8th Grade - Scientific Notations

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 $2.95\times {10}^6$, 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. 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.

Answer: $2.9 \times {10}^{14}$

2. Convert 0.0000000000012 to scientific notation.

Answer: $1.2\times {10}^{-12}$

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.
• $105\times {10}^{21}$ 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.