Decimals and Place Value

0:00 Hey everyone, and welcome to this explainer. Look, I know that prepping for the ASVAB can feel a little intimidating, especially when you realize you won't have a calculator for the math sections. But honestly, I promise you, you've totally got this. Today, we're going to build your confidence step-by-step with a completely no-calculator masterclass on decimals. Decimals are a core foundational skill for the arithmetic reasoning subtest, and by the end of our time together, you're going to see that doing all of this by hand is absolutely manageable. So, let's jump in. Here's our roadmap for today. We're going to hit place value and rounding, math with decimals, conversions and real-world math, step-by-step worked examples, common traps to avoid, and finally, a quick check yourself section to test your skills. All right, starting off with section one, place value and rounding. So, I want you to think of the decimal point as your absolute anchor. It's your grounding point. Each place to the right of the decimal point is worth exactly one-tenth of the place to its left. Take a look at the number 36.582. To the right of our decimal anchor, that first place is the tenths.

1:05 So, that's the five. The second place is the hundredths, that's the eight, and the third place is the thousandths, which is the two. Put it all together, and this is 36 and 582 thousandths. Now, you know a huge part of the ASVAB is literally just figuring out which number is bigger. If you get a question asking you to order 0.6, 0.58, and 0.605, it can look a little tricky at first glance. So, here is the secret. Line up your decimal anchors and pad the shorter numbers with zeros, so they all have the exact same number of places. We just turn 0.6 into 0.600 and 0.58 into 0.580. Now, you're just comparing 680 and 605. It becomes completely obvious that 0.605 is the largest, right? Rounding is another absolutely essential skill, and the rule is super simple. Find your target place and look at the digit right next door to its right. If it's five or more, round up. If it's four or less, just leave it alone. Let's look at 7.364. To round this to the nearest tenth, we look at the digit right after the three, which is a six.

2:10 Since six is five or more, we round up to 7.4. But if we're rounding to the nearest hundredth, we look after the six, which is a four, so we leave it as 7.36. Oh, and watch out for carrying. If you need to round 2.995 to the nearest hundredth, that five makes the nine round up, which carries over to the next nine, which carries over to the two, giving you a clean 3.00. Math with decimals. This right here brilliantly illustrates why that decimal anchor is so crucial. For addition and subtraction, you just line up those decimal points. Fill any empty spaces with zeros and calculate exactly like you're working with regular whole numbers. Check out the addition problem. 9.4 plus 2.75 plus 0.068 simply becomes 9.400 plus 2.750 plus 0.068, which drops straight down to equal 12.218. The decimal just stays right in its column. Same goes for a subtraction. 15 minus 6.38 becomes 15.00 minus 6.38, which easily gives us 8.62.

3:17 Pretty straightforward, right? All right, let's tackle multiplication. Now, here is a golden rule you need to remember. You do not need to line up the decimal points when multiplying. Actually, scratch that, you definitely shouldn't worry about lining them up. Look at 3.2 times 0.45. Step one, just multiply them as if they were whole numbers. 32 times 45 equals 1,040. Step two, count up the total number of decimal places in your original numbers. We've got one place in 3.2 and two places in 0.45, so that's 3 places total. Step three, place the point three spots in from the right. We get 1.440, which is just 1.44. Now, division requires a little shuffle, sure, but it really is straightforward. To divide by a decimal, like 8.64 divided by 0.4, you want your divisor, that's the number you're dividing by, to be a whole number. So just move the point in 0.4, one place to the right to make it a solid four. But remember, whatever you do to the outside, you absolutely have to do to the inside.

4:21 Move the point in 8.64, one place to the right as well, making it 86.4. Now, you just divide normally. 86.4 divided by 4 equals 21.6. By shifting both decimals the exact same amount, your quotient stays perfectly accurate. Okay, section three, conversions and real-world math. Honestly, knowing how to slide your decimal point left or right is like having a superpower for conversions. Multiplying by 10, 100, or 1000 simply moves the decimal point to the right, one, two, or three places. Look at the top line there. 3.07 times 1000 moves the point to the right three times. We just add a zero as a placeholder, and boom, we get 3,070. Dividing, on the other hand, moves it to the left. 52.6 divided by 100 shifts it left two places, becoming 0.526. 0.9 divided by 10 shifts left one place, becoming 0.09. This little trick makes metric conversions an absolute breeze. You're also definitely going to need to switch back and forth between fractions and decimals.

5:25 But remember, a fraction is literally just a division problem waiting to happen. 7 over 8 is simply 7 divided by 8, which equals 0.875. And to go the other way from a decimal to a fraction, just read the decimal out loud. 0.36 is read as 36 hundredths. So, write 36 over 100. And then you just simplify it by dividing both by 4 to get 9 over 25. Before diving into complex math, always estimate first. So you have a gut check on whether your final answer makes real world sense. I mean, 6.92 times 3.1 looks awful, but 7 times 3 is just 21. If your actual calculation gives you something wild like 2.14 or 214, you'll know instantly that your decimal is in the wrong spot. And for rates, say a generator burns 1.6 gallons per hour. Well, in 7.5 hours, it uses 1.6 times 7.5, giving you exactly 12 gallons. Keep your units attached to the numbers, and they'll naturally guide your math. All right, moving into section 4, step by step, worked examples.

6:29 Let's see some real ASVAB scenarios. Let's look at example 1, which is all about tracking inventory. A bin holds 14.6 kilograms of bolts. Crews use 3.85 kilograms, and then 5.4 kilograms are added back in. So how much is left? First, track what's used. We pad the numbers with zeros. 14.60 minus 3.85 equals 10.75. Then they add more, so we just pad it again. 10.75 plus 5.40 equals 16.15 kilograms. Do you see how just padding with zeros makes this whole process super smooth? Now, example 2 is asking for a unit price. If 8 batteries cost $27.60, what's the price for just 1? We divide the total dollars by the number of items. $27.60 divided by 8 gives us exactly $3.45. Example 3 is finding a rate. A drone flies 37.8 kilometers in 0.6 hours. What's its speed? We just divide the total distance by the time. 37.8 divided by 0.6. But remember our division shuffle rule.

7:33 Shift the decimal one spot to the right for both numbers to make it 378 divided by 6, which gets you a clean 63 kilometers per hour. Okay, let's knock out these last two examples. Example 4 is a multi-step purchase. Let's say you buy four manuals at $6.25 each and three pens at $1.80 each, and you pay with a $40 bill. First, figure out the manuals. Four times 6.25 is $25 even. Then the pens. Three times 1.80 is $5.40. Add those up for a total of $30.40. To find your change, subtract that from the $40 bill. $40 minus $30.40 leaves you with $9.60. And example 5, which is larger? 0.45 or 7/16. First, turn that fraction into a decimal by dividing. Seven divided by 16 is 0.4375. Then, pad 0.45 out to four places. So it's 0.4500. Comparing them side by side, it's pretty obvious that 0.4500 is greater. Common traps to avoid.

8:35 These are the mistakes you definitely want to steer clear of. Listen, the absolute biggest trap people fall into when rushing is misaligned decimal points. Take a look at the left side there. If you try to add 3.5 and 1.25 by just lazily lining up the digits on the far right, you end up adding the five to the five and getting 1.60. That is completely wrong. Look at the right side. You must line up the decimal points like an anchor and pad that 3.5 with a zero. 3.50 plus 1.25 equals 4.75. Your decimal anchor is what keeps you safe. And here's another massive trap. Judging size just by how long a number looks. On the left, it is so tempting to say 0.5 is less than 0.45 simply because five looks smaller than 45. But once again, look at the right side. If you pad 0.5 with a zero, it becomes 0.50. And now it's crystal clear. 50 is obviously greater than 45. Padding with zeros reveals the true value every single time. Seriously, don't let your eyes trick you on test day.

9:40 Finally, section six, check yourself. Let's see what you've learned. All right, here's your first practice question. A shop has four drill bits with diameters of 0.375 inch, 0.4 inch, 0.38 inch, and 0.3125 inch. Which bit has the largest diameter? I strongly encourage you to pause the explainer right now. Grab some paper, work it out, and then hit play to see if you nailed it. Okay, we're back. Did you get 0.4 inch? Because that is the correct answer. Why? Well, if you pad every single option out to four decimal places, the answer basically jumps out at you. You get 0.3750, 0.4000, 0.3800, and 0.3125. If you compare the tenths digits first, only 0.4000 has a four right there. It is the clear winner. Awesome job. Let's tackle one more. Here's your final question. A plumber cuts three pieces of pipe, measuring 3.6 meters, 2.45 meters, and 0.8 meter. What is the total length of the three pieces?

10:45 Take a deep breath, line up those decimal anchor points, pause the explainer, and solve it. All right, let's see how you did. The correct answer is 6.85 meters. You just line up your decimal points, pad any gaps with zeros, and add 3.60 plus 2.45 plus 0.80. That straight vertical addition drops the decimal point right into place perfectly at 6.85. If you got that right, you are well on your way to totally mastering ASVAB decimals. So as you sit down for that real test, ask yourself, have I anchored my decimals correctly and did I actually estimate my answer to make sure it makes real world sense? Keep those two golden rules in your back pocket and you won't even miss the calculator. Thanks so much for learning with me today and keep practicing.