Place Value

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Place Value

Place value is all about the value of each digit within a number. Each digit has a different value determined by its position.

Make sure you are happy with the following topics before continuing.

Types of Numbers revision

Place Value: Large Numbers

Going from left to right, the value of each digit decreases.

Note: A quick way to state how much a digit is worth is simply to make all the other digits in the number into zeros. This works the same way for decimal place value, as we are about to see.

Place Value: Decimals

A decimal is any number with a decimal point. They are the numbers that fall between the integers.

Digits after the decimal place also have a value, but this decreases the further you move away (to the right) from the decimal point.

Example 1: Large Number

State the place value of the $6$ in $4,609$ .

[1 mark]

Counting from right to left, we can see that the $6$ is in the third column along – the hundreds column. Therefore, the value of the ‘ $6$ digit’ in this number is $600$ .

Example 2: Decimals

In the number $0.56023$ , what is

a) The value of the $5$ ?

b) The value of the $2$ ?

[2 marks]

a) The $5$ is the first digit after the decimal place, meaning it is in the tenths column. So, it is worth

$dfrac{5}{10}$ or $0.5$

b) The $2$ is the $4$ th digit after the decimal place, meaning it is in the ten thousandths column. So, it is worth

$dfrac{2}{10,000}$ or $0.0002$

Note: In both of these cases, the trick of “making all other digits into zeros” would give us the correct answer.

Place Value Example Questions

Question 1: In the number $1,899$ , what is the value of the $8$ ?

[1 mark]

The $8$ is the $3$ rd digit from the right, meaning it’s in the hundreds column. So, the value is,

$800$ or $text{eight hundred}$

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Question 2: In the number $32.107$ , what is the value of the $1$ ?

[1 mark]

The $1$ is one place after the decimal point, meaning it is in the tenths column. So, the value is,

$dfrac{1}{10}$ or $text{one tenth}$

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Question 3: In the number $0.0461$ , what is the value of the $6$ ?

[1 mark]

The $6$ is three places after the decimal point, meaning it is in the thousandths column. So, the value is

$dfrac{6}{1000}$ or $text{six thousdandths}$

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Question 4: In the number $549,023$ , what is the value of the $5$ ?

[1 mark]

The $5$ is the $6$ th digit from the right, meaning it’s in the hundred thousands column. So, the value is,

$500,000$ or $text{five hundred thousand}$

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Question 5: Becky is thinking of a number. Her number has $3$ thousands, $5$ tens, and $1$ hundredth. What is her number?

[2 marks]

$3$ thousands $= 3,000$

$5$ tens $= 50$

$1$ hundredth $= 0.01$

Adding these all together, we get Becky’s number to be

$3,000+50+0.01=3,050.01$

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Specification Points Covered

Number – 2. apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)