The given expression, 6.97 x 10^4, represents a numerical value in scientific notation. Scientific notation is a way of expressing very large or very small numbers in a more compact and manageable form. It consists of a number between 1 and 10, multiplied by a power of 10.
Understanding Scientific Notation
In the expression 6.97 x 10^4, the number 6.97 is the coefficient, and 10^4 is the base raised to the exponent 4. This means that the number 6.97 is multiplied by 10 four times, or 10,000. Therefore, 6.97 x 10^4 is equal to 69,700.
Applications of Scientific Notation
Scientific notation has numerous applications in various fields, including physics, chemistry, biology, and engineering. It is particularly useful when dealing with very large or very small quantities, such as the size of atoms, the distance between galaxies, or the amount of a substance in a chemical reaction.
| Expression | Value |
|---|---|
| 6.97 x 10^4 | 69,700 |
| 6.97 x 10^3 | 6,970 |
| 6.97 x 10^2 | 697 |
Converting Between Notation Systems
Converting between scientific notation and standard notation is a straightforward process. To convert from scientific notation to standard notation, multiply the coefficient by the base raised to the exponent. For example, 6.97 x 10^4 becomes 69,700. To convert from standard notation to scientific notation, divide the number by the base raised to the exponent. For instance, 69,700 becomes 6.97 x 10^4.
Rules of Exponents
When working with exponents, it is essential to follow specific rules. These rules include the product rule, which states that when multiplying two numbers with the same base, add the exponents. The quotient rule states that when dividing two numbers with the same base, subtract the exponents. The power rule states that when raising a number with an exponent to another power, multiply the exponents.
Understanding and applying these rules is critical in various mathematical and scientific contexts, including algebra, calculus, and physics.
What is the value of 6.97 x 10^4 in standard notation?
+The value of 6.97 x 10^4 in standard notation is 69,700.
How do you convert from scientific notation to standard notation?
+To convert from scientific notation to standard notation, multiply the coefficient by the base raised to the exponent. For example, 6.97 x 10^4 becomes 69,700.
In conclusion, understanding scientific notation and the rules of exponents is essential in various mathematical and scientific contexts. By applying these concepts, individuals can efficiently work with large and small numbers, making it a fundamental skill in many fields.
