Divide Scientific Notation

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

Example 1

Example

Solution

Divide the front parts.
9.02 ÷ 3.75 = 2.405...

Scientific Notation - Definition

Divide the power parts.
107 ÷ 104 = 107 - 4 = 103

Quotient of Powers

So (9.02 × 107) ÷ (3.75 × 104) = 2.405... × 103.

The given front parts, 9.02 and 3.75, have three significant digits.
So, to make the front part to three significant digits, round 2.405... to the nearest hundredth: 2.41.

Round a Number

So 2.41 × 103 is the answer.

Example 2

Example

Solution

Divide the front parts.
1.57 ÷ 8.06 = 0.1742...

Divide the power parts.
108 ÷ 105 = 108 - 5 = 103

So (1.57 × 108) ÷ (8.06 × 105) = 0.1742... × 103.

The given front parts, 1.57 and 8.06, have three significant digits.
So, to make the front part to three significant digits, round 0.1742... to the nearest thousandth: 0.174.

Round a Number

0.174 is not the front part, because it doesn't satisfy
1 ≤ [front part] < 10.
So, to make the front part, split 0.174 to 1.74⋅10-1.

10-1⋅103 = 102.

So 1.74 × 102 is the answer.