## The Concept of Numbers

Reference: Course on Subject Clearing

## Introduction

This video explains how to read and write numbers up to trillions.

The NUMBERS are like words. They are made up of DIGITS, just like words are made up of letters.

In English, all the words are written with just twenty-six letters, from A to Z. In mathematics, all the numbers are written with just ten digits, from 0 to 9.

A DIGIT IS LIKE A LETTER. A NUMBER IS LIKE A WORD.

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## Place Values

The Rule of Abacus gives us beads of values one, ten, hundred, etc. These values appear in numbers as PLACE VALUES as shown below. This number is made up of 3 hundreds, 9 tens, and 5 ones. It is read as “three hundred ninety-five.”

The place value of “one” may be thought of as a penny (one cent), the place value of “ten” may be thought of as a dime (10 cents), and the place value of “hundred” may be thought of as a dollar (100 cents).

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## Written Numbers

A number written with one digit is called a single-digit number. There are nine single-digit numbers from 1 to 9. 0 (zero) is not a single-digit number because it represents nothing. It is called a place holder.

Example of a single-digit number: 7

A number written with two digits is called a double-digit number. There are ninety double-digit numbers from 10 to 99. You get ninety double-digit numbers by subtracting 9 from 99. You do not subtract 10 because it is included in double-digit numbers.

Example of a double-digit number: 43

A number written with three digits is called a three-digit number. There are nine hundred three-digit numbers from 100 to 999. You get nine hundred three-digit numbers by subtracting 99 from 999. You do not subtract 100 because it is included in three-digit numbers.

Example of a three-digit number: 478

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## Group of Digits

The place values of “one-ten-hundred” make a group. A group contains numbers from 001 to 999. All three places in a group are shown by a digit even if a place has no value.

001 is the same number as 1

The most used groups are ONES, THOUSANDS, MILLIONS, BILLIONS, and TRILLIONS. These groups are arranged from right to left as shown below. The groups are separated by commas.

From right to left, the place values increase by a factor of ten. So, 10 “hundred” become 1 “thousand”; 10 “hundred thousand” become 1 “million”; 10 “hundred million” become 1 “billion”; and 10 “hundred billion” become 1 “trillion”. This pattern continues with higher place values.

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## Reading & Writing Numbers

Here are some examples of reading and writing numbers.

We do not omit any place in a number. When a place has no count, we put “0” there as a place holder. For example, we write the number “302 trillion, 4 billion, 865 million, and Seven” as follows.

In this number the group “billion” has the value “004” (and not just 4). Since the group “thousand” is altogether missing, we put its value as “000”. The group “ones” has the value “007” (and not just 7).

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## Check your Understanding

1. What are digits?

Digits are symbols used to write numbers.

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2. How many digits are there?

There are ten different digits—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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3. How many real elephants are there in the room with you? What digit would you use to represent this number of elephants?

Most likely there is no real elephant in the room with you. You will use the digit ‘0’ in that case to represent the absence of elephants.

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4. Give examples for single-digit, double-digit, three-digit, and five-digit numbers.

7 is a single-digit number
32 is a double-digit number
483 is a three-digit number
63,153 is a five-digit number

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5. How many double-digit numbers are there?

From 10 to 99 (inclusive) there are 90 double-digit numbers.

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6. What are the three place values in a group (from right to left)?

One, ten and hundred

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7. What are the most used groups in a number (from right to left)?

Ones, Thousand, Million, Billion, and Trillion

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8. Write the number “Six billion, sixty-six thousand, sixty.”

6,000,066,060

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## Final Thought

A DIGIT IS LIKE A LETTER. A NUMBER IS LIKE A WORD.