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.

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}

$\displaystyle{0.8}$

Question 2:

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

Solution:

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

$\displaystyle{6.8}$

Question 3:

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

Solution:

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

$\displaystyle{2.7}$

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}

$\displaystyle{0.07}$

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}

$\displaystyle{0.79}$

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}

$\displaystyle{2.45}$

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}

$\displaystyle{0.008}$

Question 2:

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

Solution:

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

$\displaystyle{0.028}$

Question 3:

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

Solution:

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

$\displaystyle{8.146}$

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:

tenths

Question 2:

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

Solution:

hundredths

Question 3:

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

Solution:

$\displaystyle{9}$

Question 4:

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

Solution:

$\displaystyle{6}$

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:

(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. $\displaystyle{0.7}$

(2) $\displaystyle{0.7}$

Question 7:

What is the value of the point marked X?

$\displaystyle{1.4}$

Question 8:

What is the value of the point marked X?

$\displaystyle{0.001}$

Question 9:

What is the value of the point marked X?

$\displaystyle{0.022}$

Question 10:

What is the value of the point marked X?

$\displaystyle{0.014}$

Continue Learning
Multiplication Whole Numbers
Multiplication And Division Decimals
Model Drawing Strategy Division
Fractions Factors And Multiples
Area And Perimeter 1 Line Graphs
Conversion Of Time
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