# Multiply Scientific Notation

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

## Example(2.15 × 10^{3})⋅(1.98 × 10^{5})

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 (given) = 4.2570 × 10^{8}.

The given front parts,

2.15 and 1.98,

have three significant digits.

So, to make the front part

three significant digits,

round 4.2570

to the nearest hundredth:

4.26.

Round a Number

So 4.26 × 10^{8} is the answer.

## Example(8.73 × 10^{4})⋅(9.01 × 10^{2})

Multiply the front parts.

8.73⋅9.01 = 78.6573

Multiply the power parts.

10^{4}⋅10^{2}

= 10^{4 + 2}

= 10^{6}

So (given) = 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.

78.7 is not the front part,

because it doesn't satisfy

1 ≤ [front part] < 10.

Scientific Notation - Definition

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.