Below is the transcript of my tutorial video Multiplication and Division for Units of Ten
Leah here from leah4sci.com/MCAT and in this video I will show you how to quickly and easily Multiply and Divide numbers by a factor of 10 without a calculator.
You can find my entire series on doing MCAT Math Without A Calculator by visiting my website https://leah4sci.com/MCATMATH.
Multiplying and Dividing by factors of 10 will come up again and again in your MCAT practice including questions related to everything, from Unit Conversions to General Math. Multiplying and Dividing by 10 is a fun way to do Math in your head and 10 comes up in a lot of questions from converting something like grams to kilograms, solving gravitational acceleration questions and so much more. Or say your number does not have the factor of 10, round it to the nearest 10 and then apply the tricks. Why? Because it’s easier and faster than doing it the long way.
Now before I show you how to find the solution of 3.47 x 1000 in under 5 seconds, let’s do a fun exercise. Say I ask you to perform the calculation of 2.3 x 10 in your head. Some of you can do it, others will look at me like I’m crazy! Now maybe I am, but that’s not the topic for today. If you got it, great! If not, let’s try this quick exercise.
If I ask you 1 x 10, I hope you know that the answer is 10. If you didn’t, you need to download my MCAT Math guide by visiting my website https://leah4sci.com/MCATMATH. Now if I ask you to do 2 x 10, the answer is 20. If I ask you to do 3 x10, the answer is 30. These are simple equations, but I want you to focus not on the answer but think about what you did.
You have a number and you multiplied it by 10 so all you did was add a zero. We took the number 3, we added the 0, that’s how we got 30. Now if I ask you to do 20 x 10, once again, all I do is add a zero (0), that gives me Two Hundred Thirty (230). In other words, to multiply any number by 10, all you have to do is add a zero (0).
So what if I ask you to do 2.3 x 10 or we can’t really add a zero because we have a decimal. So let’s revisit the initial trick; when we added a zero, all we really did was move that imaginary decimal at the end of the number over one space to the right. Starting with 1, we move it over that gave us 10, 2 gave is 20, 3 gave us 30 and 23 gave us 230.
So if the decimal is not invisible, the same trick applies. Take the decimal, move it over one space to the right and 2.3 now becomes 23. Let’s crank it up a notch. What if I ask you to solve 37 x 100? We’re not dealing with 10 now we are dealing with a hundred (100) which is 10 x 10.
Anytime you have the number 1 followed by zeros (0), that number is simply 1 x 10 again and again until it equals the number of zeros that you have. Looking at the number 100 we have two zeros (0), that means we’re multiplying by two factors of 10 so we’ll take that imaginary decimal at the end of number and move it over 2 spaces, one for each zero giving me an answer of 3700.
Now let’s revisit our initial question. This may show up as part of a larger question asking you to convert 3.47 kilograms into grams. So we take our initial value of 3.47kg. I’m writing this out to show you but I want you to set this up mentally. Knowing that there’s a thousand (1000) grams every kilogram we set it up so kilograms can cancel and now our equation is simply 3.47 x 1000. A thousand has 3 zeros which means we move the decimals 3 spaces to the right – one, two, three, giving as an answer of 3470. This example when done in your head should take you under 5 seconds!
Now let’s say we want to divide a number by a factor of 10. If multiplying by 10 means you move the decimal to the right, then dividing by 10 means you move the decimal to the left. Let’s start simple: 30 divided by 10, we take the decimal, move it one space to the left that gives us 3. Given 470 divided by 100, one hundred (100) has two zeros so we take the decimal move it 2 spaces to the left, that gives us 4.7.
Now what if you’re starting with the decimal? Say you have 0.53 and you want to divide it by 1000. For example you have 0.53 grams and you want to turn this into kilograms. We have three zeros dividing by 1 and three zeros means move the decimal three spaces to the left, one, two, three. Be very careful to count your zeros here, the answer is 0.00053. you’ll probably see this in Scientific notation and that’s something I will cover in the future video.
Now what if the example given isn’t as clean, meaning you don’t see the 10 as obvious? So let’s make up a number; Say we have 3.29 and we want to multiply this by 9.73. When 9.73 is very close to 10 and on the MCAT, close enough is good enough. 9.73 is 10 that means we move the decimal one space to the right giving me an answer of 32.9.
Remember the choices on the MCAT won’t be very very close to each other because they’re testing your ability to do the right kind of Math and give you wrong answers that are simply all over the place allowing you to rule out anything that is way too far off from the number that you got.
Be sure to join me in the next video where I take this concept to the next level, showing you how to quickly multiply and divide numbers using the factor of 10 trick when you can even round your number to the nearest 10.
Are you stuck on a specific MCAT topic? I offer Private Online Tutoring where I focus on your needs to strengthen your individual weaknesses. Tutoring details can be found using the link below or by visiting my website leah4sci.com/MCATTutor.
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Watch The Video Here: MCAT Math Trick – Multiplying and Dividing Units of 10