Figure it Out — The Egyptian Number System — A Story of Numbers

1. 13 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 62

   Represent the following numbers in the Egyptian system: 10458, 1023, 2660, 784, 1111, 70707.

   Hint. The Egyptian landmark numbers are the powers of ten — 1, 10, 100, 1000, 10000, … — each with its own symbol, repeated as many times as needed.

   In the Egyptian system each power of 10 has its own symbol, and a number is written by repeating each symbol as many times as that power occurs. So the work is simply to break each number into powers of ten:

   10458 = 10000 + 400 + 50 + 8 → one 10000-symbol, four 100-symbols, five 10-symbols, eight 1-symbols (18 symbols in all)

   1023 = 1000 + 20 + 3 → one 1000-symbol, two 10-symbols, three 1-symbols (Note there are no hundreds at all, so no 100-symbol appears — the Egyptians had no need of a zero here, since a missing power simply means that symbol is absent.)

   2660 = 2000 + 600 + 60 → two 1000-symbols, six 100-symbols, six 10-symbols (No 1-symbols, since the number ends in 0.)

   784 = 700 + 80 + 4 → seven 100-symbols, eight 10-symbols, four 1-symbols

   1111 = 1000 + 100 + 10 + 1 → one each of the 1000-, 100-, 10- and 1-symbols

   70707 = 70000 + 700 + 7 → seven 10000-symbols, seven 100-symbols, seven 1-symbols

   Notice that 10458 needs eighteen symbols where the Hindu numeral needs five. The Egyptian system groups correctly by powers of ten but has no place value, so each power must be spelled out in full.

   ✦ 10458 = 10000 + 400 + 50 + 8; 1023 = 1000 + 20 + 3; 2660 = 2000 + 600 + 60; 784 = 700 + 80 + 4; 1111 = 1000 + 100 + 10 + 1; 70707 = 70000 + 700 + 7 — each power written with its own symbol, repeated that many times.

2. 22 marksGanita Prakash Cl-8 Part 1, Figure it Out, page 62

   What numbers do the two given Egyptian numerals stand for?

   Hint. Count how many times each symbol appears, multiply by the power of ten it stands for, and add.

   To read an Egyptian numeral you count each kind of symbol, multiply by the power of ten it represents, and add the results — the order in which the symbols are drawn does not matter, since each symbol carries its own fixed value.

   (i) The symbols total two hundreds, seven tens and six ones: (2 × 100) + (7 × 10) + (6 × 1) = 200 + 70 + 6 = 276

   (ii) The symbols total four thousands, three hundreds, two tens and two ones: (4 × 1000) + (3 × 100) + (2 × 10) + (2 × 1) = 4000 + 300 + 20 + 2 = 4322

   This is the reverse of the previous question, and it shows the one real convenience of the Egyptian system: because value depends on the symbol and not on where it sits, a numeral can be read in any order and still comes out the same. The price paid for that convenience is the sheer number of symbols required.

   ✦ (i) 276 (ii) 4322

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp103.pdf). This chapter is a history of number *systems* — tally marks, Roman, Egyptian, base-5, Mesopotamian, Mayan, Chinese rod and Hindu numerals — not a chapter on rational numbers. Questions appear as numbered 'Figure it Out' blocks plus 'Math Talk'/'Try This' prompts in the running text; every numeric answer here is checked against the book's own printed answer key at the end of the chapter. Four sub-parts whose questions exist only as printed Egyptian/base-5 glyph images (the addition drills on pages 65 and the products on page 68) are deliberately omitted rather than guessed at, since the operands cannot be recovered from the text.. Questions are referenced from the NCERT textbook for identification.