Test and development
Place Value of Digits in A Number (Up to Hundreds of Millions)
Place value is the value of a digit in a number based on its position or “place” within that number. The rightmost place represents ones, the next place to the left represents tens, then hundreds, thousands, and so on, increasing by factors of ten.
For example, in the number 321:
The “1” is in the ones place.
The “2” is in the tens place.
The “3” is in the hundreds place.
Hundreds of millions
Tens of millions
Millions
Hundreds of thousands
Tens of thousands
Thousands
Hundreds
Tens
Ones
1
2
3
4
5
6
7
8
9
The digit 1 is in the hundreds of millions place.
The digit 2 is in the tens of millions place.
The digit 3 is in the millions place.
The digit 4 is in the hundreds of thousands place.
The digit 5 is in the tens of thousands place.
The digit 6 is in the thousands place.
The digit 7 is in the hundreds place.
The digit 8 is in the tens place.
The digit 9 is in the ones place.
Practice Exercise
In the number 452,989,613, what is the place value of the digit 5?
What is the place value of the digit 8 in the number 78,645,327?
Identify the place value of the digit 2 in the number 620,384,150.
What is the place value of the digit 9 in the number 914,763,856?
In the number 567,892,341, what is the place value of the digit 5?
Total Value of Digits in A Number (Up to Hundreds of Millions)
Total value of digits refers to the sum obtained by adding together all the individual values represented by the digits in a number.
For example, consider the number 987,654,321:
Hundreds of millions
Tens of millions
Millions
Hundreds of thousands
Tens of thousands
Thousands
Hundreds
Tens
Ones
9
8
7
6
5
4
3
2
1
$times 100,000,000$
$times 10,000,000$
$times 1,000,000$
$times 100,000$
$times 10,000$
$times 1,000$
$times 100$
$times 10$
$times 1$
900,000,000
80,000,000
7,000,000
600,000
50,000
4,000
300
20
1
The digit 9 is in the hundreds of millions place representing 900,000,000.
The digit 8 is in the tens of millions place representing 80,000,000.
The digit 7 is in the millions place representing 7,000,000.
The digit 6 is in the hundreds of thousands place representing 600,000.
The digit 5 is in the tens of thousands place representing 50,000.
The digit 4 is in the thousands place representing 4,000.
The digit 3 is in the hundreds place representing 300.
The digit 2 is in the tens place representing 20.
The digit 1 is in the ones place representing 1.
Practice Exercise
In the number 983,465,67, what is the total value of the digit 9?
What is the total value of the digit 3 in the number 300,000,000?
What is the total value of the digit 2 in the number 11,456,204?
What is the total value of the digit 9 in the number 916,763,856?
In the number 167,509,341, what is the total value of the digit 5?
Writing Numbers in Symbols (Up to Hundreds of Millions)
For example:
65,432,109 in symbols is:
The digit 6 is in the tens of millions place representing 60,000,000.
The digit 5 is in the millions place representing 5,000,000.
The digit 4 is in the hundreds of thousands place representing 400,000.
The digit 3 is in the tens of thousands place representing 30,000.
The digit 2 is in the thousands place representing 2,000.
The digit 1 is in the hundreds place representing 100.
The digit 0 is in the tens place representing 0.
The digit 9 is in the ones place representing 9.
Now we’ll combine these place values:
$ 60,000,000 + 5,000,000 + 400,000 + 30,000 + 2,000 + 100 + 0 + 9 = 65,432,109 $
Practice Exercise
Express the number twenty-three million four hundred fifty-six thousand seven hundred eighty-nine in symbols.
What is the symbol representation of the word “thirty-nine million eight hundred seventy-one thousand two hundred fifty-four”?
Write the symbol for the word “ninety-seven thousand eight hundred six.”
What is the symbol for the word “six million two hundred thirty-four thousand five hundred”?
Write the symbol representation of the word “seventy-one million four hundred thirty-two thousand one hundred eleven.”
Writing Numbers in Words (Up to Hundreds of Millions)
For example:
123,456,789 in words is:
To write this number in words we’ll go through each digit’s place value:
The digit 1 is in the hundreds of millions place representing 100,000,000.
The digit 2 is in the tens of millions place representing 20,000,000.
The digit 3 is in the millions place representing 3,000,000.
The digit 4 is in the hundreds of thousands place representing 400,000.
The digit 5 is in the tens of thousands place representing 50,000.
The digit 6 is in the thousands place representing 6,000.
The digit 7 is in the hundreds place representing 700.
The digit 8 is in the tens place representing 80.
The digit 9 is in the ones place representing 9.
Now we’ll convert these place values into words:
Hundreds of millions: “One hundred million”
Tens of millions: “Twenty million”
Millions: “Three million”
Hundreds of thousands: “Four hundred thousand”
Tens of thousands: “Fifty thousand”
Thousands: “Six thousand”
Hundreds: “Seven hundred”
Tens: “Eighty”
Ones: “Nine”
Now we’ll combine these words:
“One hundred and twenty-three million four hundred and fifty-six thousand seven hundred and eighty-nine”
So the number 123,456,789 written in words is “One hundred and twenty-three million four hundred and fifty-six thousand seven hundred and eighty-nine.”
Practice Exercise
Write the number 56,789,123 in words.
Express the numeral 123,456,789 in words.
What is the word representation of the number 987,654,321 in words?
Write the number 234,567,890 in words.
Express the numeral 789,012,345 in words.
Rounding off Numbers (Up to Hundreds of Millions)
Rounding off whole numbers typically involves simplifying them to a specified place value. Here’s a basic criterion for rounding off numbers:
Identify the digit in the place value you are rounding to.
Look at the digit immediately to the right (if any) of the identified digit.
If the digit to the right is 5 or greater, round up by increasing the identified digit by 1.
If the digit to the right is less than 5, round down by keeping the identified digit unchanged.
For example:
Rounding 548 to the nearest ten:The digit in the ten’s place is 4.The digit to the right is 8, which is 5 or greater, so round up.Therefore, 548 rounded to the nearest ten is 550.
Rounding 72 to the nearest ten:The digit in the ten’s place is 7.There’s no digit to the right, so no need to round up or down.Therefore, 72 rounded to the nearest ten remains 70.
Rounding off 984,753,621 to the nearest hundreds of millions:To round this number to the nearest hundreds of millions, we’ll follow these steps:
Identify the digit in the hundreds of millions place, which is the first digit from the left. In our example, this digit is 9.
Look at the next digit, which is in the tens of millions place. In our example, this digit is 8.
Since the digit in the tens of millions place is 5 or greater (8), we round up the digit in the hundreds of millions place (9).
Replace all the digits to the right of the rounded digit with zeros.
So rounding 984,753,621 to the nearest hundreds of millions results in:984,753,621 rounded to the nearest hundreds of millions is 1,000,000,000.
Practice Exercise
Round off 987,654,321 to the nearest hundreds of millions.
Round off 543,210,987 to the nearest hundreds of millions.
Round off 456,789,012 to the nearest hundreds of millions.
Round off 123,456,789 to the nearest hundreds of millions.
Round off 876,543,210 to the nearest hundreds of millions.
Natural Numbers
Even and Odd Numbers
Even Numbers: An even number is any integer (whole number) that is divisible by 2 without leaving a remainder. In other words, when you divide an even number by 2, the result is an integer. Examples of even numbers include 2, 4, 6, 8, 10, and so on.
Odd Numbers: An odd number is any integer (whole number) that is not divisible by 2 without leaving a remainder. In other words, when you divide an odd number by 2, there will be a remainder. Examples of odd numbers include 1, 3, 5, 7, 9, and so on.
Even numbers
Odd numbers
266,424
333
80,008
11,880,401
14,000,000
17
200,457,998
2,577
3,644
395
Practice Exercise
Identify whether the following numbers are even or odd:
24
37
50
63
88
Write down the next three even numbers after 16.
Write down the next three odd numbers after 23.
Find the sum of the first five even numbers.
Find the product of the first four odd numbers.
Determine whether the sum of an even number and an odd number is even or odd.
If you add two even numbers together, what type of number do you get?
If you multiply an even number by an odd number, what type of number do you get?
Find the difference between the largest even number less than 30 and the smallest odd number greater than 20.
Determine whether the following statements are true or false:
The product of two even numbers is always even.
The sum of two odd numbers is always even.
Any number plus itself is always even.
Prime Numbers
A prime number is a number which has only two factors, meaning that it is only divisible by one and itself. Examples of prime numbers are:
2
3
5
7
11
13
17
19
23
29
Practice Exercise
Determine whether the following numbers are prime:
17
21
29
35
41
List all prime numbers between 20 and 40.
Find the prime factorization of the number 72.
What is the smallest prime number greater than 50?
Identify the prime number that is one less than 100.
List all prime numbers between 70 and 90.
Determine whether the number 97 is prime.
Find the sum of the first five prime numbers.
Identify the largest prime factor of the number 84.
Verify whether the statement “The product of two prime numbers is always prime” is true or false.