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A Peek Beyond the Point
Page 2


A Peek Beyond the Point
The Need for Smaller Units
Sonu's Problem
Sonu watched his 
mother try to fix his 
favorite toy car with 
a small screw that 
wasn't the right size.
The Solution
His mother found 
another screw that 
worked perfectly, 
though it looked 
almost exactly the 
same.
The Discovery
Looking closely, Sonu realized one screw was 
just a tiny bit longer than the other.
Page 3


A Peek Beyond the Point
The Need for Smaller Units
Sonu's Problem
Sonu watched his 
mother try to fix his 
favorite toy car with 
a small screw that 
wasn't the right size.
The Solution
His mother found 
another screw that 
worked perfectly, 
though it looked 
almost exactly the 
same.
The Discovery
Looking closely, Sonu realized one screw was 
just a tiny bit longer than the other.
Measuring with Greater 
Precision
Top Ruler
Only has 
markings for 
whole 
centimeters. 
Both screws 
measure 
between 2-3 
cm.
Middle Ruler
Divides each 
centimeter 
into 10 equal 
parts. First 
screw 
measures 2.7 
cm.
Bottom Ruler
Even more 
detailed 
divisions for 
more precise 
measuremen
ts.
Page 4


A Peek Beyond the Point
The Need for Smaller Units
Sonu's Problem
Sonu watched his 
mother try to fix his 
favorite toy car with 
a small screw that 
wasn't the right size.
The Solution
His mother found 
another screw that 
worked perfectly, 
though it looked 
almost exactly the 
same.
The Discovery
Looking closely, Sonu realized one screw was 
just a tiny bit longer than the other.
Measuring with Greater 
Precision
Top Ruler
Only has 
markings for 
whole 
centimeters. 
Both screws 
measure 
between 2-3 
cm.
Middle Ruler
Divides each 
centimeter 
into 10 equal 
parts. First 
screw 
measures 2.7 
cm.
Bottom Ruler
Even more 
detailed 
divisions for 
more precise 
measuremen
ts.
A Tenth Part
Measuring 
Between Units
The pencil isn't 
exactly 3 or 4 
units long. It's 3.4 
units.
Breaking It Down
3.4 means 3 
whole units plus 4 
tenths (4 × 1/10).
Different Expressions
We can write this as 3.4, 3 4/10, or 34/10 units.
Page 5


A Peek Beyond the Point
The Need for Smaller Units
Sonu's Problem
Sonu watched his 
mother try to fix his 
favorite toy car with 
a small screw that 
wasn't the right size.
The Solution
His mother found 
another screw that 
worked perfectly, 
though it looked 
almost exactly the 
same.
The Discovery
Looking closely, Sonu realized one screw was 
just a tiny bit longer than the other.
Measuring with Greater 
Precision
Top Ruler
Only has 
markings for 
whole 
centimeters. 
Both screws 
measure 
between 2-3 
cm.
Middle Ruler
Divides each 
centimeter 
into 10 equal 
parts. First 
screw 
measures 2.7 
cm.
Bottom Ruler
Even more 
detailed 
divisions for 
more precise 
measuremen
ts.
A Tenth Part
Measuring 
Between Units
The pencil isn't 
exactly 3 or 4 
units long. It's 3.4 
units.
Breaking It Down
3.4 means 3 
whole units plus 4 
tenths (4 × 1/10).
Different Expressions
We can write this as 3.4, 3 4/10, or 34/10 units.
Solved Example: Measuring Sonu's Arm
The Problem
Lower arm: 2.7 units. Upper arm: 3.6 units. What's the total length?
Method 1
Add whole units: 2+3=5. Add tenths: 7+6=13 tenths (1.3). Total: 6.3 units.
The Answer
Sonu's complete arm measures 6.3 units long.
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