What you’ll learn
Write numbers in scientific notation.
Key idea
Normalized scientific notation requires both the correct value and coefficient at least one but strictly less than ten.
A numerically equal power-of-ten product may fail the required coefficient interval.
Worked example
Enter the exact value or ordered values in the format requested below.
Write exact positive quantity 0.00012 in normalized scientific notation a×10^n, with 1≤a<10.
- 0.00012=1.2×10^-4; coefficient 1.2 lies in the required interval [1,10).
- The equal-valued expression 12×10^-5 has coefficient 12 outside that interval. Divide coefficient by ten and raise exponent by one to normalize.
Answer: 1.2×10^-4
Quick Check
Choose which candidate representation satisfies the requirements of 'Write numbers in scientific notation' and justify the choice.
Both 14×10^-6 and 1.4×10^-5 equal 0.000014. Select the normalized representation and justify its coefficient constraint.