Method

Multiply Numbers in Scientific Notation

Numbers written in scientific notation can be multiplied by using the properties of exponents. Two numbers written in scientific notation a* 10^b and c * 10^d can be multiplied by using the Commutative Property of Multiplication and the Product of Powers Property.

( a* 10^b) * ( c* 10^d)= a c * 10^(b+d)

Consider the following product. (1.5 * 10^2)*(12 * 10^5) Followed four steps to multiply these numbers.

Write Each Number in Scientific Notation

It is helpful to check whether both of the numbers are written in scientific notation. c First Factor & * & Second Factor 1.5 & * & 10^2 & ✓ 12 & * & 10^5 & * The first number is in scientific notation, but the second number is not. Its first factor 12 is greater than 10. The decimal point needs to move one unit to the left for the first factor to become less than 10. The second factor's power of 10 is then increased by that number of moves, 1. 12 * 10^5 ⇔ 1.2 * 10^(5+1) ⇔ 1.2*10^6 ✓

Multiply the First Factors

Both numbers are now written in scientific notation. The first factors of both numbers can be multiplied by using the Commutative Property of Multiplication.

(1.5 * 10^2)*(1.2* 10^6)

RemovePar

Remove parentheses

1.5 * 10^2 * 1.2* 10^6

CommutativePropMult

Commutative Property of Multiplication

1.5 * 1.2 * 10^2 * 10^6

Multiply

1.8 * 10^2 * 10^6

Multiply the Second Factors

Next, multiply the powers with base 10 using the Product of Powers Property — exponents are added when multiplying powers with the same base.

1.8 * 10^2 * 10^6

MultPow

a^m*a^n=a^(m+n)

1.8 * 10^8

Write the Result in Scientific Notation

Finally, write the resulting number in scientific notation if necessary. Our product is already in scientific notation. 1.8* 10^8

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