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Introduction

• Scientific notation is a way to express vast and tiny numbers as a product of 10 so that the manipulation is less cumbersome.
• Proxima Centauri, the closest star to earth, is 40,208,000,000,000 km away. The mass of a hydrogen atom is 0.000000000000000000000000167 grams. These are some examples that are hard to read and manipulate. Scientific notation is a way to make these numbers easier to read.

Numbers in Scientific Notation

• A scientific notation has a factor between 1 and 10 multiplied by a power of 10.
• In $2.95×{10}^{6}$, 2.95 is a factor, and 6 is the power of 10.
• The power of 10 can be positive or negative.

Numbers in Standard Form

• A number in a standard form has no exponents.
• Following are some examples of numbers in standard form.
1. 0.0000045
2. 45,000,000,000

Comparison of Scientific Notations

• While comparing two scientific notations, pay attention to the power of ten.
• The number with bigger power of 10 is greater.
• If the power of 10 is the same, then the scientific notation with the larger factor is greater.

Solved Examples

1. Convert 29,000,000,000,000,000 to scientific notation.

2. Convert 0.0000000000012 to scientific notation.

Answer: $1.2×{10}^{-12}$

Cheat Sheet

• For a number to be in a scientific notation, the factor term must be between 1 and 10.
• If the power of 10 or the exponent is negative, move the decimal point to the left.
• If the power of 10 or the exponent is positive, move the decimal point to the right.

Blunder Area

• Pay attention to the factor; it must be between 1 to 10 for a number to be in scientific notation.
• $105×{10}^{21}$ Is not a scientific notation, as factor 105 is not between 1 and 10.
• While converting scientific notation to a standard form, pay attention to the exponent sign before moving the decimal to the left or right.