How to multiply scientific notation

Steps for multiplying two numbers written in scientific notation

When you multiply two numbers in scientific notation, you want to follow the same set of steps each time.

Multiply their decimal numbers.
Multiply their powers of ???10???. By the rules of exponents, we add the exponents when we do this.
Express the results together in proper scientific notation.

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How to multiply scientific notation

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Let’s do another example where we multiply two numbers in scientific notation

Example

Find the product.

???(3.4\times10^{-6})(2.14\times10^{13})???

Let’s follow the steps we outlined above. First, we’ll multiply the decimal numbers.

???3.4\times2.14=7.276???

Now we’ll multiply the powers of ???10???, adding the exponents.

???10^{-6}\times10^{13}=10^{-6+13}=10^{7}???

Next, we’ll multiply these two values together.

???7.276\times10^7???

This is already in proper scientific notation so we can leave it as is. But if there were two or more digits to the left of the decimal point, or if we had a ???0??? in the ones (units) place, the decimal point, then we’d have to express it in proper scientific notation.