Scientific Notation

By Mr Agus Salim

Score: 0 / 100

Question 1 of 20

Convert the following number to scientific notation:

23500

Answer in format: a.bc × 10^n
Enter each digit and exponent separately below:

First digit (a):

Second digit (b):

Third digit (c):

Exponent (n):

FINISH!

Total Score: 0 / 100

Scientific Notation – Theory & Formulas

1. What is Scientific Notation?

Scientific notation is a concise way to write very large or very small numbers by using powers of 10. A number is written as the product of:

Scientific Notation = a × 10ⁿ
where 1 ≤ a < 10 and n is an integer.

2. Components

• Coefficient (a): the decimal part (1 ≤ a < 10).
  • 2 significant figures → a.b × 10n
  • 3 significant figures → a.bc × 10n
• Power (n): the integer exponent of 10.

3. Why no zeros?

Leading or trailing zeros (e.g., 0.007 or 2500) are removed by shifting the decimal point so that only non-zero digits remain in the coefficient.

4. Converting to Scientific Notation

Large numbers (positive exponent)

Move the decimal point left until one non-zero digit remains to its left.

235 000 → 2.35 × 10⁵

Small numbers (negative exponent)

Move the decimal point right until one non-zero digit remains to its left.

0.000 008 41 → 8.41 × 10⁻⁶

5. Visual Guide

6. Arithmetic Rules

Multiplication

(a × 10ⁿ) × (b × 10^m) = (a × b) × 10^n+m

Division

(a × 10ⁿ) ÷ (b × 10^m) = (a ÷ b) × 10^n−m

7. Significant-Figure Reminder

Always keep the requested number of significant figures (2 or 3 in this quiz) in the coefficient, and round correctly.

8. Quick Reference Card

Decimal Form	Scientific Notation
7 800 000	7.8 × 106
0.000 25	2.5 × 10−4
1 234 500	1.23 × 106
0.009 807	9.81 × 10−3

9. Common Mistakes

• Forgetting that the coefficient must be ≥ 1 and < 10.
• Using “10” instead of “10ⁿ” when writing the final answer.
• Leaving trailing zeros in the coefficient (e.g., 2.300 instead of 2.3).