Private: Selective School Placement Test Preparation Book

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2. Place Value

Private: Selective School Placement Test Preparation Book Basic Concepts Of Numbers 2. Place Value

1. What is Place Value?

Place value refers to the value of a digit based on its position in a number. In a number, the value of each digit depends on its position from right to left. The places follow a pattern based on powers of 10.

Place Value Chart (For a large number like 1,234,567):

PlaceValueExample in 1,234,567
Millions$latex 10^{6} $ (1,000,000)1,000,000
Hundred Thousands$latex 10^{5} $ (100,000)200,000
Ten Thousands$latex 10^{4} $ (10,000)30,000
Thousands$latex 10^{3} $ (1,000)4,000
Hundreds$latex 10^{2} $(100)500
Tens$latex 10^{1} $ (10)60
Ones (Units)$latex 10^{0} $ (1)7

2. How to Read and Write Numbers Using Place Value

When reading large numbers, divide them into groups of three digits, called periods. Each period is read separately.

Example 1:

Number: 56,321
How to read it: Fifty-six thousand, three hundred twenty-one.

Example 2:

Number: 2,103,567
How to read it: Two million, one hundred three thousand, five hundred sixty-seven.

Activity:

Write these numbers in words:

  1. 450,789
  2. 3,067,251
  3. 72,408

3. Identifying Place Value of a Digit

To find the place value of a digit, locate its position in the number.

Example 1:

In the number 6,372:

  • The place value of 6 is 6,000 (thousands place).
  • The place value of 3 is 300 (hundreds place).
  • The place value of 7 is 70 (tens place).
  • The place value of 2 is 2 (ones place).

Example 2:

In the number 97,624:

  • The place value of 9 is 90,000 (ten-thousands place).
  • The place value of 7 is 7,000 (thousands place).

Activity:

Find the place value of the underlined digit:

  1. 12,567
  2. 64,823
  3. 715,239

4. Expanded Form of Numbers

The expanded form breaks down a number based on the place value of each digit.

Example 1:

Number: 5,432
Expanded form:
5,432=5,000+400+30+25,432 = 5,000 + 400 + 30 + 25,432=5,000+400+30+2

Example 2:

Number: 68,259
Expanded form:
68,259=60,000+8,000+200+50+968,259 = 60,000 + 8,000 + 200 + 50 + 968,259=60,000+8,000+200+50+9

Activity:

Write the expanded form of these numbers:

  1. 9,326
  2. 24,501
  3. 103,457

5. Comparing Numbers Using Place Value

To compare two numbers, start by looking at the digit in the highest place value. The larger digit in the highest place indicates the larger number. If the digits are the same, compare the next place value.

Example 1:

Compare 45,327 and 46,298:

  • The digits in the ten-thousands place are the same (4).
  • In the thousands place, 6 > 5, so 46,298 > 45,327.

Example 2:

Compare 78,230 and 78,129:

  • The digits in the ten-thousands and thousands places are the same.
  • In the hundreds place, 2 > 1, so 78,230 > 78,129.

Activity:

Compare the following numbers:

  1. 93,451 and 94,510
  2. 58,607 and 58,706
  3. 7,923 and 7,932

6. Rounding Numbers Using Place Value

When rounding numbers, use the digit to the right of the place value you are rounding to:

  • If the digit is 5 or more, round up.
  • If the digit is less than 5, round down.

Example 1: Rounding to the nearest ten

Number: 562

  • The digit in the tens place is 6.
  • The next digit is 2 (which is less than 5), so we round down.
    Rounded number: 560

Example 2: Rounding to the nearest thousand

Number: 3,462

  • The digit in the thousands place is 3.
  • The next digit is 4 (which is less than 5), so we round down.
    Rounded number: 3,000

Activity:

Round the following numbers:

  1. 7,532 to the nearest hundred.
  2. 25,781 to the nearest thousand.
  3. 123,487 to the nearest ten thousand.

7. More Questions

7.1: Large Number Identification

Question:
The population of a city is 456,782. Write the population in words.
Solution:
Four hundred fifty-six thousand, seven hundred eighty-two.

7.2: Place Value Understanding

Question:
In the number 92,467, what is the value of the digit 9?
Solution:
The value of the digit 9 is 90,000 because it is in the ten-thousands place.

7.3: Expanded Form

Question:
Write 73,561 in expanded form.
Solution:
73,561=70,000+3,000+500+60+173,561 = 70,000 + 3,000 + 500 + 60 + 173,561=70,000+3,000+500+60+1

7.4: Comparing Numbers

Question:
Which is greater, 67,284 or 68,173?
Solution:
Compare the ten-thousands place:

  • 6 = 6
  • In the thousands place, 8 > 7. Therefore, 68,173 > 67,284.

7.5: Rounding Numbers

Question:
Round 74,592 to the nearest hundred.
Solution:

  • The digit in the hundreds place is 5.
  • The next digit is 9, so we round up.
    Rounded number: 74,600

8. Practice Problems

  1. Write 89,321 in words.
  2. Find the place value of 6 in the number 164,903.
  3. Compare 45,892 and 45,918. Which is larger?
  4. Write the expanded form of 29,457.
  5. Round 53,789 to the nearest thousand.

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