Week 02 — younger son, Grade 4 / Number
Millions, billions — and the ladder that never changes its rule
Big numbers need almost nothing new learnt. A place one step to the left is ten times bigger. That is the whole rule.
They feel hard only because they are long to read. So we cut them up first.
Ten ones make a ten. Ten tens make a hundred. Ten hundreds make a thousand.
You know that much already. Everything after it is the same rule, repeated.
Ten thousands, hundred thousands, and then a million.
Ten millions, hundred millions, and then a billion.
Ten billions, hundred billions, and then a trillion.
1234567890000 — unreadable as it stands. Cut it every three digits.
1 | 234 | 567 | 890 | 000
From the right: ones, thousands, millions, billions, trillions.
It reads one trillion, two hundred thirty-four billion, five hundred sixty-seven million, eight hundred ninety thousand.
English cuts every three digits: thousand, million, billion, trillion. Indonesian does the same: ribu, juta, miliar, triliun.
Japanese cuts every four: 万 (man, ten thousand), 億 (oku, hundred million), 兆 (cho, trillion).
So there is no single English word for 'oku'. We have to say 'a hundred million' — two words for what Japanese says in one.
The commas in 1,234,567 are written every three digits everywhere in the world. But Japanese is *read* in fours, so the commas and the reading breaks do not line up. That is why big numbers are awkward to read in Japanese. It is not you.
| Japanese | Number | English | Bahasa Indonesia |
|---|---|---|---|
| 一万 man | 10,000 | ten thousand | sepuluh ribu |
| 十万 | 100,000 | hundred thousand | seratus ribu |
| 百万 | 1,000,000 | million | juta |
| 一億 oku | 100,000,000 | hundred million | seratus juta |
| 十億 | 1,000,000,000 | billion | miliar |
| 一兆 cho | 1,000,000,000,000 | trillion | triliun |
Read 37200000000.
① Cut every three from the right → 37 | 200 | 000 | 000
② From the right: ones, thousands, millions, billions
③ 37.2 billion — thirty-seven billion, two hundred million
In Japanese the same number is 372 | 0000 | 0000 → 372億, read in one piece.
4.5 billion x 10.
Every digit moves one place to the left → 45 billion
You can also just see one more zero on the end: 4500000000 → 45000000000.
One tenth of 6 billion.
Every digit moves one place right → 600 million
One zero fewer. Exactly the reverse of multiplying by ten.
Which is bigger, 9,800,000 or 100,000,000 ?
Count the digits. 9,800,000 has 7; 100,000,000 has 9.
The second one is bigger.
When the digit counts differ, the longer number wins without looking at the digits at all.
Cut it every three digits from the right.
58 | 000 | 000 → 58 million
In Japanese: 5800 | 0000 → 5800万.
3 | 400 | 000 | 000 → 3.4 billion
In Japanese: 34 | 0000 | 0000 → 34億.
720,000,000
Japanese would call this 7億2000万.
One place to the left → 26 billion (26,000,000,000)
One place to the right → 8 billion
Compare the number of digits.
100,000,000 has 9 digits; 1,000,000 has 7.
Two places apart → 10 x 10 ＝ 100 times
Indonesia is larger.
280 − 120 ＝ 160 million more.
Because both are written in millions, you can subtract the millions directly and put the word back on afterwards.
This asks for a sentence, not a number.
A good answer:
"Japanese gives a new name every four digits, but English gives one every three. The cuts land in different places, so there is no English name that sits exactly on 'oku'. English has to say 'a hundred million' instead."
Knowing this stops you getting lost when you hear big numbers in English.
Niigata prefecture has about 2.1 million people; Tokyo has about 14 million.
Roughly how many times bigger is Tokyo?
14 ÷ 2.1 ＝ 6.6… → about 7 times
Both are written in millions, so you can drop the word 'million' and divide 14 by 2.1. Matching the units first is the same idea as a common denominator.
The bill says 31 yen per kWh.
Use 300 kWh in a month: 31 x 300 ＝ 9,300 yen.
Over a year: 9,300 x 12 ＝ 111,600 yen.
The whole of Japan uses roughly 900 billion kWh a year. The number is too big to picture, but 900 billion ＝ 900,000,000,000 and you can read it by counting the places one at a time.
Suppose levelling up needs 1,250,000 experience points.
① Cut it → 1 | 250 | 000 → 1.25 million
② Shared between 5: 1,250,000 ÷ 5 ＝ 250,000
Dividing big numbers is just the small division with the zeros put back: 125 ÷ 5 ＝ 25, then add the four zeros.
These are not the real exam questions — see the box for why, and the link to the official paper.
What this question is really testing：Whether the meaning of a digit count has landed. Judging by place value rather than by calculating is the thing being tested.
⑴ 42,000 x 100 ＝ 4,200,000 people (4.2 million)
Two more zeros, nothing else.
⑵ Less than 100 million.
⑶ A good reason
"4.2 million has 7 digits; 100 million has 9. Two digits fewer means it must be smaller."
Saying that the digit count settles it *is* the answer. No subtraction is needed.