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Back to Fractions
Grade 4 – 6Topic 14 of 14
Lesson 1.14 · Fractions to Decimals10 mins read

Writing Fractions as Decimals

Why we try to make the denominator 10, 100 or 1000, and how we do it.

Act 1 · Place Values

🏛️ 1. Let's Remember the Place Values

abc.def

In the last lesson we saw that every place is the place on its left divided by 10. Under each place, you can see its value.

a100
b10
c.1
d110
e1100
f11000
÷ 10
÷ 10
÷ 10
÷ 10
÷ 10

After the decimal point there are only these places:

Tenths110
Hundredths1100
Thousandths11000
👍
A decimal can only count pieces of 110, 1100 and 11000. There is no place for pieces of 15 or 14!
Act 2 · The Big Question

🤔 2. Why Do We Make the Denominator 10, 100 or 1000?

25

Let's try to write 25 as a decimal.

15
15
15
15
15

25 is 2 pieces of 15. In which place do we write these pieces?

Tenths110
Hundredths1100
Thousandths11000
Fifths?15

There is no fifths place.

Can we just write the 2 in the tenths place, as 0.2?

What we have: 25

0.2 = 210: much less!

0.2 means 2 pieces of 110, but we have 2 pieces of 15. The pieces are not the same size, so the amounts are not the same.

👍
So first we must rename the pieces: we write the same amount with pieces of 110, 1100 or 11000. That is why we expand the denominator to 10, 100 or 1000. Expanding does not change the amount; it only cuts the pieces into smaller equal pieces.
Act 3 · Tenths

🔟 3. Making the Denominator 10

25
5 × ? = 10
5 × 2 = 10

We can make 5 into 10: multiply by 2.

15
15
15
15
15
Step 1 of 4

This is 25: 2 pieces of 15. There is no place for pieces of 15.

Ones
0
no wholes
.
Tenths
4
4 of 110
12
2 × ? = 10
2 × 5 = 10
110
110
110
110
110
110
110
110
110
110

Each 12 is 5 pieces of 110.

12(×5)=510=0.5
Act 4 · Hundredths

💯 4. Making the Denominator 100

34

Can we make 4 into 10?

4 × ? = 10
4 × 2 = 84 × 3 = 12

8, then 12: we jump over 10. No whole number works.

Then let's try 100:

4 × ? = 100
4 × 25 = 100

We can make 4 into 100: multiply by 25.

14
14
14
14

Cut one 14 into pieces of 1100: 25 pieces fit in it.

To name the pieces, the whole must be cut into equal pieces, so we cut every 14.

Each 14 is 25 pieces of 1100. So 3 pieces of 14 are 3 × 25 = 75 pieces of 1100.

34(×25)=75100=0.75
Ones
0
no wholes
.
Tenths
7
7 of 110
Hundredths
5
5 of 1100
1325
25 × ? = 100
25 × 4 = 100

Each 125 is 4 pieces of 1100. So 13 pieces of 125 are 13 × 4 = 52 pieces of 1100.

1325(×4)=52100=0.52
Act 5 · Thousandths

🔬 5. Making the Denominator 1000

38
8 × ? = 10
8 × 1 = 88 × 2 = 16
8 × ? = 100
8 × 12 = 968 × 13 = 104
8 × ? = 1000
8 × 125 = 1000

We can make 8 into 1000: multiply by 125.

Each 18 is 125 pieces of 11000. So 3 pieces of 18 are 3 × 125 = 375 pieces of 11000.

38(×125)=3751000=0.375
Ones
0
no wholes
.
Tenths
3
3 of 110
Hundredths
7
7 of 1100
Thousandths
5
5 of 11000
Act 6 · Wholes

🧱 6. Mixed Numbers and Improper Fractions

134

The whole part goes in the ones place. The fraction part goes after the decimal point.

34(×25)=75100=0.75
134=1.75
Ones
1
1 whole
.
Tenths
7
7 of 110
Hundredths
5
5 of 1100
74

74 is 7 pieces of 14. 4 pieces of 14 make 1 whole, and 3 pieces of 14 are left:

74=134=1.75

We can also expand it straight away:

74(×25)=175100=1.75

175 pieces of 1100: 100 of them make 1 whole, and 75 pieces of 1100 are left.

Act 7 · Careful

🚧 7. Can Every Fraction Be Written This Way?

13
3 × ? = 10
3 × 3 = 93 × 4 = 12
3 × ? = 100
3 × 33 = 993 × 34 = 102
3 × ? = 1000
3 × 333 = 9993 × 334 = 1002

No whole number works, so we cannot write 13 as a decimal this way. Later, with rational numbers, we will learn another way: dividing.

Tip: simplify first!

6 cannot be made into 10, 100 or 1000. But 36 can be simplified to 12, and 2 can be made into 10:

36=12(×5)=510=0.5
👍
We can write a fraction as a decimal this way only if its denominator can be expanded to 10, 100 or 1000.
Act 8 · Practice

✏️ 8. Practice: Your Turn

Solve each one step by step. Type your answer and press Check.

35 = ?
  1. 1

    Which number turns the denominator 5 into 10?

    5 ×= 10
  2. 2

    Expand: multiply the numerator and the denominator by 2.

  3. 3

    Write it as a decimal.

14 = ?
  1. 1

    4 cannot become 10 (4 × 2 = 8, 4 × 3 = 12). Which number turns 4 into 100?

    4 ×= 100
  2. 2

    Expand: multiply the numerator and the denominator by 25.

  3. 3

    Write it as a decimal.

920 = ?
  1. 1

    Which number turns the denominator 20 into 100?

    20 ×= 100
  2. 2

    Expand: multiply the numerator and the denominator by 5.

  3. 3

    Write it as a decimal.

78 = ?
  1. 1

    8 cannot become 10 or 100. Which number turns 8 into 1000?

    8 ×= 1000
  2. 2

    Expand: multiply the numerator and the denominator by 125.

  3. 3

    Write it as a decimal.

212 = ?
  1. 1

    Look at the fraction part 12 first. Which number turns 2 into 10?

    2 ×= 10
  2. 2

    Expand the fraction part.

  3. 3

    Write the mixed number as a decimal.