Decimal Notation
Decimal notation is the representation of a fraction using the base 10 along with a decimal point. In other words, a number is represented with a decimal point according to the decimal place value. A decimal is a number that consists of two parts i.e. a whole number and a fractional part that is written with the help of separators such as a dot(.) that is called a decimal point. Let us learn more decimal notations, the definitions, and solve a few examples to understand the concept better.
| 1. | Definition of Decimal Notation |
| 2. | Scientific Notation and Decimal Notation |
| 3. | FAQs on Decimal Notation |
Definition of Decimal Notation
The representation of a number in the form of a fraction with the base as 10 along with a decimal point is called decimal notation. These digits are from 0-9 that is written in two parts, a whole number and a fractional part that is separated by a dot called the decimal point. Since decimals use the base as 10, the place value system is also written according. From the below image, the place value before the decimal point is written as ones, followed by tens, hundreds, and so on, while after the decimal point it is written as tenths, followed by hundredths, then thousandths, and so on. The place value after the decimal represents the fractional part of the number. For example, the number 0.48 is made up of 4 tenths and 8 hundredths. This can also be written as 0.48 = 0.4 + 0.08. In other words, it means, 0.48 = 4/10 + 8/100. Conversion of fractions to decimals and vice versa can be done anytime since they mean the same but are written differently.
The digits to the left of the decimal point i.e. the whole number can be expressed as the multiples of the positive power of ten while the digits to right are expressed as the multiples of a negative power of ten since decimals use the base as 10. For example, 13.24 in fraction is written as 1324/100 and with the base 10 it is written as 1 × 101 + 3 × 100 + 2 × 10-1 + 4 × 10-2.
Scientific Notation and Decimal Notation
Scientific notation is similar to decimal notation where numbers are written keeping in mind the base as 10. By definition when a number is written in the form of a product of two numbers where the first number is greater than or equal to one but less than 10 and the second number is the power of 10 written in exponential form, it is called as scientific notation. This form is used by scientists and engineers when they deal with large numbers or very small numbers. Positive exponents showcase large numbers while negative exponents showcase small numbers between 1 to 10. The decimal point in scientific notation is moved according to the power towards the left or right depending on the number being positive or negative. When the number is 10 or greater, the decimal point has to move to the left, and the power of 10 is positive. When the number is smaller than 1, the decimal point has to move to the right, so the power of 10 is negative. For examples, 0.0076 is written as 7.6 × 0.001 = 7.6 × 10-3. In other words, scientific notation is written in the a × 10b where a is the decimal number or number that is greater than 1 and lesser than 10 and b is the power of 10.
Convert Decimal to Scientific Notation
The steps to convert decimal notation to scientific notation are:
- Move the decimal point so that the first number is greater than or equal to 1 but lesser than 10.
- Count the number of decimal places(n) moved.
- Write the number as a product with a power of 10. If the number is greater than 1, the power of 10 will be 10n and if it is between 0 and 1, the power of 10 will be 10-n.
- Cross-check the final result.
Let us look at an example. Write 0.0025 in scientific notation.
Step 1: Move the decimal point for the number to be greater than 1. Move the decimal point towards the right.
0.0025 = 2.5
Step 2: Count the number of places it is moved.
n = 3.
Step 3: Write the product with the power 10. Since the decimal point moved towards the right, after the decimal point it will be negative.
2.5 × 10-3
Step 4: Cross-check
2.5 × 10-3 = 2.5 × 1/103 = 2.5 × 1/1000 = 2.5 × 0.001 = 0.0025.
Convert Scientific to Decimal Notation
The steps to convert scientific to decimal notation are:
- Find the exponent(n) on the power 10.
- Move the decimal points n places, if it is a positive move towards the right if the exponent is negative move towards the left. Add zeros if necessary.
- Cross-check the final result.
Let us look at an example. Convert 4.8 × 10-2 to decimal form.
Step 1: Find the exponent value (n)
n = -2
Step 2: Move the decimal point 2 places to the left since it is in negative value.
4.8 = 0.048
Step 3: Cross-check
4.8 × 10-2 = 4.8 × 1/102 = 4.8 × 1/100 = 4.8 × 0.01 = 0.048
Related Topics
Listed below are a few topics related to decimal notation, take a look.
FAQs on Decimal Notation
What is Meant by Decimal Notation?
Decimal notation is the form of expressing decimal numbers in the fraction from along with expressing the number with the base of 10. The numbers are expressed according to their place value and hence the exponents with the base 10 is written.
What is the Decimal Notation of 1?
The decimal notation of 1 is 1. Since the decimal point is after 1 and is written as 1.0. In this case, the zero can be ignored. But in the case of 0.1, the placement of 1 is after the decimal point and according to the decimal place value, 1 is written as one-tenth.
What is the Decimal Notation of 79%?
79% in fraction form is equal to 79/100. In decimal notation, it is expressed as 79/100 = 0.79.
Can Decimal Notation be a Whole Number?
No, a decimal notation cannot be a whole number as anything to the right of the decimal point is smaller than 1. However, a decimal number has two parts a whole number part and a fraction part. The fraction part is the decimal notation of the decimal number.
How Do You Write Numbers in Decimal Notation?
When a decimal number is expressed with the base of 10 along with the power of the multiples, we can write the decimal notation according to the exponential number. The exponent also determines in what direction the decimal number should go. If the exponent is positive the decimal point moves towards the right. If the exponent is negative, the decimal point moves towards the left. For example, 9.31 × 105 = 931000.