What is any landmark number multiplied by (that is )? Find the following products— Each landmark number is a power of and so multiplying it with increases the power by , which is the next landmark number.

Understand the Question The symbol represents the number . A landmark number is a power of (such as , , , , etc.). Multiplying any landmark number by increases its power by , which results in the next landmark number (). Part (i) Find the product: Step 1 · Calculate the Product Given that : Answer > (i) Part (ii) Find the product: Step 1 · Calculate the Product The symbol represents , and represents : Answer > (ii) Part (iii) Find the product of the stylized '100' symbol Step 1 · Calculate the Product The stylized symbol represents , and represents : Answer > (iii) Part (iv) Find the product: Step 1 · Calculate the Product The symbol represents , and represents : Answer > (iv) Common Mistakes Symbol Confusion: Misinterpreting the landmark value of the historical symbols instead of reading them as consecutive powers of (). Operation Error: Adding instead of multiplying by . Multiplying by appends a zero (shifts to the next power of ten).

A Story of Numbers | IT

Question 14

What is any landmark number multiplied by $\cap$ (that is $10$ )? Find the following products—

Each landmark number is a power of $10$ and so multiplying it with $10$ increases the power by $1$ , which is the next landmark number.

Solution

Understand the Question

The symbol $\cap$ represents the number $10$ .
A landmark number is a power of $10$ (such as $1$ , $10$ , $100$ , $1000$ , etc.).
Multiplying any landmark number by $10$ increases its power by $1$ , which results in the next landmark number ( $10^n \times 10 = 10^{n+1}$ ).

(i) Find the product: $\cap \times \cap$

Step 1 · Calculate the Product

Given that $\cap = 10$ : Diagram 1

\begin{aligned} \cap \times \cap &= 10 \times 10 \\[0.6em] &= 100 \end{aligned}

Answer

(i) $100$

(ii) Find the product: $\text{១} \times \cap$

Step 1 · Calculate the Product

The symbol $\text{១}$ represents $1$ , and $\cap$ represents $10$ :

\begin{aligned} \text{១} \times \cap &= 1 \times 10 \\[0.6em] &= 10 \end{aligned}

Answer

(ii) $10$

(iii) Find the product of the stylized '100' symbol $\times \cap$

Step 1 · Calculate the Product

The stylized symbol represents $100$ , and $\cap$ represents $10$ :

\begin{aligned} 100 \times \cap &= 100 \times 10 \\[0.6em] &= 1000 \end{aligned}

Answer

(iii) $1000$

(iv) Find the product: $\text{P} \times \cap$

Step 1 · Calculate the Product

The symbol $\text{P}$ represents $1000$ , and $\cap$ represents $10$ :

\begin{aligned} \text{P} \times \cap &= 1000 \times 10 \\[0.6em] &= 10000 \end{aligned}

Answer

(iv) $10000$

Common Mistakes

Symbol Confusion: Misinterpreting the landmark value of the historical symbols instead of reading them as consecutive powers of $10$ ( $1, 10, 100, 1000$ ).
Operation Error: Adding $10$ instead of multiplying by $10$ . Multiplying by $10$ appends a zero (shifts to the next power of ten).

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Q11

Do it yourself now:

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Q13

Instead of grouping together 10 collections of size equal to the previous landmark number (as in the case of the Egyptian system), can we get a number system by grouping together 5 collections of size equal to the previous landmark number? Can this 5 be replaced by any positive integer?

Q14

What is any landmark number multiplied by $\cap$ (that is $10$ )? Find the following products—

Each landmark number is a power of $10$ and so multiplying it with $10$ increases the power by $1$ , which is the next landmark number.

Q15

What is any landmark number multiplied by $?$ ( $10^2$ )? Find the following products—

Q16

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Thus, the product of any two landmark numbers is another landmark number!

Q17

Context: Thus, the product of any two landmark numbers is another landmark number!

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Q18

Now find the following products—

Q19

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Q21

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