By Peter Flom Updated Aug 30, 2022

Scientific notation expresses numbers in the form a × 10^b, where 1 ≤ a < 10 and b is an integer. For instance, 1 234 becomes 1.234 × 10³, while 0.000123 is written as 1.23 × 10⁻⁴. This compact format is ideal for handling extremely large or tiny values.

By keeping the coefficient within a single digit range, scientific notation immediately reveals the relative magnitude of numbers—easily distinguishing 1.23 × 10⁻⁴ from 1.23 × 10⁻⁵, which would be harder to spot in decimal form.

Step 1: Multiply the coefficient

Multiply the whole number by the coefficient (the “a” in a × 10^b). For example, 2.5 × 10³ × 6 → 2.5 × 6 = 15.

Step 2: Normalize the coefficient

Check whether the result lies between 1 and 10. If it does not, shift the decimal point by powers of ten.

Step 3: Adjust the coefficient and exponent

Divide the product by the appropriate power of ten to bring it into the 1–10 range. In our example, 15 ÷ 10¹ = 1.5.

Step 4: Update the exponent

Increase the original exponent by the number of tens you removed. Here, 3 + 1 = 4.

Step 5: Write the result

Combine the adjusted coefficient with the new exponent: 1.5 × 10⁴.