Write each of the following in scientific notation:
d. 9 100 000

Verified step by step guidance

1. Identify the given number: 9,100,000. The goal is to express this number in scientific notation, which is in the form $a\; \times \; 10n$, where and $n$ is an integer.
2. Locate the decimal point in the number. If the decimal point is not visible, it is understood to be at the end of the number: 9,100,000. becomes 9,100,000.0.
3. Move the decimal point to the left until only one non-zero digit remains to the left of the decimal point. In this case, move the decimal point 6 places to the left, resulting in 9.1.
4. Count the number of places the decimal point was moved. Since the decimal point was moved 6 places to the left, the exponent $n$ will be positive 6.
5. Combine the coefficient (9.1) and the power of 10 ($106$) to write the number in scientific notation: $9.1\; \times \; 106$.

Key Concepts

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 9,100,000 can be expressed as 9.1 x 10^6, where 9.1 is the coefficient and 6 is the exponent indicating the number of places the decimal point has moved.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient are considered significant. For instance, in the number 9.1 x 10^6, the digits '9' and '1' are significant, while the zeros in the exponent do not affect the precision of the coefficient.

Exponent Rules

Exponent rules govern how to manipulate numbers expressed in exponential form. When converting to scientific notation, the exponent indicates how many times the base (10) is multiplied by itself. Understanding these rules is essential for correctly interpreting and performing calculations with numbers in scientific notation, such as adjusting the exponent when moving the decimal point.