Decimals & Fractions
Understanding tenths
Example 1: Look at the rectangle below
Let’s divide it in 10 equal parts and colour one of them.
We have coloured one part out of 10, That is \(1\over 10\) or one tenth of the rectangle.
\(1\over 10\)is smaller than 1 whole, You can see that 10 one tenths make 1 whole
\(\begin{gathered} \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} = \frac{{10}}{{10}} \hfill \\ 10 \times \frac{1}{{10}} = 1 \hfill \\ \end{gathered} \)
Decimal is way of writing fractional numbers without having numerator and denominator
Recall the place value chart
To show one tenth of a whole, we will add another column of tenths in it. Since, one tenth is smaller than one. We will add the column on the right side after a decimal point
The decimal 0.1 has 0 ones and 1 tenth. We read it as zero point one
A decimal has a whole number part and a fraction part that is separated by a decimal point
4 out of 10 parts of the circle are coloured.
4 one tenths of the circle are coloured
\(\begin{gathered} \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} + \frac{1}{{10}} = \frac{4}{{10}} \hfill \\ 0.1 + 0.1 + 0.1 + 0.1 = 0.4 \hfill \\ \end{gathered} \)
\(4\over 10\) or 0.4 of the circle is coloured.
Let’s make a place value table for decimal 0.4.
In the decimal 0.4,
The digit 0 is in the ones place. It has a value of 0,
The digit 4 is in the tenths place. It has 0 value of 0.4.
We read it as zero point four
We know that 10 one tenths make a whole
lf we have 10 tenths, we can regroup them into 1 ones and 0 tenths
Look at the parts of circles coloured below
We can also say that 14 tenths is equal to 1 one and 4 tenths
Example 2: Let’s write 14 tenths as a decimal.
We will regroup 14 tenths into 1 ones and 4 tenths.
14 tenths = 1 ones and 4 tenths
= 1 + 0.4 4 tenths
= 1.4
We read it as one point four
So, \({14 \over 10}=1{4 \over 10}\)
Let’s write 53 tenths as a decimal.
We will regroup 14 tenths into 1 ones and 4 tenths. We will regroup 53 tenths into 5 ones and 3 tenths
Look at the place value table
In the decimal 5.3,
The digit 5 is in the ones place. It has a value of 5
The digit 3 is in the tenths place. It has a value of 0.3
53 tenths = 5 ones + 3 tenths
5.3 = 5 + 0.3
We read it as five point three.