4th Grade Math
Whole Numbers, Place Value, and Rounding
Unit 1
Lesson One: Place Value, Standard and Expanded Forms
The Value of a Digit and Converting
Place value is the value of each digit in a number. The value of a number is determined by the place of its digits. Look at the pictures on the right!
The 6 in 269 represents 6 tens, or 60. Also, the 2 in 2,458 represents 2 thousands, or 2,000.
In a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right.
When converting between place values, remember that-
1 ten = 10 ones
1 hundred = 10 tens
1 thousand = 10 hundreds
1 ten thousand = 10 thousands
1 hundred thousand = 10 ten thousands
For example, convert 600 to tens. Each hundred has 10 tens. If there are 6 hundreds, with 10 tens in each, then you can multiply 6x10 to see the amount of tens in 600. There are 60 tens in 600.
Practice Question: Convert 400 to tens
The answer would be 40 tens. Each hundred has 10 tens. There are four hundreds because there is a 4 in the hundreds place. 4 x 10= 40. There are 40 tens in 400.
Practice Question: Convert 900 to tens
The answer would be 90 tens. Each hundred has 10 tens. There are nine hundreds because there is a 9 in the hundreds place. 9 x 10= 90. There are 90 tens in 900.
Standard and Expanded Form and Converting
Standard form is the usual way of writing numbers, and it is what you are most used to seeing. On the bottom picture on the left, you can see that 7,294 is the basic, standard way of writing the number.
Expanded form shows the value of each digit, and it shows how the standard number is made up. In the same example on the left, you see that the number 7,294 in expanded form is 7000+ 200+ 90+ 4. Each digit has a specific value based on its place value.
While standard form simplifies the value of each digit, expanded form shows the value of each digit in the number.
When converting between standard and expanded form, you either simplify the number into the standard notation (the numbers you're used to seeing!) or expand it to show the value of each digit.
For example, when converting 8936 to expanded form you would expand each digit to its real value. In this example, 8 is 8,000, 9 is 900, 3 is 30, and 6 is 6. The expanded form is 8,000+ 900+ 30+ 6.
Practice Question: What is 2347 in expanded form?
The expanded form of 2347 is 2000+ 300+ 40+ 7. Again, expanded form shows the value of each digit. In this number, 2 is in the thousands place, 3 is in the hundreds place, 4 is in the tens place, and 7 is in the ones place.
Lesson Two: Reading, Writing, and Comparing Multi-Digit Whole Numbers
Reading and Writing Multi-Digit Whole Numbers
Let's use the number 408,029,356 (on the right) as an example. In order to read whole numbers, you must read the numeral on the left first, in this case 408, then the group name after. So you would read, four hundred eight million. The next part in the number is the thousands. In this number there is a zero in the hundred thousands place. Therefore, there is no hundred thousands and you only say 29,000 (twenty-nine thousand). Lastly, are the hundreds, tens, and ones places. The number is pronounced normally. The number 408,029,356 is read and written as four hundred eight million, twenty-nine thousand, three hundred fifty-six.
In the other example on the left, it shows the name of each place value! Use this as a resource! This number would be read and written as five million, eight hundred ninety-two thousand, six hundred fourty-three.
Practice Question: How would you write 206,375,114?
Two hundred six million, three hundred seventy-five thousand, one hundred fourteen.
Practice Question: How would you write 1,632?
One thousand, six hundred thirty-two.
Comparing Multi-Digit Whole Numbers
The three signs that are used when comparing multi-digit whole numbers are >,<, and =. Think of the sign like an alligator! The mouth will open up to whichever number is larger.
In order to figure out what number is larger, look at place value! Lets start simple. Take the numbers 43 and 34. Start by looking at the place value most on the left. In this number, the place value most on the left is the tens spot. 43 has 4 in its tens spot while 34 has 3. This immediately tells us that 43 > 34 since it has a higher number in the more valued place (in this case the tens).
Next lets try 1,063 and 178. In these numbers, one has a place value that the other number does not. 1,063 has a number in thousands place while 178 does not. Since 1,063 has a higher number in an early (left) place value, it is greater. Therefore, 1,063>178.
Less Than Symbol
Greater than Symbol
Lets take two more complicated numbers, 4,187,327 and 4,187,329. Which number is greater?
Lets go one place value at a time.
In the millions place, both numbers have 4 and are equal in the millions. Next, lets look at the hundred thousands, where again both numbers have the same number, 1.
Again they are equal in the amount of hundred thousands. Lets keep going! In the ten thousands spot, both numbers have 8 and in the thousands spot both numbers have 7.
Next the hundreds, where both numbers have 3.
The next spot, the tens, again have the same number 2. Now, lets look at what makes one of these numbers greater.
In this number, it comes down to the last place value. In one number, the ones place has 7. The other number has 9. Since the second number has a higher number in the ones place, and has more units, it is greater.
Therefore, 4,187,329 > 4,187,327.
When two numbers are equal, they have the same digit in every place! 4,063=4,063
Practice Question: What sign makes this equation true? 4,046 _ 4, 146
Answer: <. The number on the right is greater than the one on the left. It has a higher place value in the hundreds place. Even though the other digits are equal to each other, the hundreds place on the right number has a higher digit.
Lesson Three: Rounding
Rounding Numbers Using Place Value
When rounding, you are finding what the number is closer too!
When rounding numbers, there is a rule of thumb! When the number is four or less, you round it down. When the number is five or more, you round it up to the next number. A common saying for this is 4 or less, let it rest, 5 or more let it soar!
Let's look at the number 47 and round it to the nearest ten. In order to round it, we need to look at the number before it, in this case the 7 in the ones place. Since it is greater than 5, we must round it up. We round up the number in the tens place. Therefore, it is rounded up to 50. 47 is closer to 50 than it is to 40.
Let's look at 1,063.
If we round it to the nearest tens place, we look at the ones place. Since three is "four or less" we let it rest. This means we keep the tens place the same. 1,063 rounded to the nearest tens place would be 1,060.
When we round to the nearest hundred, we look at the tens place. The number is 6. Since it is greater than five, we round the number up. 60 is closer to 100 than it is to 0. 1,063 rounded to the nearest hundred is 1,100.
Lastly, round this number to the nearest thousands. The place value before the thousands is the hundreds place. In this number, there is a 0 in the hundreds place. Since this is four or less, you would round this DOWN to the nearest thousand which is 1,000. 1,063 rounded to the nearest thousand is 1,000.
Practice Question: What is 4,673 rounded to the nearest hundred?
4,673 rounded to the nearest hundred is 4,700. Because the tens place, the place between the hundreds place, has a 7 in its place, it is rounded up.
Lesson Four: Adding and Subtracting and Problem Solving- Four-Step Plan
Adding Multi-Digit Numbers
To add numbers when they are in standard form, you add the digits going down the columns. You then add the totals below the line.
You need to "carry" the number to the left. This is done when the total or sum is more than one digit. Carrying means you add the digit to the column on its left.
For example, add the sum 672 + 607 + 275, then draw a line beneath. Going from right to left, you have to add 2 + 7 + 5. The sum is 14. This is where we need to carry. Put the 4 underneath the line under the ones column. Then "carry" the 1 by putting it over the tens place.
In the tens column, you have to include this 1 in your sum. So you would have to add 7 + 0 + 7 + 1. This is 15. Put 5 below the line under the tens place, and carry the 1 by putting it over the hundreds place.
Now, you have to add the digits in the hundreds column. Add 6 + 6 + 2 + 1. When you add these numbers, you get 15. Put 5 below the line under the hundreds column and carry the 1. There is no number in the thousands place, so you can write in your 1 there.
Look at the sum now written below the line: 1,554. This is your total.
Subtracting Multi-Digit Whole Numbers
Subtracting multi-digit whole numbers can be done through a similar process to addition. You want to arrange the numbers up in columns and go from right to left. Take a look at the diagram on the right. You can see that they go digit by digit from right to left. Subtracting them and writing under the line will let you get the answer.
In this example however, you see that the top number in every place is always larger than the one below it. This doesn't always happen, and when the top number is lower than the bottom one you must subtract by "regrouping". Regrouping is borrowing from the other places.
Watch these videos and follow along with them!
In these videos, you learn how to regroup and subtract with multiple digits in columns.
When Solving Word Problems...
Use the four-step identification and solving process.
The four steps in solving a problem are
Step 1: Understand the problem.- read and see what the question is asking you
Step 2: Devise a plan (translate)- translate the problem to an equation
Step 3: Carry out the plan (solve).- use the methods!
Step 4: Look back (check and interpret)- double check