Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by 10^3, what does this multiplication do to the decimal point in 6.2?

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Understand the problem: Multiplying a number by a power of 10 shifts its decimal point. The direction and number of shifts depend on the exponent of 10.

Identify the given number and the power of 10: The number is 6.2, and it is being multiplied by 10^3.

Analyze the power of 10: The exponent 3 in 10^3 indicates that the decimal point will move 3 places to the right because the exponent is positive.

Perform the shift conceptually: Start with 6.2. Move the decimal point 3 places to the right, filling in any empty places with zeros as needed.

Conclude the effect: Multiplying 6.2 by 10^3 increases the value of the number by shifting the decimal point 3 places to the right, effectively making the number much larger.

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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 way of expressing numbers that are too large or too small in a compact form. It is typically written as a product of a number between 1 and 10 and a power of ten. For example, 6.2 can be expressed as 6.2 x 10^0, and multiplying by 10^3 shifts the decimal point three places to the right.

Decimal Point Movement

When multiplying a decimal number by a power of ten, the decimal point moves to the right for positive exponents and to the left for negative exponents. In this case, multiplying 6.2 by 10^3 means moving the decimal point three places to the right, resulting in 6200.

Place Value

Place value refers to the value of a digit based on its position within a number. In the context of decimal numbers, each position to the left of the decimal point represents increasing powers of ten. Understanding place value is crucial for accurately determining the new value of a number after shifting the decimal point.

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