Multiply numbers written in scientific notation

key notes :

Very large or very small numbers can be written in scientific notation to make them easier to work with. Numbers in scientific notation are written as the product of two factors.

• The first factor is always a number greater than or equal to 1 but less than 10.
• The second factor is always a power of 10.

For example, you can write the number 39,000,000 in scientific notation as 3.9×10⁷.

Multiplying numbers in scientific notation

You can follow these steps to multiply numbers in scientific notation:

1. Rewrite the multiplication expression to group the first factors and the powers of 10.
2. Multiply the first factors.
3. Multiply the powers of 10 using the product of powers property.
4. Rewrite the product to be in proper scientific notation, if needed.

Let’s try it! Multiply (1.5×10⁵)×(6.8×10⁷).

(1.5×10⁵)×(6.8×10⁷)

= (1.5×6.8)×(10⁵×10⁷) ——-> Group the first factors and the powers of 10.

= 10.2×(10⁵×10⁷) ——–>Multiply the first factors.

= 10.2×10⁵⁺⁷ —-> Multiply the powers of 10 using the product of powers property.

= 10.2×10¹²

Since the first factor in the product, 10.2, is greater than 10, the product is not written in proper scientific form. Rewrite the product so the first factor is greater than 1 but less than 10.

10.2×10¹²

= 1.02×10×10¹² ——>Rewrite 10.2 as 1.02×10.

= 1.02×(10×10¹²) —–>Multiply 10×10¹².

=1.02×10¹³

So, 10.2×10¹² = 1.02×10¹³, and (1.5×10⁵)×(6.8×10⁷) = 1.02×10¹³.

Learn with an example

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