# 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.

10^{3}⋅10^{5} = 10^{3 + 5} = 10^{8}

Product of Powers

So (2.15 × 10^{3})(1.98 × 10^{5}) = 4.2570 × 10^{8}.

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 × 10^{8} is the answer.

## Example 2

### Example

### Solution

Multiply the front parts.

8.73⋅9.01 = 78.6573

Multiply the power parts.

10^{4}⋅10^{2} = 10^{4 + 2} = 10^{6}

So (8.73 × 10^{4})(9.01 × 10^{2}) = 78.6573 × 10^{6}.

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⋅10^{6} = 10^{7}.

So 7.87 × 10^{7} is the answer.