Ordering Fractions and Decimals on a Number Line worksheet | Live ... - Free Printable

Let’s solve each part step by step.

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Problem 1: Write the decimal number that is equal to each fraction below.

We know:
- To turn a fraction into a decimal, divide the top (numerator) by the bottom (denominator).
- If the denominator is 10 or 100, it’s easy — just write the numerator with the decimal point in the right place.

a) 5/10 → 5 ÷ 10 = 0.5

b) 50/100 → 50 ÷ 100 = 0.50 (or just 0.5, but we’ll keep two decimals for consistency)

c) 75/100 → 75 ÷ 100 = 0.75

d) 1/4 → 1 ÷ 4 = 0.25

e) 1/2 → 1 ÷ 2 = 0.5

f) 3/4 → 3 ÷ 4 = 0.75

g) 10/10 → 10 ÷ 10 = 1.0

✔ All done for Problem 1.

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Problem 2: Write each decimal number in the box where it belongs.

Given decimals:
0.28, 0.06, 0.92, 0.3, 0.8, 0.6, 0.15, 0.71

We need to sort them into categories based on fractions:

First, convert the fractions to decimals so we can compare:

- 1/4 = 0.25
- 1/2 = 0.5
- 3/4 = 0.75

Now categories:

→ less than 1/4 (0.25): numbers < 0.25
→ between 1/4 and 1/2 (0.25 to 0.5): numbers > 0.25 and < 0.5
→ between 1/2 and 3/4 (0.5 to 0.75): numbers > 0.5 and < 0.75
→ greater than 3/4 (0.75): numbers > 0.75

Let’s sort:

- 0.06 → less than 0.25 → ✔ less than 1/4
- 0.15 → less than 0.25 → ✔ less than 1/4
- 0.28 → between 0.25 and 0.5 → ✔ between 1/4 and 1/2
- 0.3 → between 0.25 and 0.5 → ✔ between 1/4 and 1/2
- 0.6 → between 0.5 and 0.75 → ✔ between 1/2 and 3/4
- 0.71 → between 0.5 and 0.75? Wait — 0.71 is less than 0.75? Yes! So still ✔ between 1/2 and 3/4
- 0.8 → greater than 0.75 → ✔ greater than 3/4
- 0.92 → greater than 0.75 → ✔ greater than 3/4

Wait — let’s double-check 0.71:
Is 0.71 > 0.5? Yes.
Is 0.71 < 0.75? Yes → so it goes in “between 1/2 and 3/4”

And 0.8 and 0.92 are both > 0.75 → correct.

So final sorting:

less than 1/4: 0.06, 0.15
between 1/4 and 1/2: 0.28, 0.3
between 1/2 and 3/4: 0.6, 0.71
greater than 3/4: 0.8, 0.92

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Part a: Write the decimal numbers above in order from least to greatest.

List all: 0.28, 0.06, 0.92, 0.3, 0.8, 0.6, 0.15, 0.71

Sort them:

Start smallest:
0.06
then 0.15
then 0.28
then 0.3
then 0.6
then 0.71
then 0.8
then 0.92

✔ Ordered: 0.06, 0.15, 0.28, 0.3, 0.6, 0.71, 0.8, 0.92

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Problem 3: Put the fractions and decimal numbers in the correct places on the number line.

Numbers given:
0.4, 9/10, 0.20, 1/4, 50/100, 3/4

Convert all to decimals for easier placement:

- 0.4 → 0.4
- 9/10 → 0.9
- 0.20 → 0.2
- 1/4 → 0.25
- 50/100 → 0.5
- 3/4 → 0.75

Number line goes from 0 to 1, with tick marks at every 0.1? Let’s see how many ticks there are.

Looking at the image description (since I can’t see the actual image, but based on standard layout), there are 10 intervals between 0 and 1 → so each tick is 0.1.

But wait — the problem says “put in the correct places”, and there are gray boxes under the line. We assume the boxes correspond to positions along the line.

Since we don’t have the exact positions of the boxes, we’ll list the values in order and assign them logically.

Order from least to greatest:

0.20 (0.2)
0.25 (1/4)
0.4
0.5 (50/100)
0.75 (3/4)
0.9 (9/10)

So if the number line has 6 gray boxes, they should be filled in this order from left to right:

Leftmost box: 0.20
Next: 1/4 (0.25)
Next: 0.4
Next: 50/100 (0.5)
Next: 3/4 (0.75)
Rightmost: 9/10 (0.9)

✔ That makes sense.

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Problem 4: Put the fractions, mixed numbers, and decimal numbers in the correct places on the number line.

Numbers given:
2.2, 2/3, 1/3, 3.0, 1 1/2, 4/2, 1.00, 3 4/8

First, simplify and convert all to decimals:

- 2.2 → 2.2
- 2/3 ≈ 0.666... → ~0.67
- 1/3 ≈ 0.333... → ~0.33
- 3.0 → 3.0
- 1 1/2 = 1 + 0.5 = 1.5
- 4/2 = 2.0
- 1.00 → 1.0
- 3 4/8 = 3 + 0.5 = 3.5 (since 4/8 = 1/2)

Now list all values:

0.33 (1/3)
0.67 (2/3)
1.0 (1.00)
1.5 (1 1/2)
2.0 (4/2)
2.2
3.0
3.5 (3 4/8)

Number line goes from 0 to 4, with 8 gray boxes → likely one per value.

Order from least to greatest:

1/3 (~0.33)
2/3 (~0.67)
1.00
1 1/2 (1.5)
4/2 (2.0)
2.2
3.0
3 4/8 (3.5)

So fill the boxes from left to right with these in order.

✔ Done.

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Final Answers:

Problem 1:
a) 0.5
b) 0.50
c) 0.75
d) 0.25
e) 0.5
f) 0.75
g) 1.0

Problem 2:
less than 1/4: 0.06, 0.15
between 1/4 and 1/2: 0.28, 0.3
between 1/2 and 3/4: 0.6, 0.71
greater than 3/4: 0.8, 0.92

Part a: 0.06, 0.15, 0.28, 0.3, 0.6, 0.71, 0.8, 0.92

Problem 3: (in order from left to right on number line)
0.20, 1/4, 0.4, 50/100, 3/4, 9/10

Problem 4: (in order from left to right on number line)
1/3, 2/3, 1.00, 1 1/2, 4/2, 2.2, 3.0, 3 4/8

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Final Answer:
Problem 1: a) 0.5, b) 0.50, c) 0.75, d) 0.25, e) 0.5, f) 0.75, g) 1.0
Problem 2: less than 1/4: 0.06, 0.15; between 1/4 and 1/2: 0.28, 0.3; between 1/2 and 3/4: 0.6, 0.71; greater than 3/4: 0.8, 0.92
Part a: 0.06, 0.15, 0.28, 0.3, 0.6, 0.71, 0.8, 0.92
Problem 3: 0.20, 1/4, 0.4, 50/100, 3/4, 9/10
Problem 4: 1/3, 2/3, 1.00, 1 1/2, 4/2, 2.2, 3.0, 3 4/8