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For every learner 💚
Let's look at this number:
3.14159
Before the dot
This is 3 whole things. Like 3 apples.
1st decimal
This is 1 tenth (1/10).
2nd decimal
This is 4 hundredths (4/100).
3rd, 4th, 5th
TINY pieces!
💰 Money: 3.14159 in any currency doesn't make sense! We round to 3.14
📏 Measurements: "1.456789 metres" is too exact. "1.46 metres" is easier!
🧮 Maths: 2 decimal places is usually enough!
Three important parts of a circle:
1. Radius
Distance from CENTER to EDGE
Example: If radius = 5cm, that's center to edge
2. Diameter
Distance ACROSS the whole circle (through center)
Diameter = Radius × 2
If radius = 5cm, diameter = 10cm
3. Circumference
Distance AROUND the circle (like a fence around it)
Circumference = Diameter × π
If diameter = 10cm, circumference = 10 × 3.14 = 31.4cm
🍕 Pizza Example:
π is a special number:
π (Pi)
3.14159265358979323846...
Goes on FOREVER! Never stops!
What does it do?
🍕 If you have a pizza:
🤯 Why It's Magic:
♾️ It NEVER ENDS:
People have calculated π to TRILLIONS of digits and it's STILL going! That's why it's special.
How computers turn 0s and 1s into sound:
1. Boolean (Computer Language)
0 1 0 1 0 1
Just two states: ON (1) or OFF (0)
2. Add Decimals (Smoother)
0.00 → 0.25 → 0.50 → 0.75 → 1.00
SMOOTH steps! More decimals = smoother!
3. Sine Wave (Sound!)
This smooth wave IS music!
The Magic:
🎵 Music files use MILLIONS of decimals per second
💿 High quality = more decimals = smoother sound
Decimals CREATE the music you hear! 🎶
When rounding to 2 decimal places, look at the 3rd decimal:
If 3rd decimal is 5 or more (5,6,7,8,9): Round UP ⬆️
If 3rd decimal is less than 5 (0,1,2,3,4): Round DOWN ⬇️
Original:
3.456
Look at 3rd decimal: 6
6 is ≥ 5, so round UP
Answer:
3.46
Original:
7.892
Look at 3rd decimal: 2
2 is < 5, so round DOWN
Answer:
7.89
Original:
12.345
Look at 3rd decimal: 5
5 means round UP
Answer:
12.35
Original:
9.123
Look at 3rd decimal: 3
3 is < 5, so round DOWN
Answer:
9.12
Round this to 2 decimal places:
37.9359
Round UP if 3rd digit is:
Round DOWN if 3rd digit is: