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We use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to write numbers. The value of each digit or numeral depends on its position or place. In this lesson, we will try to gain deeper **understanding of place values** and how to compare multi-digits based on the digits in the different place values.

**See the fact file below for more information on the Understanding Place Value System or alternatively, you can download our 35-page Understanding Place Value System worksheet pack to utilise within the classroom or home environment.**

## Key Facts & Information

### PLACE VALUES: A REVIEW

- Let’s have a review session.
- Ones stands for one digits. Moving to the left, tens means x10, and then as we move from tens to hundreds, we multiply the 10 (from tens) by another 10, which will give us 100.
- The digit 1 is in the thousands place. Its value is 1000.
- The digit 3 is in the hundreds place. Its value is 300.
- The digit 7 is in the tens place. Its value is 70.
- The digit 2 is in the ones place. Its value is 2.
- The standard form is 1372.
- You read it as one thousand three hundred seventy-two.
- The expanded form is 1000 + 300 + 70 + 2.

### RELATION TO TEN

- Now, let’s understand how the number ten is related to place values.
- What is the relationship between 7, 70, 700, and 7000?
- Let’s understand this place value by place value.
- 7 x 10 = 70
- 70 x 10 = 700
- 700 x 10 = 7000
- 7000

- Therefore, we can say that a digit in the ones place value multiplied by ten will give us a two-digit number, which in our case is 70. This understanding is applicable to the succeeding place values.
- We can say that, as we multiply a number by 10, the number increases in value and becomes 10 times larger.
- We can use this understanding to relate this to division.
- 7000 ÷ 10 = 700
- 700 ÷ 10 = 70
- 70 ÷ 10 = 7

- This time, whenever we divide a number by 10, the number decreases in value and becomes 10 times smaller.
- Notice also that, whenever we multiply the number by 10, an additional zero (0) gets inserted on the right side of the number. On the other hand, whenever we divide the number by 10, we remove a zero from the right side of the number.

### PLACE VALUE SYSTEM FOR DECIMALS

- The decimal system for whole numbers is based on place values, which increase 10 times as each place moves to the left, and is 1/10 less each time a place moves to the right, as seen in the table on the next page.
- The place value system for decimal numbers is just an extension of the same system for whole numbers. You can see that the decimal point separates whole numbers to the left from the decimal numbers to the right.
- Looking at the whole numbers on the chart and starting with 1, we can see this carries a place value of just one. We can see that the next column is the tens place which is ten times bigger than the ones place and so on.
- Similarly, every time a place moves to the right, the value of any digit in that place decreases by 10 or is 1/10th the value of the previous column.
- Let’s now look at the decimal numbers or numbers less than one. We will notice that they also decrease by 1/10 as we move to the right. Starting with the first decimal place column and moving to the right, 1/10 is ten times smaller than 1 whole. 1/100 is ten times smaller than 1/10 and 1/1000 is ten times smaller than 1/100.
- Let’s now look at how the numeral 5 can change its value by being in a different “place” in our decimal place value system.

### EXPANDED NOTATION FOR DECIMALS

- Example 1. The expanded form for 7392 would be:
- 7000 + 300 + 90 + 2

- Example 2. The expanded form for 435.68 would be:
- 400 + 30 + 5 + 6/10 + 8/100

- These values can then be further expanded to include the place value of each digit:
- 400 + 30 + 5 + 6/10 + 8/100
- (4 x 100) + (3 x 10) + (5 x 1) + (6 x 1/10) + (8 x 100)

### COMPARING DECIMALS

- Given two decimals, it is fairly straightforward to compare them and decide greater or lesser when the same number of digits are involved.
- 0.305 < 0.406

- Most students have a problem, though, when the number of digits is different, such as comparing:
- 0.30
- 0.27

- This is because learners often relate more digits to bigger numbers when thinking about whole numbers. A good way to overcome this problem is to write the decimals out in columns with headings. This highlights how zeros to the right make no difference to the value of the decimal.
- Zeros to the right do not change the size of decimal numbers.
- However, notice that the zeros are very important sometimes, as they are place holders and keep other numbers in the correct place.
- Zeros to the right have their uses, though. Aside from helping us compare values, they can indicate how accurately something has been measured.
- When comparing decimals, start in the tenths place. The decimal with the biggest value is greater. If they are the same, move to the hundredths place and compare these values. If the values are still the same, keep moving to the right until you find one that is greater or until you find that they are equal. If it helps, add zeros to the right so that both decimals have the same number of digits.

### ROUNDING DECIMALS

- Rounding decimals refers to the rounding of decimal numbers to a certain degree of accuracy.
- We can round decimals to the nearest wholes, tenths, hundredths, and so on.

### ROUNDING TO THE NEAREST WHOLE

- STEPS TO ROUND NUMBERS TO THE NEAREST WHOLE NUMBER
- Look at the number we want to round.
- As we are rounding the number to the nearest whole, mark the digit in the ones place.
- Now, look at the tenths place or the digit to the right of the decimal point.
- If the digit in the tenths column is 0, 1, 2, 3, or 4, we will round the number in the ones place down to the nearest whole number. If the digit in the tenths column is 5, 6, 7, 8, or 9, we will round the number in the ones place up to the nearest whole number.
- Remove all the digits after the decimal point. The remaining number is the desired answer.
- For example, round 965.87 to the nearest whole number.
- 965.87 -> 966
- Since 8 is in the tenths place, we round up. We add 1 to 5 and remove all the digits from the right of the ones place, resulting in 966.

### ROUNDING TO THE NEAREST TENTHS

- Rounding to the nearest tenths is almost similar to rounding decimals to the nearest whole. Simply follow the steps on the next page.
- STEPS TO ROUND NUMBERS TO THE NEAREST TENTHS
- Look at the number we want to round.
- As we are rounding the number to the nearest tenth, mark the digit in the tenths place.
- Now, look at the hundredths place or the digit to the right of the tenths column.
- If the digit in the hundredths column is 0, 1, 2, 3, or 4, we will round the number in the tenths place down to the nearest tenth. If the digit in the hundredths column is 5, 6, 7, 8, or 9, we will round the number in the tenths place up to the nearest tenth.
- Remove all the digits to the right of the tenths column. The remaining number is the desired answer.
- For example, round 112.33 to the nearest tenth.
- 112.33 -> 112.3
- SInce 3 is in the hundredths place, and it is less than 5, we round down. We keep 3 as it is and remove all the digits from the right of the tenths column.

### ROUNDING TO THE NEAREST HUNDREDTHS

- STEPS TO ROUND NUMBERS TO THE NEAREST HUNDREDTHS
- Look at the number we want to round.
- As we are rounding the number to the nearest hundredth, mark the digit in the hundredths place.
- Now, look at the thousandths place or the digit to the right of the hundredths column.
- STEPS TO ROUND NUMBERS TO THE NEAREST HUNDREDTHS
- Look at the number we want to round.
- As we are rounding the number to the nearest hundredths, mark the digit in the hundredths place.
- Now, look at the thousandths place or the digit to the right of the hundredths column.
- If the digit in the thousandths column is 0, 1, 2, 3, or 4, we will round the number in the hundredths place down to the nearest hundredth. If the digit in the thousandths column is 5, 6, 7, 8, or 9, we will round the number in the hundredths place up to the nearest hundredth.
- Remove all the digits to the right of the hundredths column. The remaining number is the desired answer.
- For example, round 1780.129 to the nearest hundredth.
- 1780.129 -> 1780.13
- SInce 9 is in the thousandths place, and it is greater than 5, we round up. We add 1 to 2 and remove all the digits from the right of the hundredths column.

**Understanding Place Value System Worksheets**

This is a fantastic bundle which includes everything you need to know about the Understanding Place Value System across 35 in-depth pages. These are** ready-to-use Understanding Place Value System worksheets that are perfect for teaching students how to use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to write numbers. The value of each digit or numeral depends on its position or place. In this lesson, we will try to gain deeper understanding of place values and how to compare multi-digits based on the digits in the different place values. **

### Complete List Of Included Worksheets

- Lesson Plan
- Understanding Place Value System
- Wholes Times Ten
- Wholes Divided By Ten
- Name and Expand
- What’s the Number?
- What’s My Place?
- What Decimal Place?
- Fill It
- Solve Then Compare
- Arranging Decimals
- Rounding Off

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Link will appear as Understanding Place Value System Facts & Worksheets: https://kidskonnect.com - KidsKonnect, June 29, 2020

**Use With Any Curriculum**

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