Questions: Is the number 1.98 × 10^2 written in scientific notation, engineering notation, both, or neither?
- scientific notation
- both
- engineering notation
- neither
Transcript text: Is the number $1.98 \times 10^{2}$ written in scientific notation, engineering notation, both, or neither?
- scientific notation
- both
- engineering notation
- neither
Solution
Solution Steps
Step 1: Understand the definitions of scientific and engineering notation
Scientific notation requires a number to be written in the form \(a \times 10^{n}\), where \(1 \leq |a| < 10\) and \(n\) is an integer.
Engineering notation requires a number to be written in the form \(a \times 10^{n}\), where \(n\) is a multiple of 3 and \(1 \leq |a| < 1000\).
Step 2: Analyze the given number
The number \(1.98 \times 10^{2}\) has \(a = 1.98\) and \(n = 2\).
Check if \(1.98\) satisfies \(1 \leq |a| < 10\): Yes, it does.
Check if \(n = 2\) is a multiple of 3: No, it is not.
Step 3: Determine the notation type
Since \(1.98 \times 10^{2}\) satisfies the condition for scientific notation but not for engineering notation, it is written in scientific notation only.