**Scientific notation**

is a form of presenting very large numbers or very modest numbers in a simpler form. As we know, the whole numbers can exist extended till infinity, simply we cannot write such huge numbers on a slice of newspaper. Also, the numbers which are present at the millions identify after the decimal needed to exist represented in a simpler form. Thus, it is hard to represent a few numbers in their expanded form. Hence, nosotros use scientific notations. Also learn, Numbers In Full general Form.

For example, 100000000 can be written as x^{8}, which is the scientific annotation. Here the exponent is positive. Similarly, 0.0000001 is a very modest number which tin be represented equally 10^{-8}, where the exponent is negative.

##
Scientific Notation Definition

As discussed in the introduction, the scientific annotation helps the states to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small. Learn power and exponents for meliorate understanding.

The general representation of scientific notation is:

**Also, read:**

- Scientific notation formula reckoner
- Scientific Annotation Calculator

## Scientific Notation Rules

To make up one’s mind the power or exponent of 10,nosotros must follow the rule listed below:

- The base should be always 10
- The exponent must exist a non-zero integer, that means it tin can be either positive or negative
- The absolute value of the coefficient is greater than or equal to 1 but information technology should exist less than 10
- Coefficients can be positive or negative numbers including whole and decimal numbers
- The mantissa carries the residue of the meaning digits of the number

Let us empathise how many places we need to move the decimal point later the single-digit number with the aid of the below representation.

- If the given number is multiples of 10 then the decimal point has to move to the left, and the power of x will exist positive.

Instance: 6000 = half-dozen × 10^{3}

is in scientific notation. - If the given number is smaller than 1, then the decimal bespeak has to motility to the correct, so the ability of x volition exist negative.

Example: 0.006 = 6 × 0.001 = half-dozen × ten^{-iii}is in scientific notation.

## Scientific Annotation Examples

The examples of scientific note are:

490000000 = iv.ix×x^{8}

1230000000 = ane.23×10^{ix}

50500000 = v.05 10 10^{7}

0.000000097 = 9.7 10 10^{-8}

0.0000212 = 2.12 10 10^{-5}

## Positive and Negative Exponent

When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10. For example:

20000 = 2 x 10^{iv}, where 4 is the positive exponent.

When the scientific notation of any pocket-size numbers is expressed, and then we use negative exponents for base 10. For example:

0.0002 = ii x 10^{-4}, where -4 is the negative exponent.

From the above, we can say that the number greater than i can be written every bit the expression with positive exponent, whereas the numbers less than 1 with negative exponent.

## Problems and Solutions

**Question i:**

**Convert 0.00000046 into scientific notation.**

Solution: Motion the decimal point to the right of 0.00000046 up to 7 places.

The decimal bespeak was moved vii places to the right to form the number 4.vi

Since the numbers are less than 10 and the decimal is moved to the right. Hence, nosotros utilise a negative exponent here.

⇒ 0.00000046 = 4.6 × 10^{-seven}

This is the scientific notation.

**Question two: Convert 301000000 in scientific notation.**

**Solution:**

Move the decimal to the left viii places and so it is positioned to the right of the leftmost non nil digits 3.01000000. Remove all the zeroes and multiply the number by x.

At present the number has get = 3.01.

Since the number is greater than 10 and the decimal is moved to left, therefore, we apply here a positive exponent.

Hence, three.01 × 10^{8}

is the scientific notation of the number.

**Question 3:Convert ane.36 × ten ^{vii}
from scientific note to standard notation.**

**Solution:**

Given, i.36 × ten^{seven}

in scientific notation.

Exponent = 7

Since the exponent is positive we need to move the decimal place vii places to the right.

Therefore,

1.36 × ten^{7}

= 1.36 × 10000000 = one,36,00,000.

### Practice Questions

Problem 1: Convert the following numbers into scientific notation.

- 28100000
- 7890000000
- 0.00000542

Problem 2: Catechumen the post-obit into standard form.

- 3.5 × 10
^{5} - 2.89 × 10
^{-6} - 9.8 × 10
^{-two}

##
Frequently Asked Questions on Scientific Notation – FAQs

### How practice yous write 0.00001 in scientific annotation?

The scientific notation for 0.0001 is 1 × 10^{-4}.

Here,

Coefficient = one

Base of operations = 10

Exponent = -4

### What are the 5 rules of scientific notation?

The five rules of scientific note are given beneath:

ane. The base should be ever 10

2. The exponent must be a non-null integer, that means it tin can be either positive or negative

3. The absolute value of the coefficient is greater than or equal to 1 but it should be less than ten

4. Coefficients tin be positive or negative numbers including whole and decimal numbers

v. The mantissa carries the remainder of the significant digits of the number

### What are the 3 parts of a scientific notation?

The three main parts of a scientific annotation are coefficient, base and exponent.

### How do you write 75 in scientific notation?

The scientific notation of 75 is:

seven.five × 10^1 = 7.v × ten

Here,

Coefficient = vii.5

Base = x

Exponent = 1

### How do you put scientific notation into standard form?

To convert a number from scientific note to standard form, nosotros should move the decimal point (if any) to the left if the exponent of x is negative; otherwise, proceed to the right. We must shift the decimal point as many times equally the exponent indicates in ability so that at that place will be no powers of 10 in the final representation.

## Which Number is Not in Scientific Notation

Source: https://byjus.com/maths/scientific-notation/

Originally posted 2022-08-07 21:14:10.