Express the following numbers in scientific notation. a. 120.7 b. 0.0034 c. 231.00 d. 23,000 e.

step 1 Problem 47, we are expressing the following in scientific notation. So again, just as a reminder

Express the following numbers in scientific notation. a....

Key Concepts

Scientific Notation

Scientific notation is a method for writing very large or very small numbers in a compact form using powers of ten. This format simplifies both the representation and computations with such numbers by separating the significant digits from the scale factor.

Significand

The significand (or mantissa) is the part of the number in scientific notation that contains the significant digits. It is usually a number between 1 and 10, which encapsulates the precision of the original number while excluding the magnitude provided by the exponent.

Exponent

The exponent in scientific notation indicates how many places the decimal point is moved to convert the original number into the significand. A positive exponent suggests that the original number is large (the decimal point is moved to the left), while a negative exponent indicates a small number (the decimal point is moved to the right).

Decimal Point Shifting

Decimal point shifting is the process of moving the decimal point in the original number to form the significand in scientific notation. The number of moves required directly determines the value of the exponent, making this concept key to accurately converting numbers into and out of scientific notation.

Significant Figures

Significant figures refer to the digits in a number that contribute to its accuracy and precision. When converting to scientific notation, it is important to retain the correct number of significant figures from the original number, as these indicate the precision and reliability of the measurement.

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