Textbook Question
Which number in each of the following pairs is larger?
a. 7.2 × 103 or 8.2 × 102
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1. Matter and Measurements
Scientific Notation
1:35 minutesProblem 56a
Textbook Question
Write each of the following in scientific notation:
a. 0.072
Verified step by step guidance1
Identify the decimal number given: 0.072.
Determine the position of the decimal point and count how many places it needs to move to the right to create a number between 1 and 10. In this case, the decimal point moves 2 places to the right, resulting in 7.2.
Express the number in scientific notation by multiplying the adjusted number (7.2) by 10 raised to the power of the number of places the decimal point moved. This gives 7.2 × 10-2.
The negative exponent (-2) indicates that the original number is less than 1, as the decimal point was moved to the right.
Write the final result in scientific notation: 7.2 × 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 0.072 can be expressed as 7.2 x 10^-2, where 7.2 is the coefficient and -2 indicates the decimal point is moved two places to the right.
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Significant Figures
Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to maintain the correct number of significant figures to accurately represent the original value, such as ensuring 0.072 retains its two significant figures in the form of 7.2.
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Exponent Rules
Exponent rules govern how to manipulate powers of ten in scientific notation. When converting a number to scientific notation, moving the decimal point to the right results in a negative exponent, while moving it to the left results in a positive exponent. Understanding these rules is essential for correctly expressing numbers in scientific notation, as seen in the conversion of 0.072 to 7.2 x 10^-2.
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