# Divide Scientific Notation

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

## Example(9.02 × 10^{7}) ÷ (3.75 × 10^{4})

Divide the front parts.

9.02 ÷ 3.75 = 2.405...

Scientific Notation - Definition

Divide the power parts.

10^{7} ÷ 10^{4}

= 10^{7 - 4}

= 10^{3}

Quotient of Powers

So (given) = 2.405... × 10^{3}.

The given front parts,

9.02 and 3.75,

have three significant digits.

So, to make the front part

three significant digits,

round 2.405...

to the nearest hundredth:

2.41.

Round a Number

So 2.41 × 10^{3} is the answer.

## Example(1.57 × 10^{8}) ÷ (8.06 × 10^{5})

Divide the front parts.

1.57 ÷ 8.06 = 0.1742...

Divide the power parts.

10^{8} ÷ 10^{5}

= 10^{8 - 5}

= 10^{3}

So (given) = 0.1742... × 10^{3}.

The given front parts,

1.57 and 8.06,

have three significant digits.

So, to make the front part

three significant digits,

round 0.1742...

to the nearest thousandth:

0.174.

0.174 is not the front part,

because it doesn't satisfy

1 ≤ [front part] < 10.

Scientific Notation - Definition

So, to make the front part,

split 0.174 to 1.74⋅10^{-1}.

10^{-1}⋅10^{3} = 10^{2}

So 1.74 × 10^{2} is the answer.