Class 5
Numbers
Indian place value system
In the Indian system, large numbers are grouped as follows:
– Ones (1)
– Tens (10)
– Hundreds (100)
– Thousands (1,000)
– Ten Thousands (10,000)
– Lakhs (1,00,000)
– Ten Lakhs (10,00,000)
– Crores (1,00,00,000)
Examples of Counting up to Crores
1. From Ones to Thousands:
– 1 (One)
– 10 (Ten)
– 100 (Hundred)
– 1,000 (Thousand)
– 10,000 (Ten Thousand)
2. From Lakhs to Crores:
– 1,00,000 (One Lakh)
– 10,00,000 (Ten Lakh)
– 1,00,00,000 (One Crore)
Visualizing the Numbers
Let’s look at how these numbers appear with their zeroes and commas:
| Number | Written in figure | Name |
|---|---|---|
|
1 |
1 |
One |
|
10 |
10 |
Ten |
|
100 |
100 |
Hundred |
|
1,000 |
1,000 |
Thousand |
|
10,000 |
Content |
Ten Thousand |
|
1,00,000 |
Content |
One Lakkh |
|
10,00,000 |
Content |
Ten Lakh |
|
1,00,00,000 |
Content |
One Crore |
How to Count Up in Words
To make counting easy:
- Add one to each unit (like “one thousand,” “one lakh,” “one crore”) up to nine, and then move to the next unit.
For example:
- 9,99,999 is read as “nine lakh ninety-nine thousand nine hundred ninety-nine.”
- After that, you reach 10,00,000, which is “ten lakh.”
- Continue this way, until you reach 1,00,00,000 which is “one crore.”
Expanded form and short form
1. Expanded Form
Expanded form of a number means breaking down the number to show the value of each digit. This helps you understand how much each digit contributes to the whole number based on its place value.
For example:
– The number 5,432 in expanded form is:
5,000 + 400 + 30 + 2
Here, each part represents a place:
– 5,000 is the value of the thousands place (5 × 1,000),
– 400 is the value of the hundreds place (4 × 100),
– 30 is the value of the tens place (3 × 10),
– 2 is the value of the ones place (2 × 1).
Steps to Write in Expanded Form
1. Identify each digit and its place value.
2. Multiply each digit by its place value.
3. Write the number as the sum of each place value.
2. Short Form
Short form is just the opposite! It’s the usual way we write numbers by combining all the place values together into a single number.
For example:
– If you are given the expanded form 40,000 + 3,000 + 500 + 60 + 7, the short form is:
43,567
Steps to Write in Short Form
1. Add all the values together, keeping each digit in the correct place.
2. Write them together as a single number.
More Examples:
– If you have 50,000 + 6,000 + 300 + 20 + 8 in expanded form, the short form is:
56,328
– If you have 9,000 + 500 + 40 + 3 in expanded form, the short form is:
9,543
International system of numeration
The International System of Numeration is a way to read and write large numbers that is commonly used worldwide, especially in English-speaking countries. This system uses commas to separate numbers into groups of three, making it easy to read numbers in thousands, millions, and billions.
Place Values in the International System
In the International System, place values are grouped by thousands and then by millions and billions. Commas are placed after every three digits from the right to help us read the number easily.
The main place values are:
– Ones (1)
– Tens (10)
– Hundreds (100)
– Thousands (1,000)
– Ten Thousands (10,000)
– Hundred Thousands (100,000)
– Millions (1,000,000)
– Ten Millions (10,000,000)
– Hundred Millions (100,000,000)
– Billions (1,000,000,000)
Using Commas to Separate Numbers
In the International System, commas separate large numbers into groups of three digits, called periods:
– The first comma is placed after the hundreds place (thousands period),
– The second comma is placed after the hundred thousands place (millions period),
– The third comma is placed after the hundred millions place (billions period).
For example:
– 1,234 is read as “One thousand, two hundred thirty-four.”
– 12,345,678 is read as “Twelve million, three hundred forty-five thousand, six hundred seventy-eight.”
Examples of Numbers in the International System
| Number | Written in words |
|---|---|
|
1000 |
One thousand |
|
10,000 |
Ten thousand |
|
100,000 |
One hundred thousand |
|
1,000,000 |
One million |
|
10,000,000 |
Ten million |
|
100,000,000 |
One hundred million |
|
100,000,000 |
One billion |
Comparing indian and intenational system
Indian System of Numeration
In the Indian system, large numbers are grouped using lakhs and crores after thousands.
The place values go like this:
– Ones, Tens, Hundreds
– Thousands, Ten Thousands
– Lakhs, Ten Lakhs
– Crores, Ten Crores
Example:
– 15,23,456 is read as “Fifteen lakh, twenty-three thousand, four hundred fifty-six.”
International System of Numeration
In the International system, large numbers are grouped using thousands, millions, and billions.
The place values go like this:
– Ones, Tens, Hundreds
– Thousands, Ten Thousands, Hundred Thousands
– Millions, Ten Millions, Hundred Millions
– Billions, Ten Billions, Hundred Billions
Example:
– 1,523,456 is read as “One million, five hundred twenty-three thousand, four hundred fifty-six.”
Commas in Each System
The placement of commas is different in each system, which makes it easier to read large numbers correctly.
Indian System
– Commas are placed after two digits from the right and then every two digits after that.
– Example: 1,23,45,678 (reads as 1 crore, 23 lakhs, 45 thousand, six hundred seventy-eight).
International System
– Commas are placed after every three digits from the right.
– Example: 12,345,678 (reads as twelve million, three hundred forty-five thousand, six hundred seventy-eight).
Comparison Table
| Number | Indian system | International system |
|---|---|---|
|
1000 |
1000 (One thousand) |
1000 (One thousand) |
|
10,000 |
10,000 (Ten thousand) |
10,000 (Ten thousand) |
|
1,00,000 |
1,00,000 (One lakh) |
100,000 (One hundred thousand) |
|
10,00,000 |
10,00,000 (Ten lakh) |
1,000,000 (One million) |
|
1,00,00,000 |
1,00,00,000 (One crore) |
10,000,000 (Ten million) |
|
10,00,00,000 |
10,00,00,000 (Ten crore) |
100,000,000 (One hundred million) |
Example: Writing Numbers in Both Systems
1. Indian System: 75,30,125
– Reads as: “Seventy-five lakh, thirty thousand, one hundred twenty-five.”
International System: 7,530,125
– Reads as: “Seven million, five hundred thirty thousand, one hundred twenty-five.”
Key Differences
1. Place Values:
– Indian system uses lakhs and crores.
– International system uses millions and billions.
2. Commas:
– In the Indian system, commas are used after two digits, then every two digits (e.g., 1,00,00,000).
– In the International system, commas are used every three digits (e.g., 10,000,000).
Predecessor and successor
1. Predecessor for Crore Numbers
The predecessor of a number is found by subtracting 1 from that number, even for large numbers like those in crores.
Examples:
– The predecessor of 1 crore (1,00,00,000) is 99,99,999.
1,00,00,000 – 1 = 99,99,999
– The predecessor of 5 crores (5,00,00,000) is 4,99,99,999.
5,00,00,000 – 1 = 4,99,99,999
– The predecessor of 10 crores (10,00,00,000) is 9,99,99,999.
10,00,00,000 – 1 = 9,99,99,999
So, for any number n, the predecessor is n – 1.
2. Successor for Crore Numbers
The successor of a number is found by adding 1 to that number.
Examples:
– The successor of 1 crore (1,00,00,000) is 1,00,00,001.
1,00,00,000 + 1 = 1,00,00,001
– The successor of 5 crores (5,00,00,000) is 5,00,00,001.
5,00,00,000 + 1 = 5,00,00,001
– The successor of 10 crores (10,00,00,000) is 10,00,00,001.
10,00,00,000 + 1 = 10,00,00,001
So, for any number n, the successor is n + 1.
Comparing and ordering numbers
To help a 5th grader understand comparing and ordering numbers in crores, let’s break it down with a simple guide:
1. Understanding “Crores”
– 1 crore is equal to 10 million or 1,00,00,000 (one followed by seven zeros).
– In the Indian numbering system, the place values go like this: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores.
2. Reading Large Numbers in Crores
– For example:
– 5,00,00,000 is read as 5 crores.
– 12,00,00,000 is read as 12 crores.
– This helps to recognize the size of the numbers quickly.
3. Comparing Numbers in Crores
– Look at the crore place first:
– If two numbers have different values in the crore place, the number with the higher digit in the crore place is larger.
– For example, between 5,00,00,000 (5 crores) and 8,00,00,000 (8 crores), 8 crores is larger.
– If the crore places are the same, check the next highest place value:
– For example, 5,20,00,000 (5 crores and 20 lakhs) is larger than 5,10,00,000 (5 crores and 10 lakhs).
4. Ordering Numbers in Crores
– Ascending Order means arranging from the smallest to the largest.
– Descending Order means arranging from the largest to the smallest.
– Example:
– To arrange 3,00,00,000 (3 crores), 12,00,00,000 (12 crores), and 7,50,00,000 (7.5 crores) in ascending order:
– First, compare the crores: 3 crores < 7.5 crores < 12 crores.
– So, the order is 3,00,00,000, 7,50,00,000, 12,00,00,000.
Rounding of numbers
Rounding numbers in crores might seem challenging at first, but it follows the same basic rounding rules we use with smaller numbers.
1. Understanding Rounding in Crores
– When rounding to the nearest crore, you’re focusing on the crore place.
– If a number is closer to a higher crore, we round up. If it’s closer to a lower crore, we round down.
2. Steps for Rounding to the Nearest Crore
– Step 1: Identify the crore place in the number.
– Step 2: Look at the ten lakh place (the digit immediately to the right of the crore place).
– Step 3:
– If the digit in the ten lakh place is 5 or more, round up.
– If the digit in the ten lakh place is 4 or less, round down.
– Step 4: Change all the digits to the right of the crore place to zeros.
3. Examples of Rounding to the Nearest Crore
– Example 1: Round 3,45,00,000 to the nearest crore.
– The crore place is 3.
– The ten lakh place is 4 (which is less than 5).
– So, we round down to 3,00,00,000.
– Example 2: Round 7,56,00,000 to the nearest crore.
– The crore place is 7.
– The ten lakh place is 5 (which is 5 or more).
– So, we round up to 8,00,00,000.
– Example 3: Round 12,89,00,000 to the nearest crore.
– The crore place is 12.
– The ten lakh place is 8 (which is 5 or more).
– So, we round up to 13,00,00,000.
4. Rounding to the Nearest Ten Crores
– To round to the nearest ten crores, we look at the crore place.
– Example: Round 56,73,00,000 to the nearest ten crores.
– The ten crore place is 5.
– The crore place is 6 (which is 5 or more).
– So, we round up to 60,00,00,000.
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