Understanding Place Value Decimals, Large Numbers, and Easy Charts

Understanding Place Value Decimals, Large Numbers, and Easy Charts SAT / ACT Prep Online Guides and Tips How do you read 4,349,394.382? What does each digit mean? How do you know what number means what? With place values, that’s how! If you don’t understand how decimal place values work, a number like that can look like a bunch of nonsense. In this article, we’re going to cover what place value is, why you need to know it, and how to work through place value problems to better understand large, complex numbers with ease. What Is Place Value? Let’s start with the basics. Place value refers to the meaning of a single digit in a specific position in a number. Unfortunately, that definition doesn’t make a whole lot of sense without an example, so let’s look at a number: 14. We know that number is fourteen, just as we know that 14 is the number that comes between 13 and 15. We can even break it down further- 14 is 4 more than 10. 10 + 4 = 14. Clearly, the different digits- the individual numerals that form a number- mean something. The 1 doesn’t mean 1, it means 10. That’s because the 1 in 14 is in the tens place. It tells us how many tens are in a number. So in the number 14, there is one ten and four ones- 10 + 4 = 14. If we change that 1 to a 2, we get 24, or twenty-four. The number 2 in the tens place tells us there are two tens. Each place value is 10 times larger than the place value to the right of it. So when we look at a number like 4,349,394.382, our example from earlier, we can see that there are: 4 ones 9 tens 3 hundreds 9 thousands 4 ten-thousands 3 hundred-thousands 4 millions That gives us a better idea of how to read the number aloud. It’s four million, three hundred forty-nine thousand, three hundred ninety-four. But what about all those digits to the right of the period, or decimal point? Those digits represent parts of one. Imagine this number represents the number of leaves on a particularly big tree. The .382 might represent a fraction of a leaf- perhaps one that’s been nibbled on by bugs. So how do we read those numbers? In the same way we read all the others, except the digits represent fractions of a whole. The digits to the right of a decimal point work almost exactly the same way, except there is no â€Å"ones† equivalent. We end the place values representing fractions with â€Å"th,† so instead of tens, hundreds, thousands, the numbers to the right of a decimal are tenths, hundredths, thousandths. More specifically, in our example, .382 equates to: 3 tenths 8 hundredths 2 thousandths Or, read aloud, three hundred eighty-two thousandths. The same rule holds true of numbers to the right of the decimal: each place value is ten times the place value to the right of it. Ten thousandths equal one hundredth, ten hundredths equal one tenth, and ten tenths equal one whole. Put the whole number together, and you get four million, three hundred forty-nine thousand, three hundred ninety-four and three hundred eighty-two thousandths. It may sound confusing, but once you’ve spent a little time with it, it’ll become second nature. Just remember that a digit’s place value represents the meaning of a single digit and that every place value is 10 times larger than the place value directly to the right and you’ll be on the right track. Why Do You Need to Know About Place Values? All of this can seem pretty complex. Why do we even need to know place values? Place values become increasingly important as you work more frequently with decimals and large numbers, because without understanding place values, you’ll have a really difficult time understanding how to read them. Place value is also really important in solving word problems. If a word problem says that somebody bought one thousand and four tacks, you might write that number as 1,400, 1,040, or 1,004 if you don’t understand place values. Only one of those answers can be correct, and you’ll have a much easier time of understanding those kinds of problems with a solid grasp on place values. Place Value Chart One of the best ways to learn place value is using a chart. You can write the different place values along the top and line the digits of numbers up with their correct position on the chart. Here’s what a place value chart might look like, though you can include more or less columns depending on the number you’re working with. Hundred Thousands 0 Ten Thousands 0 Thousands 0 Hundreds 0 Tens 0 Ones 0 Tenths 0 Hundredths 0 Thousandths 0 Ten Thousandths 0 Let’s try filling out a chart with an example number, like 156,412.5485 Hundred Thousands 1 Ten Thousands 5 Thousands 6 Hundreds 4 Tens 1 Ones 2 Tenths 5 Hundredths 4 Thousandths 8 Ten Thousandths 5 We took each digit and wrote it into its proper place. Now if we have a question about what any digit represents, we can answer it quite easily. For example, the 6 in this number represents 6 thousands. This is especially useful when dealing with numbers that contain zeroes. Let’s take this chart and turn it into a recognizable number: Hundred Thousands 3 Ten Thousands 0 Thousands 3 Hundreds 0 Tens 0 Ones 5 Tenths 0 Hundredths 0 Thousandths 3 Ten Thousandths 0 Remember, having a 0 in the place value of a number doesn’t mean that you skip it- it means that there are zero of that particular value in the number. 104 means that there are no tens, just one hundred and four ones- you can’t write 14 instead of 104 just because there’s a zero in it. So in this case, the number would be written 303,005.003. We can drop the last zero since nothing follows it. It might be tempting to write 335.3, but, as you can see, that’s a very different number from 303,005.003. Understanding place values helps us hold a place for the value that goes into that spot! Place Value Example Problem Let’s work through some example place value problems to get a better handle on how place value works. What Is the Place Value of the 4 in the Number 1,459.235? First, we have to write the number into our place value chart. The decimal will always fall between the ones and tenths place, so we write the nine in the ones place and the 2 in the tenths place, and fill the rest out from there. Hundred Thousands 0 Ten Thousands 0 Thousands 1 Hundreds 4 Tens 5 Ones 9 Tenths 2 Hundredths 3 Thousandths 5 Ten Thousandths 0 The question asks the place value of the 4. We look at the digits in the chart to find the 4 and see that it’s in the hundreds position. That tells us there are 4 hundreds, so the place value is 400. What Digit Is in the Thousandths Place in the Number 6,872,485.495? This one is a little different. The number is larger, so we’ll have to extend our chart a bit to fit it. Once again, you can start with the numbers on either side of the decimal, so 5 goes into the ones box and 4 goes into the tenths box, then fill out the rest of the chart from there. Millions 1 Hundred Thousands 8 Ten Thousands 7 Thousands 2 Hundreds 4 Tens 5 Ones 5 Tenths 4 Hundredths 9 Thousandths 5 This time we need to figure out what digit is in the thousandths place. Find the box labeled â€Å"thousandths† and see what number is next to it. It’s 5, and since we’re only asked for the digit rather than the place value, that’s our answer. What Number has 4 Thousands, 0 Tens, 3 Hundredths, 0 Ones, 5 Hundreds, and 6 Tenths? Notice the zeroes in this question- that’s where things start to get difficult. We’ll use a chart to help us figure it out! Fill the proper columns, but pay attention, because the numbers are out of order. Hundred Thousands 0 Ten Thousands 0 Thousands 4 Hundreds 5 Tens 0 Ones 0 Tenths 6 Hundredths 3 Thousandths 0 Ten Thousandths 0 Now that we have the numbers placed, we can write it out properly. Remember that the decimal goes between the ones and tenths place. Write it out, and you’ll get 4,500.63! Practicing place value probably won't make you better at dogsledding, but it can't hurt. Practice Problems Here are a few more practice problems you can work through to work on your own, with solutions down below! What Is the Place Value of 7 in 1,508,005.078? HINT: Pay attention to the question. Is it asking for place value or digit? HINT: Remember, zeroes still take up a place! Answer: First, we need to fill out our chart. Millions 1 Hundred Thousands 5 Ten Thousands 0 Thousands 8 Hundreds 0 Tens 0 Ones 5 Tenths 0 Hundredths 7 Thousandths 8 Next, we need to find the 7. It’s in the hundredths position, so there are 7 hundredths, or .07! What Digit Is in the Ten-Thousandths Place of 1.284681? HINT: Is the question asking for place value or digit? HINT: Does the place value end in s or ths? Answer: Let’s start with a chart. We’ll have to make some adjustments, because there are a lot more numbers to the right of the decimal this time. Ones 1 Tenths 2 Hundredths 8 Thousandths 4 Ten Thousandths 6 Hundred Thousandths 8 Millionths 1 Next we look for the ten-thousandths column, since that’s what the question asked for. The number in that column is 6, and since it’s asking specifically for the digit and not the place value, 6 is our answer! What Is the Place Value of 3 in 3,042.28? HINT: Are we looking for place value or the digit? HINT: Pay attention to zeroes! Answer: As always, we start with a chart. Millions 0 Hundred Thousands 0 Ten Thousands 0 Thousands 3 Hundreds 0 Tens 4 Ones 2 Tenths 2 Hundredths 8 Thousandths 0 We’re looking for the place value of the 3, so we need to find that first. It’s in the thousands place, which means the number has 3 thousands, so our answer is 3,000! What Digit Is in the Thousands Place of 32,734.426? HINT: Is this question about digits or place values? HINT: Are we looking for a number to the left or right of the decimal? Answer: Start with a chart! Millions 0 Hundred Thousands 0 Ten Thousands 3 Thousands 2 Hundreds 7 Tens 3 Ones 4 Tenths 4 Hundredths 2 Thousandths 6 The question asks us the digit in the thousands place, so first we’ll find the thousands row. The number in that row is 2, and since the question asks for the digit, that’s our answer! What Number Is Made up of 2 Hundreds, 0 Thousands, 6 Ten Thousands, 4 Tenths, 9 Ones, and 3 Tens? HINT: Remember, zeroes still take up space! HINT: The decimal always goes between the ones and tenths place. Answer: Let’s make a chart! Millions 0 Hundred Thousands 0 Ten Thousands 6 Thousands 0 Hundreds 2 Tens 3 Ones 9 Tenths 3 Hundredths 0 Thousandths 0 Once we’ve filled in all the blanks, we can write out the number: 602394. However, we’ll need to add a comma and decimal. The decimal goes between the ones and tenths place, so we’ll get 60239.4, and commas go between every third digit starting from the decimal and working to the left. Following that, we’ll end up with 60,239.4! 3 Key Tips for Decimal Place Value Problems Place value is an important skill to develop; once you understand it, you’ll have an easier time understanding large numbers. Understanding it can be tricky, though- it’s a concept that requires a lot of practice and memorization. Use these tips to help you improve your place value understanding until it becomes second nature! Memorize Ths Versus S Whole numbers versus fractions are an easy place to get tripped up when working on place values. Remember: numbers that end in â€Å"ths† are part of a whole- that means tenths, hundredths, thousandths, and so on. Numbers that end in â€Å"s† are whole numbers, so tens, hundreds, thousands, et cetera. Always double-check to make sure that you’re looking for the right number. Thousands and thousandths are very different from one another! Draw a Chart Though you will likely eventually develop the ability to tell place values without one, when you’re first starting out it’s wise to use a chart. It’s way easier to line the numbers up that way than to rely on counting and potentially get them wrong. Don’t Forget Zeroes Zeroes are the nemesis of people just learning place values. Remember, a zero in the middle of a number, such as 104, doesn’t literally mean nothing- it’s a place holder telling you there are no tens. If you skip the zero when writing the number, you’ll end up with an incorrect answer, so be sure that you fill every place! What’s Next? One of the places you'll be needing place value most is in understanding decimals. Check out this guide to converting decimals to fractions to learn more about how decimals and fractions are related to one another! Want to boost your math understanding? This guide to adding and subtracting fractions will walk you through everything you need to know about numerators, denominators, and how they work. Brushing up on math before you take the SAT? Check out this guide to prepping for SAT Math, including strategies, tips, and practice problems!