Perform the indicated operation and write the answer in decimal n...

Question

Perform the indicated operation and write the answer in decimal notation. (3*10^3)(1.3*10^2)

Accepted Answer

Welcome back. I'm so glad you're here. We are multiplying these terms. We've got two times 10 to the fourth times 7.2 times 10 to the third. These numbers are in decimal notation and we want to get an answer that's in decimal notation. We know from the associative property of multiplication that we can regroup. These things that are all being multiplied together. And so we can say instead, I'm just going to drop the grouping for this 1, 10, 2 times 10 to the fourth times 7.2 times 10 to the third. And we know from the community property of multiplication we can reorder things. So I'm going to put the things with no exponents together two times 7.2. And then I'm gonna put the tens that have their exponents together, times 10 to the fourth times 10 to the third. So we know we can rewrite it like this now we've got two times 7.2, that's going to be 14. and 10 to the fourth times 10 to the third. When we are multiplying two numbers that are the same on the bottom and um they've got exponents, we can add their exponents together. So this can be 14.4 times 10 raised to the seventh. And now that that's close to decimal notation however we know that there can only be one number in front of the decimal point for decimal notations, we've got to scoot that decimal. Place one over to the left. If we were to write it out four Okay. Getting rid of that decimal point. We'd have seven numbers over here to the right of the decimal. So four is the 1st, 2nd, 3rd 4th 5th 6th, 7th to fill those all in with zeros. If we are going to scoot this decimal over one more to the left then instead of seven numbers to the right of the decimal place, we're going to have eight numbers to the right of the decimal place. So our answer is going to be 1.44 times 10 to the eighth. We look at our answer choices and that is answer choice C. You've done it. That's it. We'll catch you on the next one.