Lesson 10

Numbers

A number is a mathematical object used to count, measure, and label. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, “5” is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits.

Here are some of the different types of numbers:

• Natural numbers: These are the counting numbers, starting from 1.
• Whole numbers: These include natural numbers and 0.
• Integers: These include whole numbers and their opposites, such as -1, -2, -3, etc.
• Rational numbers: These are numbers that can be expressed as a fraction of two integers, such as 1/2, 3/4, 5/6, etc.
• Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers, such as pi (π) and the square root of 2.
• Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Numbers are used in many different ways in our everyday lives. We use them to count things, measure things, and make calculations. We also use them to represent dates, times, and addresses. Numbers are a fundamental part of mathematics, and they are essential for many different fields of study, such as science, engineering, and economics.

1 – one	11 – eleven	21 – twenty-one*	31 – thirty-one
2 – two	12 – twelve	22 – twenty-two	40 – forty
3 – three	13 – thirteen	23 – twenty-three	50 – fifty
4 – four	14 – fourteen	24 – twenty-four	60 – sixty
5 – five	15 – fifteen	25 – twenty-five	70 – seventy
6 – six	16 – sixteen	26 – twenty-six	80 – eighty
7 – seven	17 – seventeen	27 – twenty-seven	90 – ninety
8 – eight	18 – eighteen	28 – twenty-eight	100 – one hundred
9 – nine	19 – nineteen	29 – twenty-nine
10 – ten	20 – twenty	30 – thirty

Write a dash between intervals and units.
Big numbers
1,000 – one thousand
1,000,000 – one million
1,000,000,000 – one billion
1,000,000,000,000 – one trillion
examples
3,072,643,503,948 = three trillion seventy-two billion six hundred forty-three million five hundred
three thousand nine hundred forty-eight

How to describe prices

There are many ways to describe prices in English. Here are some common words and phrases you can use:

• Affordable: This means that the price is within your budget. For example, you might say “This dress is affordable for me” or “Affordable housing is in short supply in this city.”
• Expensive: This means that the price is high. For example, you might say “This car is too expensive for me” or “The cost of living in this city is expensive.”
• Inexpensive: This means that the price is low. For example, you might say “This book is inexpensive” or “I found some inexpensive clothes at the thrift store.”
• Cheap: This means that the price is very low, but it can also have a negative connotation, suggesting that the quality of the product is not good. For example, you might say “I bought this shirt for a cheap price” or “This furniture is cheap, but it’s not very sturdy.”
• Overpriced: This means that the price is too high for the value of the product. For example, you might say “This coffee is overpriced” or “This hotel is overpriced for what it offers.”

You can also use comparative and superlative adjectives to describe prices. For example, you might say “This dress is more expensive than the one I saw yesterday” or “This is the most affordable car I’ve seen in a long time.”

Finally, you can use idioms and expressions to describe prices. For example, you might say “It costs an arm and a leg” to mean that something is very expensive. Or, you might say “It’s a steal” to mean that something is a great deal.

The best way to describe prices is to use the words and phrases that are most natural and appropriate for the situation. Consider the context, your audience, and your purpose when choosing how to describe prices.

Practice

Here is a sample conversation between a customer and a cashier at a grocery store:

Cashier: Hi, welcome to the store! How can I help you today?

Customer: Hi, I’m looking for some milk, eggs, and bread.

Cashier: Sure, I can help you with that. What kind of milk would you like? We have whole milk, skim milk, and almond milk.

Customer: I’ll take the whole milk.

Cashier: And how many eggs would you like? We have a dozen for $2.99 or two dozen for $5.99.

Customer: I’ll take a dozen.

Cashier: And what kind of bread would you like? We have white bread, wheat bread, and sourdough bread.

Customer: I’ll take the white bread.

Cashier: Great! That will be $7.98. Would you like to use cash or credit?

Customer: I’ll use my credit card.

Cashier: Okay, just swipe your card here.

(The customer swipes their credit card.)

Cashier: Thank you. Your total is $7.98. Would you like a receipt?

Customer: Yes, please.

Cashier: Here you go. Have a nice day!

Customer: You too!

This is just a sample conversation, of course. The specific words and phrases that you use will vary depending on the situation and the people involved. But this should give you a good idea of how to have a regular conversation with a cashier.

Here are some additional tips for having a good conversation with a cashier:

• Be polite and friendly.
• Make eye contact and smile.
• Be prepared to answer the cashier’s questions.
• Be patient if the cashier is busy.
• Thank the cashier for their help.
• Leave a positive review if you had a good experience.

By following these tips, you can make your experience at the store more pleasant for everyone involved.

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This That These Those

The words “this”, “that”, “these”, and “those” are demonstrative pronouns. They are used to point to or refer to specific things or ideas. The main difference between the four words is the distance between the speaker and the thing or idea being referred to.

• This is used to refer to something that is near the speaker.
• That is used to refer to something that is farther away from the speaker.
• These is used to refer to two or more things that are near the speaker.
• Those is used to refer to two or more things that are farther away from the speaker.

For example, if you are holding a book in your hand, you would say “this book”. But if you are talking about a book that is on the table, you would say “that book”. If you are pointing to two books that are on the table, you would say “these books”. And if you are pointing to two books that are on the shelf, you would say “those books”.

The words “this” and “that” can also be used to refer to time.

• This is used to refer to the present time.
• That is used to refer to the past or future.

For example, you would say “this is the year 2023”. But you would say “that was the year 2022”.

The words “these” and “those” can also be used to refer to time, but they are less common. For example, you could say “these are the days of our lives” or “those were the days”.

In some cases, the words “this”, “that”, “these”, and “those” can be used interchangeably. For example, you could say “this is my friend” or “that is my friend”. However, in general, it is best to use the word that is most appropriate for the distance between the speaker and the thing or idea being referred to.

Here are some more examples of how to use the words “this”, “that”, “these”, and “those”:

• This is my house.
• That is my car.
• These are my books.
• Those are the books on the shelf.
• This is the year 2023.
• That was the year 2022.
• These are the days of our lives.
• Those were the days.

Here are some more examples:

• This is the pen I was using. (The pen is near the speaker.)
• That is the book I was reading. (The book is farther away from the speaker.)
• These are the flowers I bought. (The flowers are near the speaker.)
• Those are the cars I saw in the parking lot. (The cars are farther away from the speaker.)
• This is the year 2023. (The year is present time.)
• That was the year 2022. (The year is past time.)
• These are the days of our lives. (The phrase refers to the present time.)
• Those were the days. (The phrase refers to the past time.)
• This is a good idea. (The idea is being emphasized.)
• That is a bad idea. (The idea is being contrasted with another idea.)
• These are the parts of the story I was talking about. (The speaker is referring to specific parts of a story.)
• I mentioned those earlier. (The speaker is referring to something that has already been said.)

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Pronunciation of CH and J

The main difference in pronunciation between ch and j is that ch is a voiceless fricative, while j is a voiced fricative. This means that when you pronounce ch, your vocal cords do not vibrate, but when you pronounce j, your vocal cords do vibrate.

Here is a table that summarizes the difference in pronunciation between ch and j:

Sound	Description
ch	Voiceless fricative. The tongue is placed behind the alveolar ridge (the ridge behind the teeth), and the air is forced out creating a hissing sound.
j	Voiced fricative. The tongue is placed behind the alveolar ridge, and the air is forced out creating a hissing sound. However, the vocal cords vibrate, creating a buzzing sound.

Here are some examples of words that are pronounced with the ch sound:

• chip
• cheese
• chat
• chicken
• check

Here are some examples of words that are pronounced with the j sound:

• jump
• juice
• joy
• giant
• jazz

It is important to note that these are just general pronunciation rules. There are many exceptions to these rules, and the pronunciation of ch and j can vary depending on the speaker’s dialect.

For example, in some dialects of English, the ch sound is pronounced as a k sound when it is followed by l or r. For example, the ch in “chlorine” and “Christ” is pronounced as a k sound in some dialects.

In other dialects of English, the j sound is pronounced as a y sound when it is followed by a consonant. For example, the j in “judge” and “juice” is pronounced as a y sound in some dialects.

The pronunciation of the letters ch and j in English depends on the following:

• The position of the letter in the word.
• The letters that surround the letter.

In general, the ch sound is pronounced as a voiceless fricative, which means that the vocal cords do not vibrate when the sound is made. The j sound is pronounced as a voiced fricative, which means that the vocal cords vibrate when the sound is made.

Here are some specific pronunciation rules for ch and j:

• The ch sound is usually pronounced as a voiceless fricative when it is followed by a vowel or a voiced consonant. For example, the ch in “chip” and “church” is pronounced as a voiceless fricative.
• The ch sound is sometimes pronounced as a k sound when it is followed by l or r. For example, the ch in “chlorine” and “Christ” is pronounced as a k sound.
• The j sound is usually pronounced as a voiced fricative when it is followed by a vowel or a voiced consonant. For example, the j in “jump” and “general” is pronounced as a voiced fricative.
• The j sound is sometimes pronounced as a y sound when it is followed by a consonant. For example, the j in “judge” and “juice” is pronounced as a y sound.

It is important to note that these are just general pronunciation rules. There are many exceptions to these rules, and the pronunciation of ch and j can vary depending on the speaker’s dialect.

Here are some additional examples of words that are pronounced with the ch sound:

• cheese
• chat
• chicken
• cheap
• check

Here are some additional examples of words that are pronounced with the j sound:

• jump
• juice
• joy
• giant
• jazz