Multiply Scientific Notation

How to multiply numbers in scientific notation: 2 examples and their solutions.

Example 1

Example

Solution

Multiply the front parts.
2.15⋅1.98 = 4.2570

Scientific Notation - Definition

Multiply the power parts.
103⋅105 = 103 + 5 = 108

Product of Powers

So (2.15 × 103)(1.98 × 105) = 4.2570 × 108.

The given front parts, 2.15 and 1.98, have three significant digits.
So, to make the front part to three significant digits, round 4.2570 to the nearest hundredth: 4.26.

Round a Number

So 4.26 × 108 is the answer.

Example 2

Example

Solution

Multiply the front parts.
8.73⋅9.01 = 78.6573

Multiply the power parts.
104⋅102 = 104 + 2 = 106

So (8.73 × 104)(9.01 × 102) = 78.6573 × 106.

The given front parts, 8.73 and 9.01, have three significant digits.
So, to make the front part to three significant digits, round 78.6573 to the nearest tenth: 78.7.

Round a Number

78.7 is not the front part, because it doesn't satisfy
1 ≤ [front part] < 10.
So, to make the front part, split 78.7 to 7.87⋅10.

10⋅106 = 107.

So 7.87 × 107 is the answer.