Write each of the following in scientific notation:f. 670 000

Verified step by step guidance

1. Identify the significant figures in the number 670,000. In this case, the significant figures are 6.7.
2. Determine the power of 10 needed to express the number in scientific notation. Count how many places you move the decimal point to the left to place it after the first significant figure. For 670,000, you move the decimal 5 places to the left.
3. Express the number as a product of the significant figures and 10 raised to the power determined in the previous step. This will be in the form of \( a \times 10^n \), where \( a \) is the significant figures and \( n \) is the power of 10.
4. Combine the significant figures and the power of 10 to write the number in scientific notation.
5. Double-check your work to ensure that the number of significant figures and the power of 10 are correct.

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 670,000 can be expressed as 6.7 x 10^5, where 6.7 is the coefficient and 5 is the exponent.

Place Value

Place value refers to the value of a digit based on its position within a number. In the number 670,000, the digit '6' is in the hundred-thousands place, '7' is in the ten-thousands place, and the remaining zeros indicate the absence of values in the lower places. Understanding place value is essential for converting standard numbers into scientific notation.

Exponent Rules

Exponent rules are mathematical principles that govern the operations involving powers of ten. When converting to scientific notation, the exponent indicates how many places the decimal point has moved. For instance, moving the decimal point five places to the left in 670,000 results in an exponent of 5, reflecting the original number's magnitude.