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:

\(\displaystyle{0.014}\)