Liri was supposed to multiply 340 squares by 100 – and was already reaching for paper and pencil.
Erklärus: “Wait! You can do that in your head, in one second. When multiplying and dividing by 10, 100 or 1000 you only need to count the zeros.”
The quickest calculating trick
✖️ Multiplying by 10, 100, 1000
When you multiply by a power of ten, the number is simply shifted to the left by as many places as the power of ten has zeros.
34 × 10 = 340
34 × 100 = 3400
34 × 1000 = 34000
Erklärus: “34 has no zeros. Times 100 (2 zeros) – so you simply add 2 zeros: 3400.”
Work out: 27 × 100 =
➗ Dividing by 10, 100, 1000
When dividing it is exactly the other way round: the number is shifted to the right by that many places – so cross out the matching number of zeros.
3400 ÷ 100 = 34
Liri: “So just take the zeros away?”
Erklärus: “Almost – only as many as the power of ten itself has. With awkward numbers even the decimal point shifts, but that comes later.”
Work out: 45000 ÷ 1000 =
🌌 Big numbers in the universe
A light-year is about 9.46 trillion km – astronomers constantly work with powers of ten to make such huge numbers manageable.
If a satellite takes 10 times as many photos as planned (e.g. 500 instead of 50), one look at the zeros is enough to see it straight away.
❌ Common mistake
With 34 × 100 some people add only one zero (340) instead of two (3400) – they count the zeros of the power of ten wrongly.
Tip: count the zeros in the power of ten exactly before you add them: 100 has two zeros, so add two!
✖️ Exercise 1
Work out: 56 × 1000
➗ Exercise 2
Work out: 8200 ÷ 10
🔟 Exercise 3
Work out: 12 × 100
A trick you never forget
Liri worked out 340 × 100 in her head, without paper. 34000 squares – that was how far the distance was that she was checking.
Liri: “I don’t have to calculate any more – I only have to count zeros.”
“Times 10/100/1000: add the matching number of zeros. Divided by 10/100/1000: cross out the matching number of zeros.”
What you learned today
34 × 100 = 3400 · 3400 ÷ 100 = 34
Times: add zeros · Divided by: cross out zeros
🌟
Chapter 27 mastered!
Liri can now calculate with 10, 100 and 1000 in a flash – without any paper.
Erklärus’s notebook – page 27:
“Times 10/100/1000: add as many zeros as the power of ten has. Divided by 10/100/1000: cross out the matching number of zeros.”
“Times 10/100/1000: add as many zeros as the power of ten has. Divided by 10/100/1000: cross out the matching number of zeros.”