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.

Free printable Worksheets

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) \(0.742 = \)

Answers

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) \(0.742 = \)\( \ \color{red}{7.42 \times 10^{-1}}\)

How to convert a number to scientific notation