Example: \(1.50\)
Each digit in a decimal number has a place value.
Example: \(15.75\)
Hundreds  Tens  Ones 
Decimal Point 
Tenths  Hundredths  Thousandths  Ten Thousandths 
Hundred Thousandths 
Millionths 
1  5  .  7  5 

Examples:
A \(49.58\)
B \(49.058\)
C \(58.49\)
D \(58.049\)
Example: \(5.6742.5\)
\(5.6742.500\)
Next, we write the decimal numbers vertically, lining up the decimal points and each digit according to its place value.
\(\begin{array}\\ &5&.&6&7&4\\ &2&.&5&0&0\\ \hline\\ \hline \end{array}\)
\(\begin{array}\\ &5&.&6&7&4\\ &2&.&5&0&0 \\ \hline &3&.&1&7&4 \\\hline \end{array}\)
Example: \(5.23×2.1\)
\(\begin{array}\\ &5&.&2&3\\ ×&&2&.&1\\ \hline\\ \hline \end{array}\)
\(\begin{array}\\ &&5&.&2&3\ \rightarrow2 \text{ digits}\\ ×&&&2&.&1\ \rightarrow1 \text{ digit}\\ \hline &&&5&2&3\\ +&1&0&4&6&0&\\ \hline &1&0&9&8&3&\\ \end{array}\)
\(10.983\)
Note:
When we multiply decimals by power of \(10\), then we can simply move the decimal point to the right, by the number of places per multiple of \(10\).
Example: \(6.45\times10=64.5\)
Here, we move decimal by one place value.
\(7.234×1000=7234\)
Here, we move decimal by three place values.
For example: We want to represent \(3.7\) on the number line.
Now, we have to find the part \(0.7\) on the number line. To find \(0.7\) on the number line, divide the interval between \(3\) and \(4\) into \(10\) equal sections, each having a scale of \(0.1\).
A Point A
B Point B
C Point C
D Point D
Example: Add \(3.4\) and \(7.347\)
\(3.400+7.347\)
\(\begin{array}\\ &3&.&4&0&0\\ +&7&.&3&4&7\\ \hline\\ \hline \end{array}\)
\(\begin{array}\\ &3&.&4&0&0\\ +&7&.&3&4&7\\ \hline 1&0&.&7&4&7\\ \hline \end{array}\)
Example: Evaluate \(7.2\div3.6\)
\(3.6×10=36\)
\(7.2×10=72\)
Note:
While dividing a decimal number by another decimal number, if a part of the quotient is repeating, then it is called repeating or recurring decimal.
Example:
We divide \(0.1\) by \(0.3\).
Note:
When we divide decimals by power of \(10\), then we can simply move the decimal point to the left, by the number of places per multiple of \(10\).
Example 1: \(17.25\div1000\)
Here, we will move decimal by three place values.
Example 2: \(57.6\div10\)
Here, we will move decimal point by one place value.
Example: Compare \(13.2,\;13.299,\;13.213,\;13.226\)
Tens  Ones  .  Tenths  Hundredths  Thousandths 
1  3  .  2  0  0 
1  3  .  2  9  9 
1  3  .  2  1  3 
1  3  .  2  2  6 
\(0<1<2<9\)
A \(6.921,\;6.531,\;6.466,\;6.189\)
B \(6.921,\;6.189,\;6.446,\;6.531\)
C \(6.189,\;6.921,\;6.446,\;6.531\)
D \(6.189,\;6.446,\;6.531,\;6.921\)
\(\therefore\) We need to multiply \(1.2\) by \(6\) to find out the cost of \(6\) brushes.
\(=1.2×6\)
\(=7.2\)
So, cost of \(6\) brushes \(=$7.2\)
Alex has \($12.5\) and he takes \($10\) more from his father.
\(\therefore\) Total money Alex has \(=12.5+10\)
\(=$22.5\)
\(=$22.5$7.2\)
\(=$15.3\)
Thus, he is left with \($15.3\) to buy colors.
A \(\text{0.26 liters}\)
B \(\text{0.8 liters}\)
C \(\text{2.4 liters}\)
D \(\text{1.8 liters}\)