Question 14
What is any landmark number multiplied by (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.
The symbol '∩' represents the number 10. A landmark number is a power of 10.
Step 1 — Understand the symbols and the rule
The question tells us that the symbol '∩' means 10. It also says that each first symbol in the expressions is a "landmark number". A landmark number is a power of 10, like 1, 10, 100, 1000, and so on. The rule is: multiplying a landmark number by 10 gives the next landmark number.
Step 2 — Determine the value of each first symbol
Let's find the value of the first symbol in each expression.
For expression (i), the first symbol is '∩'. We know '∩' is 10.
For expression (ii), the first symbol is '១'. This symbol is the Khmer numeral for 1. So, '១' represents 1.
For expression (iii), the first symbol is a stylized symbol. Following the pattern of landmark numbers (1, 10, ...), this symbol represents 100.
For expression (iv), the first symbol is 'P'. Following the pattern of landmark numbers (1, 10, 100, ...), this symbol represents 1000.
Step 3 — Calculate the products
Now we will calculate each product.
(i) Product of ∩ × ∩ The first symbol is 10. We multiply it by 10.
(ii) Product of ១ × ∩ The first symbol is 1. We multiply it by 10.
(iii) Product of the stylized '100' symbol × ∩ The first symbol is 100. We multiply it by 10.
(iv) Product of 'P' symbol × ∩ The first symbol is 1000. We multiply it by 10.
Answer
(i) 100 (ii) 10 (iii) 1000 (iv) 10000
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Context: A group of indigenous people in Australia called the Gumulgal had the following words for their numbers:
- urapon
- ukasar
- ukasar-urapon
- ukasar-ukasar
- ukasar-ukasar-urapon
- ukasar-ukasar-ukasar
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Context: A group of indigenous people in Australia called the Gumulgal had the following words for their numbers:
- urapon
- ukasar
- ukasar-urapon
- ukasar-ukasar
- ukasar-ukasar-urapon
- ukasar-ukasar-ukasar
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Do it yourself now:
(b) LXXXVII + LXXVIII
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What is any landmark number multiplied by (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.
What is any landmark number multiplied by ()? Find the following products—
Find the following products—
Thus, the product of any two landmark numbers is another landmark number!
Context: Thus, the product of any two landmark numbers is another landmark number!
Q. Does this property hold true in the base-5 system that we created? Does this hold for any number system with a base?
Now find the following products—
What would be a simple rule to multiply a number with ∩?
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