## How to convert a number to scientific notation

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) $$0.742 =$$

1) $$0.581 =$$$$\ \color{red}{5.81 \times 10^{-1}}$$
2) $$0.086 =$$$$\ \color{red}{8.6 \times 10^{-2}}$$
3) $$757,000 =$$$$\ \color{red}{7.57 \times 10^5}$$
4) $$436,000,000 =$$$$\ \color{red}{4.36 \times 10^8}$$
5) $$381,000 =$$$$\ \color{red}{3.81 \times 10^5}$$
6) $$43,900,000 =$$$$\ \color{red}{4.39 \times 10^7}$$
7) $$46,000,000 =$$$$\ \color{red}{4.6 \times 10^7}$$
8) $$0.0784 =$$$$\ \color{red}{7.84 \times 10^{-2}}$$
9) $$0.00239 =$$$$\ \color{red}{2.39 \times 10^{-3}}$$
10) $$0.742 =$$$$\ \color{red}{7.42 \times 10^{-1}}$$

## Scientific Notation Quiz

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