**Multiply numbers written in scientific notation : **

Here we are going to see some example problems to understand how to multiply numbers written in scientific notation.

- If the given numbers are already in scientific notation, we can do the next step.
- If the given number are in usual form, then we have to convert it into scientific notation and then we can combine.

**Example 1 :**

Find the value of (8.18 × 10⁻⁶)(1.15 × 10⁻⁵)

**Solution :**

The given two terms are in scientific notation already, so we have to multiply 8.18 by 1.15 and combine the number which are having the same base 10.

= 8.18 x 1.15 × 10⁻⁶ × 10⁻⁵

= 8.18 x 1.15 × 10⁻⁶ × 10⁻⁵

= 9.407 x 10^(-6 - 5)

= 9.407 x 10^(-11)

**Example 2 :**

Find the value of (5000)⁴ x (200)³

**Solution :**

Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.

5000 = 5.0 x 10³ (5000)⁴ = (5 x 10³)⁴ |
(200) = 2.0 x 10² (200)⁶ = (2 x 10²)³ |

By distributing the power, we get

= (5.0)⁴ x (10³)⁴ = 5⁴ x 10^12 = 625 x 10^12 |
= (2 x 10²)³ = 2³ x (10²)³ = 8 x 10^6 |

By combining the above two terms, we get

= 625 x 10^12 x 8 x 10^6

= 5000 x 10 ^(12 + 6)

= 5000 x 10 ^(18)

= 5.0 x 10³ x 10 ^(18)

= 5.0 x 10^(3+18)

= 5 x 10^21

**Example 3 :**

Find the value of (2000)⁴ x (0.0001)⁻³

**Solution :**

Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.

2000 = 2.0 x 10³ (2000)⁴ = (2 x 10³)⁴ = 2⁴ x (10³)⁴ = 16 x 10^12 |
0.0001 = 1.0 x 10⁴ (0.0001)⁻³ = (1 x 10⁴)⁻³ = 1⁻³ x (10⁴)⁻³ = 1 x 10^-12 |

By combining the above two terms, we get

= 16 x 10^12 x 1 x 10^-12

= 16 x 10^(12 - 12)

= 16 x 10⁰

= 16

After having gone through the stuff given above, we hope that the students would have understood "Multiply numbers written in scientific notation".

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