Decimal Notation

We use decimal notation to expand a number with a fractional part using 10 as the base. We can easily rewrite any number in its decimal notation using a calculator. But let us understand the concept.

Here we will deal with writing larger numbers in decimal notations. But, let us take a simple example.

For 7/100, the decimal notation is 0.07.

What is Decimal Notation

Decimal Notation represents a number from the context of a fraction using the base 10. In other words, decimal notation means the expanded notation with decimals in terms of the place value (including the decimal place values) following the place value chart.

Each digit to the left of the decimal point represents an increasing power of 10 starting from 10⁰, 10¹, 10², 10³, and so on. However, each digit to the right of the decimal point represents a decreasing power of 10 starting from 10^-1, 10^-2, 10^-3.

So, for 56.43, the decimal notation is (5 x 10)+ (6 x 1)+ (3 x 0.01)+ (4 x 0.1)

The place values of the given number are:

40 – Thousands

5– Thousands

3 – Hundreds

6 – Tens

7 – Ones

.  – Decimal point

2 – Tenths

4 – Hundredths

8 – Thousandths

Solved Examples

Write 5983 in decimal notation.

Solution:

The number 5983.12 in decimal notation = 5 × 1000 + 9 × 100 + 8 × 10 + 3 × 1 + 12 × 0.01 + 1 × 0.1

Convert 1.6759 × 10¹ to decimal notation. Write the place values of each digit in the number.

Solution:

Writing the number in general form
1.6759 × 10¹ = 16.759
= 1 × 10¹ + 6 × 10⁰ + 7 × 10^-1 + 5 × 10^-2 + 9 × 10^-3
= 1 × 10 + 6 × 1 + 0.7 + 0.05 + 0.009
The decimal notation is 1 × 10 + 6 × 1 + 0.7 + 0.05 + 0.009

What is 1/8 as a decimal notation?

Solution:

Dividing 1 by 8, we get 0.125
Now, 0.125 = 1 × 0.1 + 2 × 0.01 + 5 × 0.001
1/8 in decimal notation is 1 × 0.1 + 2 × 0.01 + 5 × 0.001