A decimal number is a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits after the decimal point show a value smaller than one.
In number 345, digit 5 is at the ones place, 4 at tens place and 3 at hundreds place. In expanded form:
345 = 3 × 100 + 4 × 10 + 5 × 1
Let’s learn about the place values that lie to the right of the ones place.
Anything to the right of the decimal point has a place value smaller than one.
As we move towards the left of the decimal point, each position is ten times bigger. And as we move to the right of the decimal point, each position is ten times smaller
|
Thousands 1000s |
Hundreds 100s |
Tens 10s |
Ones 1s |
. |
Tenths 1/10th |
Hundredths 1/100th |
Thousandths 1/1000th |
| 3 | 4 | 5 | . | 1 | 2 | 6 |
Digits after decimal point represent a value less than 1. A decimal is a fractional part of a number. Let us try to understand this here.
 |
One whole |
 |
division of a whole into 10 equal parts or pieces. Each part represent \(^1/_{10}\) or tenth part of 1 or 0.1. |
 |
Dividing each tenth into 10 equal parts. A whole is divided into hundred equal parts and each part represent \(^1/_{100}\) or a hundredth part of 1 or 0.01. |
 |
divide each hundredth part into 10 equal parts, so a whole is divided into 1000 equal parts. Each part represent \(^1/_{1000}\) or a thousandth part of 1 or 0.001. |
This can be continued further to ten thousandths, hundred thousandths and so on. In this number 345.126
| Question | Answer |
| How many ones? | 5 ones , ones place is the first digit to the left of the decimal point. |
| How many tens and hundreds? | 4 tens and 3 hundreds. |
| How many tenths? | 1 tenth, tenth place is the first digit to the right of the decimal point. |
| How many hundredths? | 2 hundredths. |
| How many thousandths? | 6 thousandths. |
In Expanded form –
| \(345.126 = 3 \times 100 + 4 \times 10+ 5 \times 1+1 \times \frac{1}{10}+2 \times \frac{1}{100}+6 \times \frac{1}{1000}\) |
| \(345.126 = 3\times100 + 4 \times10+ 5\times1+\frac{1}{10}+\frac{2}{100}+\frac{6}{1000}\) |
345.126 = Three Hundred Forty-Five and One hundred Twenty-Six Thousandths.
7000.12 = Seven Thousand and Twelve Hundredths.
Few commonly used decimal/fractional value:
.svg)
Let’s represent 2.5 in number line:
The distance between two whole numbers is divided into ten equal parts, where each part represents 1/10 or 0.1.
We can convert decimal to fraction and vice-versa. For example
\(0.2 = \frac{2}{10}\)
\(2.2= \frac{22}{10}=2\frac{2}{10}\)
\(2.02=\frac{202}{100}=2\frac{2}{100}\)
Note that value of 34.6, 34.60 and 34.600 are all same because trailing zero (zero that appear to the right of both the decimal point and every non-zero digit) has no value.
We can also write 345.126 as \(345\frac{126}{1000}\)
How?
Express \(\frac{1}{10}\) as \(\frac{1\times100}{1000}\)
\(\therefore \frac{1\times100}{1000}\) +\(\frac{2\times10}{1000}\) + \(\frac{6}{1000}\) = \(\frac{126}{1000}\)
