## How to convert a number to scientific notation

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Using scientific notation, a given quantity is expressed as a number with the significant digits required for a particular degree of accuracy multiplied by \(10\) to the relevant power, such as \(1.56 \times 10^7\). It is a method of displaying **extremely large **or **extremely small **numbers in a more straightforward manner.

Scientific notation allows us to represent extremely large or extremely small numbers in the form of **multiplication **of single-digit values and a power of \(10\) raised to the power of the exponent in question. When the number is extremely large, the exponent is **positive**; when the number is extremely small, the exponent is **negative**. Let's have a look at the formula for scientific notation.

### Scientific Notation Formula

In mathematics, scientific notation is a method of recording a given number, an equation, or an expression in a format that adheres to a set of principles. Writing a high number in its number form, such as \(7.2\) billion, is not only unclear, but it is also **time-consuming**, and there is a probability that we will write a few zeros less or more than the actual number while writing in the number form.

As a result, scientific notation is used to represent extremely big or extremely small numbers in a **simple **manner. The following is an example of a broad representation of scientific notation or a scientific notation formula:

\(a \times 10^b\) ; \(1 \ ≤ \ a \ < \ 10\), where ‘\(a\)’ always represents any number between \(1\) to \(10\) (not including 10).

### Some Rules in Scientific Notations

To **determine **the power or **exponent **of \(10\), we must first establish how many places the decimal point must be moved after the single-digit value.

- If the given integer is a
**multiple**of ten, the decimal point must be moved to the**left**, and the power of ten will be**positive**. For example, the number \(6000 \ = \ 6 \times 10^3\) is written in scientific notation. - If the specified value is
**less**than one, the decimal point must be moved to the**right**, resulting in a power of ten that is**negative**. For example, in scientific notation, \(0.0005 \ = \ 5 \times 0.0001 \ = \ 5 \times 10^{-4}\).

### Positive and Negative Exponents

When **huge **numbers are stated in scientific notation, we employ **positive **exponents for base \(10\) to express them. For example, \(9000000 \ = \ 9 \times 10^6\), where \(6\) is the positive exponent of the number \(9000000\).

When **small **numbers are written in scientific notation, we utilise **negative **exponents for base \(10\) to express them. For example, \(0.000007 \ = \ 7 \times 10^{-6}\), where \(-6\) denotes the negative exponent of the fraction.

### Exercises for Scientific Notation

**1) **\(0.581 = \)

**2) **\(0.086 = \)

**3) **\(757,000 = \)

**4) **\(436,000,000 = \)

**5) **\(381,000 = \)

**6) **\(43,900,000 = \)

**7) **\(46,000,000 = \)

**8) **\(0.0784 = \)

**9) **\(0.00239 = \)

**10) **\(0.742 = \)