“About” is good enough too

Liri tried to count a cloud of stars from her memory while she thought about the next step on the way home.

Liri: “387… no, 391… I keep miscounting!”
Erklärus: “Then don’t count exactly. Estimate. Sometimes ‘about 400’ is quite enough to know where you are.”

🔍 Estimating sensibly

Before you calculate exactly, it is often worth making an estimate: a rough advance guess of whether the answer will be about right.

Erklärus: “Question: 198 + 203 – about how much? I round both numbers roughly: 200 + 200 = 400. The real answer is very close to that.”
Estimate: 297 + 102 ≈

🎯 The rounding rule

To round to the nearest ten, you look at the ones digit:

0,1,2,3,4 → round down   |   5,6,7,8,9 → round up

60
67
70
⭐

67 is closer to 70 than to 60 – so we round up: 67 ≈ 70.

Round 83 to the nearest ten:
Round 346 to the nearest hundred:

🛍️ Is there enough money?

Liri has a 10-euro note. Three star maps cost, rounded, €3, €4 and €2. Is there enough money?

Erklärus: “Estimate: 3 + 4 + 2 = 9. That is roughly 9 euros – with 10 euros it just about works!”
Yes, roughly €9 is enough with €10
No, that will be too expensive
🌌 Estimating in the universe

Astronomers estimate the number of stars in our galaxy at about 200 billion – nobody has counted them one by one.
Distances in space are also often given rounded, e.g. “the Moon is around 380,000 km away”.
Without estimating and rounding, it would be impossible to work with the unimaginably big numbers of the universe.

❌ Common mistake

With the number 45 many people hesitate: up or down? The rule is clear – the 5 is always rounded up, so 45 → 50.

Tip: only 0,1,2,3,4 round down. The 5 belongs to the “round up” group, even if it lies exactly in the middle!

🎯 Exercise 1 – Rounding
Round 124 to the nearest hundred.
🔍 Exercise 2 – Estimating
Liri counts two star clusters: about 198 and about 301 stars. Estimate the total.
🎯 Exercise 3 – Tens
Round 55 to the nearest ten.

Roughly at home

Liri no longer had to know every single memory exactly. Sometimes “about” was enough to know that she was on the right course.

Liri: “I don’t know exactly whether it’s 387 or 391 squares – but I know it’s about 400. That’s enough to keep my direction.”
Erklärus: “That is exactly what makes rounding so powerful: it quickly gives you a reliable overview, even if you don’t know every detail.”
“Rounding: ones digit 0–4 → round down, 5–9 → round up. Estimating helps to check results roughly in advance, before you calculate exactly.”
What you learned today
67 ≈ 70  ·  346 ≈ 300
0,1,2,3,4 round down · 5,6,7,8,9 round up
🌟

Chapter 15 mastered!

Liri can now estimate and round – even when the exact number isn’t important.

Erklärus’s notebook – page 15:
“Rounding: ones digit 0–4 → round down, 5–9 → round up. Estimating: calculate roughly in advance to check results. On the number line you can see straight away which ten or hundred is closer.”
← Back to overview 15 – Rounding & Estimating