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In this lesson, we will try to understand how **decimal notation for fractions** works and how we can compare decimal fractions.

**See the fact file below for more information on the decimal notation for fractions or alternatively, you can download our 35-page Decimal Notation for Fractions worksheet pack to utilise within the classroom or home environment.**

## Key Facts & Information

### 10 AND 100 DENOMINATORS

- In this section, we will identify the relationship between fractions who have 10 and 100 as their denominators.
- From previous lessons about fractions, we know that fractions that lie on the same point on the number line despite having different numerators and denominators are equivalent. This is also true for fractions with 10 and 100 as their denominators.
- First, we have to establish that 10/10 and 100/100 are both equal to 1.
- Now, let’s look at 50/100 and 5/10.
- Look at 50/100 and 5/10, both lie on the same point on the number line, which means that 50/100 and 5/10 are equivalent.
- One shortcut to understand this is to “remove” excess zeros.

10/10 has one zero in the numerator and another one in the denominator, which means, that we can “remove” each zero. - 100/100 has two zeros in the numerator and another two in the denominator, which means that we can “remove” two zeros from each.

### ADDING FRACTIONS WITH 10 AND 100 DENOMINATORS

- Just like in the previous lessons, to be able to add fractions of different denominators, we have to make their denominators the same.
- 2/10 + 3/100 = ?

- From the previous lessons, we have found out about finding the LCD then transforming the fractions according to the LCD found. In case you have forgotten, LCD means Least Common Denominator.
- But this time, since we have 10 and 100 as our denominators, we can just use the shortcut method.
- This shortcut allows us to just add one zero to both the numerator and the denominator of the fraction with 10 as the denominator.
- Now, we already have fractions of the same denominator.
- We can now proceed with the normal routine of addition.
- 20/100 + 3/100 = 23/100

### CONVERTING FRACTIONS TO DECIMALS

- In this section, we will try to understand how we can convert fractions into decimals.
- 55/100 = 0.55

- Now, we will place the numerator of the fraction with 10 as its denominator on the tenths place value. Thus, we will have 0.5
- Then, we will place the numerator of the fraction with 100 as its denominator on the hundredths place value. Thus, we will have 0.55.
- 5/10 + 5/100 = 55/100

- Therefore, we can express 55/100 as 0.55
- This time, we will talk about another method of expressing fractions with denominators of 10 and 100 as decimals.
- 7/10 = ?

- We know, by the previous method, that 7/10 in decimal is 0.7.
- In this method, we will think of the horizontal line as a division sign.
- Thus, we can think of 7/10 as 7 ÷ 10.
- Since we know that 7 is greater than 10, this is a bit more complicated division. We will therefore use long division method to show the steps.
- 7 is less than 10, therefore we cannot divide 7 directly by 10.
- Since this is the case, we would have to add a zero to 7, making it 70.
- The added zero means that we are now in the tenths place value (decimals).
- The red line indicated that there is a decimal point in that area.
- Now, we can already divide 70 by 10, which will give us 7.
- Since there is a decimal point on the red line, instead of getting 7 as the quotient, we will get .7 or 0.7
- This method is also applicable to fractions with 100 as their denominators.
- 8/100 = ?

- Now, let us do the same thing that we did previously.
- Just like before, we cannot divide 8 directly by 100 since 8 is less than 100.
- 8 is less than 100, therefore we will add a zero, giving us 80.
- Notice that 80 is still less than 100, so we still need to add another zero, making it 800.
- Note that since the original number is 8, the red line still indicates the location of the decimal point.
- Also, since 80 is still not divisible by 100, the number above that (next to the decimal point) would just be 0.
- Now, we can already divide 800 by 100 which will give us 8.
- Thus, the quotient is .08 or 0.08.

### COMPARING DECIMALS

- In this section, we will discuss how we can compare decimals.
- We know that 17 is greater than 4. But is 0.17 greater than 0.4?
- To have a better grasp of it, we can transform 0.17 and 0.4 into fractions.
- 17/100 and 4/10

- Here, we can use the methods we’ve learned from previous lessons on how to compare fractions.
- But first, we have to have a visual understanding of the two fractions.
- Notice how this is not a good way to compare them. One has 100 boxes while the other one has only 10. The best way to represent them is to change their denominators to be of 100. So both would have 100 boxes.
- Note that if we change the denominator of 4/10, the numerator would also change.
- 17/100 and 40/100

- Now, we can visually represent them.
- As you can see, the grid on the right side has more shaded parts than the grid on the left side. Which means that 40/100 or 4/10 is greater than 17/100.
- Going back to previous lessons, if we already have two fractions of the same denominator, we can just look at their numerator and compare them without using visual aids to represent the fractions. In this case, 40 is greater than 17.
- We can also use the method discussed in the previous lessons, the cross multiplication method.
- Following the rules of the cross multiplication method, we know the right side has a product of 400 while the left side has a product of 170.
- Thus, 4/10 or 0.4 is greater than 17/100 or 0.17 since 400 is greater than 170.
- 17/100 < 4/10

**Decimal Notation for Fractions Worksheets**

This is a fantastic bundle which includes everything you need to know about the decimal notation for fractions across 35 in-depth pages. These are** ready-to-use Decimal Notation for Fractions worksheets that are perfect for teaching students how decimal notation for fractions works and how we can compare decimal fractions. **

### Complete List Of Included Worksheets

- Lesson Plan
- Decimal Notation for Fractions
- 10 to 100
- Add Them
- Convert X
- Shade
- Convert C
- Denominator
- Long Division
- Cross
- SFD
- Problems

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**Use With Any Curriculum**

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