Between two whole numbers

Liri found an old note on her map: “Distance: 4.7 light-years.” “That isn’t a whole number any more – what kind of number is 4.7?”

Erklärus: “That is a decimal number. It lies exactly between 4 and 5 – a bit more than 4, but not yet 5. For your journey home you need exactly such precise in-between values.”

🔢 What is a decimal number?

A decimal number is made of two parts, separated by a decimal point: the whole-number part (the whole number) and the decimal part (the fraction).

4 . 7 whole part decimal part
Liri: “So 4.7 is almost like 4 plus a little bit more?”
Erklärus: “Exactly – 4.7 means 4 wholes and 7 tenths on top.”
For 6.3 – what is the whole-number part?

📊 Place values – the steps after the decimal point

Every place after the decimal point is a new step, each ten times smaller than the one before: tenths, hundredths, thousandths.

Ones
Tenths
Hundredths
Thousandths
.

That makes: 4.251

Erklärus: “0.1 is one tenth, 0.01 is one hundredth, 0.001 is one thousandth. Each step is ten times smaller – just as with whole numbers, only in the other direction.”
The steps after the decimal point

1st place: tenths (0.1)
2nd place: hundredths (0.01)
3rd place: thousandths (0.001)

0️⃣ Zeros at the end – they change nothing

Liri: “5.38 and 5.3800 – are those two different numbers?”
Erklärus: “No, exactly the same! Zeros at the end of the decimal part don’t change the value – just as 5 stars are the same amount as 05 stars.”
Key point

5.3800 = 5.38

You may leave out zeros right at the end after the decimal point.

Remove the zeros at the end: 7.2000 = 7.?
🌌 Decimals in the universe

The distance to the nearest star (Proxima Centauri) is about 4.25 light-years.
The Earth takes exactly 365.25 days to go round the Sun – that is why there is a leap day every four years.

❌ Common mistake

4.7 is not bigger than 4.25 just because the 7 looks bigger than the 25! Compare place by place: tenths first (7 against 2) – 4.7 is bigger.

📝 Exercise 1
For 9.64 – which digit is in the hundredths place?
📝 Exercise 2
Remove the zero at the end: 12.50 = 12.?
📝 Exercise 3
Which number is bigger: 3.08 or 3.2? (Answer: 1 = the first, 2 = the second)

Precise numbers for a precise journey

Liri now wrote every distance in with decimal places – no longer just rough whole numbers.

Liri: “4 light-years would have been far too imprecise. With 4.25 light-years I know exactly how far it really is – and how much fuel I need.”
Erklärus: “That is exactly why whole numbers are never enough in the real universe. Anyone who wants to find the way home needs precise in-between values – decimals are your tool for that.”
“Decimal number: whole part.decimal part. Steps after the decimal point: tenths, hundredths, thousandths – each ten times smaller. Zeros at the end don’t change the value.”
What you learned today
4.7 = 4 + 0.7
Whole part + decimal part, separated by the decimal point
🌟

Chapter 33 mastered!

Liri can now read and write precise in-between values.

Erklärus’s notebook – page 33:
“Decimals are numbers between the whole numbers. Every decimal place is a step, ten times smaller than the one before.”
← Back to overview 33 – Decimals