Multiplying Scientific Notation

Multiplying Scientific Notation

How to solve multiplying numbers in scientific notation problems: examples and their solutions.

Example 1

Evaluate. (2.15 * 10^3) * (1.98 * 10^5)

Multiply the blue parts and the red parts separately.

Product of powers (red)

2.15 × 1.98 is 4.2570.

But both 2.15 and 1.98 has 3 significant digits.

So round 4.257 to 3 significant digits: 4.26.

Rounding:
0-4 → round down
5-9 → round up

Example 2

Evaluate. (8.73 * 10^4) * (9.01 * 10^2)

Multiply the blue parts and the red parts separately.

Product of powers (red)

8.73 × 9.01 is 78.6573.
So, by rounding, it'll be 78.7.

But 78.7 is not in this interval:
1 ≤ 78.4 < 10.

So change 78.7 to 7.87 × 10.

And multiply this 10 and 106.

So the answer is 7.87 × 107.