In Exercises 15–30, write each number in scientific notation.
3.14159
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Identify the decimal point in the number 3.14159.
Move the decimal point to the right of the first non-zero digit, which is 3, resulting in 3.14159 becoming 3.14159.
Count the number of places the decimal point was moved. In this case, it was moved 0 places to the right.
Express the number in the form , where is a number between 1 and 10, and is the number of places the decimal was moved. Here, and .
Write the final expression in scientific notation as .
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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 written as the product of a number between 1 and 10 and a power of ten. For example, the number 3.14159 can be expressed as 3.14159 × 10^0, since it is already between 1 and 10.
Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient (the number between 1 and 10) are considered significant. For 3.14159, all five digits are significant, which is important for maintaining accuracy when converting to scientific notation.
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Powers of Ten
Powers of ten are used in scientific notation to indicate the scale of the number. Each power of ten represents a factor of ten multiplied by itself. For instance, 10^1 equals 10, 10^2 equals 100, and so on. Understanding how to manipulate powers of ten is essential for converting numbers into scientific notation correctly.