Standard form is a method of writing very large or very small numbers succinctly, commonly used in scientific, mathematical, and engineering contexts. It simplifies numbers to a format of , where is a coefficient between 1 and 10 (including 1 but not 10), and is an integer indicating the power of 10.
What is Standard Form?
The standard form notation allows us to express numbers in a more manageable way, especially when dealing with extremely large or small values.
![Scientific notation](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F9818acb1-87f6-4650-993b-b4ad067a9844-file.png&w=1080&q=75)
Key Concepts
- Coefficient : A number between 1 and 10.
- Power of 10 : Indicates how many places the decimal point has been moved. can be positive, negative, or zero.
Converting Numbers into Standard Form
Converting a number into standard form involves two steps:
1. Find the Coefficient: Adjust the decimal point so there is only one non-zero digit to the left.
2. Determine the Power of 10: Count the decimal moves. This count, , is positive if moved left, negative if right.
![Standard form](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fd9919086-15c6-46dd-9be3-d2a1322247da-file.png&w=1080&q=75)
Example 1: Large Number
- Original: 123,456
- Standard Form:
Example 2: Small Number
- Original: 0.00789
- Standard Form:
Converting Numbers Out of Standard Form
To convert from standard form to a normal number:
1. Move the Decimal Point: Based on , move the decimal point right (if is positive) or left (if is negative).
2. Adjust with Zeros: Add zeros as needed to fill gaps.
![Converting to Standard Form](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F5aa8ea7f-d716-4cd9-9899-d2d7cd300dcf-file.png&w=1080&q=75)
Example 1: From Standard Form
- Standard Form:
- Normal Number: 36,500
Example 2: From Standard Form
- Standard Form:
- Normal Number: 0.0042
Practice Questions
1. Convert 5,000,000 into standard form.
Solution:
2. Convert into a normal number.
Solution:
3. Calculate in standard form.
Solution: