Times 10 and 100

Zeros on the end — but know why

You have known the trick since the second lesson: times ten = add a zero. Today we upgrade it.

Times 10: add one zero. 23 × 10 = 230.

Times 100: add two zeros. 23 × 100 = 2 300.

Why does it work? Remember the floors of a number. When you times by ten, every floor goes up: ones become tens, tens become hundreds. The digits shift one place to the left — and into the freed ones place a zero slides. With times 100 you shift two places, so two zeros.

This opens the big times tables: 30 × 4 looks scary, but it is just 3 × 4 with a zero on top: 120. Split, times with the small tables, put the zeros back.

The next lesson will build written multiplying on this. Today we will handle zeros so thoroughly that they will never confuse you again.

Adam is stacking boxes of crayons into the after-school club store. In one box there are 10 crayons. “How many in seven boxes?” the leader asks. “Seventy,” Adam fires — a seven and a zero. Then a delivery of bigger crates comes: in each 100 crayons. “And in three crates?” Adam hesitates a moment, then remembers: times a hundred = two zeros. “Three hundred!” The leader nods and Adam notices a nice thing: the number 7 or 3 stays, only zeros grow after it according to the size of the box.

Shifting floors and the big times tables

Times 10:

23 × 10: digits 2 and 3 shift one floor up (the two from tens to hundreds, the three from ones to tens), a zero comes to the ones → 230.

Times 100:

23 × 100: a shift of two floors, two zeros → 2 300.

The big times tables — numbers with zeros on the end:

Example 30 × 4:

1. Hide the zeros: from 30, 3 is left (I hold one zero in my hand).
2. Small times tables: 3 × 4 = 12.
3. Put the zeros back: 12 and one zero → 120.

Example 200 × 3:

1. I hide two zeros: 2 is left.
2. 2 × 3 = 6.
3. I put two zeros back: 600.

It works with zeros on both sides too: 20 × 30 → I hide two zeros (one from each number), 2 × 3 = 6, I put both back: 600.

One trap: when the small times tables themselves end in a zero, the zero from the calculation does not count among the ones you put back. 50 × 4: I hide one zero, 5 × 4 = 20, I put one zero back → 200. That zero in 20 was from the times tables, the returned one was added after it.

Times ten and times a hundred

Example: 46 × 10.

One zero on the end: 460.

Floors: 4 tens became 4 hundreds, 6 ones 6 tens.

Example: 46 × 100.

Two zeros: 4 600.

Example: 80 × 10.

Eighty already has one zero, I add another: 800. Zeros add up — each times-ten adds one.

The big times tables: 30 × 4

Example: 30 × 4.

Step 1: I hide the zero: I calculate 3 × 4.

Step 2: 3 × 4 = 12.

Step 3: I put the zero back: 120.

Check by thinking: 30 × 4 means four piles of thirty. 30 + 30 = 60, 60 + 30 = 90, 90 + 30 = 120. It fits — the zero trick only shortens this adding.

The trap with a zero from the times tables

Example: 50 × 6.

Step 1: I hide one zero: I calculate 5 × 6.

Step 2: 5 × 6 = 30. (Watch — thirty has its own zero from the times tables!)

Step 3: I put the hidden zero back: 300.

A common mistake is to write only 30 (“there is a zero there already”). But that one belongs to the times tables. The hidden zero comes back on top. 50 × 6 = 300, check: 50 + 50 + 50 = 150, and once more that much = 300.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Mulai with ten. When it goes well, add more.

Hide the zeros, times with the small tables, put the zeros back.

Practise the questions

On paper

Always write three steps: hidden zeros, small times tables, zeros put back.

1. Work out: 34 × 10, 34 × 100, 90 × 10, 7 × 100.

2. Big times tables in steps: 40 × 6, 300 × 2, 70 × 8, 20 × 50.

3. Crayons: in a box there are 10 crayons, in a crate 100. How many crayons are in 6 boxes and 2 crates together? (First each on its own, then add.)

4. Find the mistake: a friend wrote 60 × 5 = 30. Explain where the zero went, and fix it.

Now you 💪

1. You know why times 10 adds a zero (the floors shift, the ones free a place).
2. You work out 40 × 6 by hiding and putting back the zero: 240.
3. You do not mix up 50 × 6 — you know the result is 300, not 30.

What to take from this lesson

• Times 10 = one extra zero, times 100 = two extra zeros.
• It works because the digits go up a floor and the ones free a place for a zero.
• Big times tables: hide the zeros, calculate with the small tables, put the zeros back.
• A zero from the times tables (5 × 6 = 30) does not count among the returned ones — the returned one goes after it.
• The trick holds only for multiplying, with adding do not add zeros.

© 2026 Ing. Martin Polak / AlgoRhino · Ketentuan penggunaan konten