Place Value of Numbers

Place Value of Numbers

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Place value in mathematics refers to a digit's value based on its position in a number. This value will include unit (or ones), tens, hundreds, thousands, tens of thousands and so on.

Place value forms the foundation of the base 10 numbering system. An understanding on place value helps with number comparison, rounding off and writing numbers in expanded form.

Please read on rounding off numbers here.

 

Below is a breakdown of the place values of numbers for whole numbers.

 

Whole Numbers (Right to Left)

• Ones or Unit: This is the first digit on the far right. For example, the '4' in 1234 is termed '4 ones' or '4 unit' or '4 × 1' or '4'.

• Tens: This is the 2nd digit to the far right. For example, the '3' in 1234 is termed '3 tens' or '3 × 10' or '30'.

• Hundreds: This is the third digit to the far right. For example, the '2' in 1234 is termed '2 hundreds' or '2 × 100' or '200.

• Thousands: This is the fourth digit to the far right. For example, the '1' in 1234 is termed '1 thousands' or '1 × 1000' or '1000'.

 

Below is an illustration of the place value of numbers.

Please read on significant numbers here.

 

 

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Worked Examples on Place Value of Numbers

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Find the place value of the following numbers:

Question 1

• 3 in 243

Solution

• The place value of 3 in 243 is 3 units or 3

 

Question 2

• 6 in 468

Solution

• The place value of 6 in 468 is 6 tens or 60

 

Question 3

• 2  in 8249

Solution

• The place value of 2 in 8249 is 2 hundreds or 200

 

Question 4

• 1 in 1859

Solution

• The place value of 1 in 1859 is 1 thousands or 1,000

 

Question 5

• Find the place value of 4, 5, 0, 6 and 3 in 36054

Solution

• The place value of 4 in 36054 is 4 units or 4

• The place value of 5 in 36054 is 5 tens or 50

• The place value of 0 in 36054 is 0 hundred or 000

• The place value of 6 in 36054 is 6 thousands or 6,000

• The place value of 3 in 36054 is 3 tens of thousands or 30,000

Please read on prime numbers here.

 

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Place Value of Decimals

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Decimal place value refers to the position of digits to the right of the decimal point. The consecutive numbers immediately after the decimal place has the place value of tenths, hundredths, thousandths and so on. This implies that each place value is ten times smaller than the one to its left.

Bolow is a breakdown of the place value of decimal numbers.

 

Decimal Numbers (Left to Right after a Decimal Point)

For decimal numbers, we begin counting the place value right after the decimal point.

• Decimal Point: Separates whole numbers from fractional parts. Please read on how to convert decimals to fractions here.

• Tenths: This is the first digit after the decimal point. For example, the '5' in 1234.5678 is termed '5 tenths' or '5/10' or '0.5'.

• Hundredths: This is the second digit after the decimal point. For example, the '6' in 1234.5678 is termed '6 hundredths' or '6/100' or '0.06'.

• Thousandths: This is the third digit after the decimal point. For example, the '7' in 1234.5678 is termed '7 thousandths' or '7/1000' or '0.007'.

• Ten-Thousandths: This is the fourth digit after the decimal point. For example, the '8' in 1234.5678 is termed '8 ten-thousandths' or '8/10000' or '0.0008'.

Please read more on decimal places here.

 

The image below shows the place value of decimals.

 

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Worked Examples on Place Values of Decimal Numbers

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Find the place value of the following numbers (after the decimal):

Question 1

• 9 in 41.95

Solution 

• The place value of 9 in 41.95 is 9 tenths or 9/10 or 0.9

 

Question 2

• 5 in 2.854

Solution 

• The place value of 5 in 2.854 is 5 hundredths or 5/100 or 0.05

 

Question 7

• 4 in 2.854

Solution

• The place value of 4 in 2.854 is 4 thousandths or 4/1000 or 0.004

Please read on the factors of numbers here.

 

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Values of Numbers

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The value of a number simple refers to the place value of that specific digit or number (in a number). For example, 3 in the number 35 has a value of 3 tens (30), while 4 in the number 435 has a place value of 4 hundreds (400).

In simple terms, a number's value refers to the position or worth of the specific digit in a number.

The place value of a number helps us understand the magnitude and value of that particular number through its position. For example; 1 has a bigger magnitude (or value) than 9 in the number 197. This is true because 1 has a place value of 1 hundreds (100) while 9 has a value of  9 tens (90).

You can read on the number base system here.

 

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Worked Examples on the Values of Numbers

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What is the value of each of the following numbers?

Question 1

• 3 in 2431

Solution 

• The place  value of 3 in 2431 is 3 tens which is equivalent to 30.

 

Question 2

• 9 in 879

Solution

• The place value of 9 in 879 is 9 unit which is equal (or equivalent) to 9.

 

Question 3

• 5 in 56709

Solution

• The place value of 5 in 56709 is 5 tens of thousands with us equal to 50,000.

You can read on the highest common factor here.

 

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Assignment on Place Values of Numbers

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1. What is the place value of each of the following numbers?

• 4 in 6402

• 4 in 2984

• 2 in 6402

• 2 in 2984

• 2 in 10 269

 

2. What is the place value of each of the following decimal numbers?

• 9 in 2.984.

• 8 in 84.02

• 0 in 1.504

• 1 in 169.45

• 9 in 11.009

• 6 in 7.0967

• 0 in 40.326

• 7 in 56.09867

 

3. What is the value of each of the following?

• 2 in 6,402

• 8 in 2,984

• 4 in 6,402

• 3 in 3,984

• 1 in 10,269

• 6 in 698,000

• 5 in 5,896,334

 

4. What is the value of each of the following?

• 8 in 2.984.

• 4 in 84.02

• 5 in 1.504

• 6 in 169.45

• 7 in 71.009

• 0 in 7.0967

• 3 in 40.326

• 7 in 56.09867

Please read on week 2 mathematics for jss1 first term here.

Please read on mathematics scheme of work for jss1 first term here.