Understanding Scientific Notation And Decimal Conversion
Scientific notation is an important concept in mathematics and science. It is used to express very large or very small numbers in a more convenient way. This notation is also known as standard form or exponential notation. In this article, we will learn how to convert scientific notation to decimal and vice versa.
Scientific Notation
Scientific notation is a way of representing a number as a product of a coefficient and a power of 10. The coefficient is usually a number between 1 and 10. The power of 10 indicates how many times the decimal point must be moved to obtain the original number. For example, the number 123,000 in scientific notation is written as 1.23 x 105.
Scientific notation is commonly used in science, engineering, and technology to represent very large or very small numbers. For instance, the distance between the sun and the earth is about 149.6 million kilometers, which can be written in scientific notation as 1.496 x 108 km.
Decimal to Scientific Notation Conversion
To convert a decimal number to scientific notation, we need to move the decimal point to the left or right until the coefficient is between 1 and 10. The number of times we move the decimal point determines the power of 10. For example, the number 0.0000123 can be converted to scientific notation as 1.23 x 10-5.
Another way to do this is to count the number of decimal places we moved the decimal point. If we move the decimal point to the left, the power of 10 is positive. If we move the decimal point to the right, the power of 10 is negative. For example, the number 0.0000123 has 5 decimal places, so the power of 10 is -5.
Scientific Notation to Decimal Conversion
To convert a number from scientific notation to decimal, we need to multiply the coefficient by 10 raised to the power of the exponent. If the exponent is positive, we move the decimal point to the right. If the exponent is negative, we move the decimal point to the left. For example, the number 1.23 x 105 can be converted to decimal as 123,000.
Examples of Conversion
Let us look at some examples of converting numbers from scientific notation to decimal and vice versa.
- Convert 3.2 x 104 to decimal. Solution: 32,000
- Convert 0.0005 to scientific notation. Solution: 5 x 10-4
- Convert 6.022 x 1023 to decimal. Solution: 602,200,000,000,000,000,000,000
- Convert 9.81 x 10-1 to decimal. Solution: 0.981
Significant Figures in Scientific Notation
When we write a number in scientific notation, we need to consider the significant figures. The coefficient in scientific notation should have the same number of significant figures as the original number. For example, the number 123 has three significant figures, so it should be written in scientific notation as 1.23 x 102.
Conclusion
Scientific notation is a powerful tool for expressing very large or very small numbers. It is widely used in science, engineering, and technology. Converting numbers from scientific notation to decimal and vice versa is an important skill that every student should learn. By following the steps outlined in this article, you can easily convert numbers between scientific notation and decimal.
Remember to always double-check your work and use the appropriate number of significant figures.
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