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 1.56×107. 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×10b ; 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 = 6×103 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 = 5×0.0001 = 5×10−4.
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 = 9×106, 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 = 7×10−6, 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=
1) 0.581= 5.81×10−1
2) 0.086= 8.6×10−2
3) 757,000= 7.57×105
4) 436,000,000= 4.36×108
5) 381,000= 3.81×105
6) 43,900,000= 4.39×107
7) 46,000,000= 4.6×107
8) 0.0784= 7.84×10−2
9) 0.00239= 2.39×10−3
10) 0.742= 7.42×10−1
Scientific Notation Quiz
