystyle{2}$. The digit $\displaystyle{2}$ is in the ones place.

Question 1: 

In $\displaystyle{25.49}$, the digit $\displaystyle{4}$ is in the __________ place.

Solution:

Answer:

tenths

Question 2: 

In $\displaystyle{13.074}$, the digit $\displaystyle{7}$ is in the __________ place.

Solution: 

Answer:

hundredths

Question 3: 

In $\displaystyle{18.093}$, which digit is in the hundredths place? 

Solution:

Answer:

$\displaystyle{9}$

Question 4: 

In $\displaystyle{542.603}$, which digit is in the tenths place? 

Solution: 

Answer:

$\displaystyle{6}$

Question 5: 

What is the value of the point marked X?

The point marked X is __________.

1. $\displaystyle{0.44}$
2. $\displaystyle{0.452}$
3. $\displaystyle{0.454}$
4. $\displaystyle{0.47}$

Solution: 

Answer:

(4) $\displaystyle{0.47}$

Question 6:

What is the value of the point marked X?

The point marked X is __________. 

1. $\displaystyle{0.2}$
2. $\displaystyle{0.7}$
3. $\displaystyle{2}$
4. $\displaystyle{0.7}$

Answer:

(2) $\displaystyle{0.7}$

Question 7: 

What is the value of the point marked X?

Answer:

$\displaystyle{1.4}$

Question 8: 

What is the value of the point marked X? 

Answer:

$\displaystyle{0.001}$

Question 9:

What is the value of the point marked X? 

Answer:

$\displaystyle{0.022}$

Question 10: 

What is the value of the point marked X? 

Answer:

$\displaystyle{0.014}$