Write each of the following in scientific notation:
b. 650

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Identify the number to be converted into scientific notation: 650.

Determine the position of the decimal point in the number. For 650, the decimal point is currently at the end of the number (650.0).

Move the decimal point to create a number between 1 and 10. In this case, move the decimal point two places to the left, resulting in 6.5.

Count the number of places the decimal point was moved. Since it was moved two places to the left, the exponent for the power of 10 will be +2.

Express the number in scientific notation using the format \( a \times 10^n \), where \( a \) is the number between 1 and 10 and \( n \) is the exponent. The result is \( 6.5 \times 10^2 \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 650 can be expressed as 6.5 x 10^2, where 6.5 is the coefficient and 2 is the exponent indicating the number of places the decimal point is moved.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, the significant figures are represented in the coefficient. For instance, in the number 6.5 x 10^2, both digits '6' and '5' are significant, indicating the precision of the measurement being represented.

Exponent Rules

Exponent rules govern how to manipulate powers of ten in mathematical expressions. When converting numbers to scientific notation, understanding how to apply these rules is essential. For example, when multiplying numbers in scientific notation, you add the exponents, while for division, you subtract them. This is crucial for correctly interpreting and calculating values in scientific contexts.

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