Math · Stage 3
Count total digits used to number pages and how often a digit appears
A book's pages fall into bands — 1-digit (1–9), 2-digit (10–99), 3-digit (100…). Count each band and add, and page-numbering puzzles crack open.
✦ Math📘 Stage 3 · S3⏱ ~10 min🧒 Ages 7–8★ Free to start
I can count the total digits used to number a book's pages, and count how often a chosen digit appears, by working place-value band by band.
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Kavi Numbers the Big Book 📖
Kavi is printing page numbers into a thick book. "If every page took one key-press it would be easy," hoots Kavi, "but page 9 needs 1 digit, page 10 needs 2, and page 100 needs 3! So I sort the pages into bands of the same width, count each band, and add. One tidy plan — and I never lose count."
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What your child will learn
1A page number is made of digitsA digit is one single number-symbol: 0,1,2,…,9. Count the digits in a page number. Build page 10 — it is 1 ten and 0 ones, so it is written with two digits. Every page from 10 to 99 needs two.
2Count each band, then addHere is a 99-page book. Band 1–9 has 9 pages × 1 digit = 9 digits. Band 10–99 has 90 pages × 2 digits = 180 digits. The bars show how much each band costs.
3Add the band totalsOnce each band is counted, the last step is just a sum. For the 99-page book, add the 9 from the first band and the 180 from the second. Tap Step → to add column by column.
4How often does a digit appear?Now count how many times one chosen digit is printed — again band by band, but this time by place. How often is 1 printed in pages 1–20? In the units place: pages 1 and 11 → 2 times. In the tens place: pages 10,11,…,19 → 10 times.
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A peek inside
Kavi numbers a 20-page booklet 📖. How many digits are printed in all?
band 1–9 → 9 pages × 1 = 9 · band 10–20 → 11 pages × 2 = 22 · 9 + 22
Try this at home: A comic has pages 1 to 9. How many digits are printed to number them? __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.