# SCIENTIFIC NOTATION

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# SCIENTIFIC NOTATION

Scientific Notation worksheets here teach you the best way to express very large numbers and very small numbers. It is represented conveniently using exponents. The numbers are shortened (a number between 1 to 10) and multiplied in the power of 10. The powers for very large numbers are expressed using positive exponents and very small numbers using negative exponents. In these worksheets, learn to express standard numbers in scientific form and scientific numbers in standard form. Also scientific notation Addition, Subtraction, Multiplication, and Division worksheets have been prepared for advanced learning.

## SCIENTIFIC NOTATION WORKSHEETS

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##### Let us learn how to express the numbers

The mass of earth is 5,970,000,000,000,000,000,000,000 kg. Such large numbers are represented using exponents. We represent it as 5.97 x 1024

Thus 10 is base here and 24 is the power in 5.97 x 1024

Lets us see how to represent it. Look into the number.

Place a decimal point at the end of the number. Now move the decimal 24 places to the left, such that you place the decimal point imediately after the first digit of the given number.

What does this expression 5.97 x 1024 mean?

5.97 x 1000000000000000000000000 (24 zeros)

OR

5.97 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

Eg. Negative Integer

The size of a atom is 0.0000000008 m. We represent it as 8 x 10-10 m. Here you need to move the decimal point10 places right.

What does the expression 8 x 10-10 mean?

8 x 0.0000000001

OR

8 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1

As the exponent decreases by 1, the value becomes one- tenth of the previous value.

Generally mathematicians, scientists and engineers deal with very large and very small numbers on daily basis. They also do exponent addition, subtraction, multiplication, and division. Here is an example for each operation.

When you add two or more exponents, the powers should be made equal first. Its is always better to convert the smaller power to the highest power.

Just like addition, when you subtract exponents, the powers should be the same.

When you multiply two exponents, just add the powers. am x an = am+n, where m and n are natural numbers.

When you divide two exponents, subtract the powers. am/ an = am-n, where m and n are natural numbers.

## Frequently Asked Questions!!

### 1) What is scientific notation in math?

Scientific notation is an easy way to express very large and very small numbers using exponents. Positive exponents are used to represent large numbers and negative exponents for small numbers. Eg. The mass of earth is 5,970,000,000,000,000,000,000,000 kg. It is represented as 5.97 x 10^24

### 2) Define the three parts of scientific notation?

Consider this number 786,000,000,000. Expressing it in scientific form as 7.86 x 10^11
7.86 is the number.
10 is the base.
11 is the exponent.

### 3) How to convert scientific notation into standard form?

First make a note of the power. Also make a note of the decimal number. If there are 2 numbers after the decimal dot, subtract if from the power. This difference is the number of zeros to be added. Now write the number with zeros. Eg. 1.46 x 10^15
Power- 15
Digits after decimal dot= 2
Difference= 13
Therefor the standard form is 1,460,000,000,000,000 (Number and 13 zeros)

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