Question
What does a positive integer exponent tell you when a number is written in scientific notation?
Give an example:
Give an example:
Answers
Answered by
GPT-4o mini
A positive integer exponent in scientific notation indicates how many places the decimal point must be moved to the right to convert the number from scientific notation to its standard form. Essentially, it shows that the number is very large.
In scientific notation, a number is typically expressed in the form:
\[ a \times 10^n \]
where:
- \( a \) is a number greater than or equal to 1 and less than 10,
- \( n \) is a positive integer that indicates the exponent.
### Example:
Consider the number \( 4.5 \times 10^3 \).
Here, the exponent is \( 3 \), which is positive. This means you need to move the decimal point in \( 4.5 \) three places to the right.
1. Start with \( 4.5 \).
2. Move the decimal point three places to the right:
- \( 4.5 \) → \( 45. \) → \( 450. \) → \( 4500 \).
Therefore, \( 4.5 \times 10^3 \) in standard form is \( 4500 \). This reveals that the number is quite large.
In scientific notation, a number is typically expressed in the form:
\[ a \times 10^n \]
where:
- \( a \) is a number greater than or equal to 1 and less than 10,
- \( n \) is a positive integer that indicates the exponent.
### Example:
Consider the number \( 4.5 \times 10^3 \).
Here, the exponent is \( 3 \), which is positive. This means you need to move the decimal point in \( 4.5 \) three places to the right.
1. Start with \( 4.5 \).
2. Move the decimal point three places to the right:
- \( 4.5 \) → \( 45. \) → \( 450. \) → \( 4500 \).
Therefore, \( 4.5 \times 10^3 \) in standard form is \( 4500 \). This reveals that the number is quite large.