Place Value

Place Value

Place value is all about understanding what each digit in a number really means. It helps you see the difference between numbers like 34 and 304, and it makes tricky things like rounding and decimals much easier to understand. Once you know how place value works, you’ll find it quicker to add, subtract, multiply and divide.

What Is Place Value?

Place value helps your child understand what each digit in a number really means. For example, in the number 527, the 5 means 500, because it sits in the hundreds column.

Whole Numbers

Each digit in a number has a different value depending on its place. The main columns your child needs to know are:

  • Millions
  • Hundreds of thousands
  • Tens of thousands
  • Thousands
  • Hundreds
  • Tens
  • Ones (sometimes called units)

The example above shows what each digit is worth in the number 6, 543, 179. This number can be spoken in words as:

six million, five hundred and forty–three thousand, one hundred and seventy–nine 

 

  • Always start from the right-hand side when placing digits in columns
  • Each place is 10 times bigger than the one to the right
  • Whole numbers have a greater value when they have more digits e.g. 4561 is greater than 984 because it has a thousands digit.
  • To work out the bigger number between whole numbers with the same number of digits, you will need to look at the value of each digit starting from the left e.g. 361 is greater than 298 because the hundreds digit is larger.

Decimals

Your child will also need to understand place value in decimal numbers, especially for the 11+.

Here’s how to explain it:

In the number 3.475:

  • The 3 is in the ones place
  • The 4 is in the tenths place
  • The 7 is in the hundredths place
  • The 5 is in the thousands place

 

Each digit is worth 10 times as much as the digit to the right. For example 2 tenths =20 hundredths

Number Lines

What number is the arrow pointing to on this number line? 

Let’s start by looking at the two numbers at the ends of the number line. It starts at 4.0 and ends at 4.1, so we know the arrow must be pointing to a number between those two.

Now count how many spaces the number line is divided into. There are 10 equal parts between 4.0 and 4.1. That means each step is worth 0.01 – these are called hundredths.

Next, count how many steps the arrow is from 4.0. If the arrow is pointing to the third mark, then we just do:

4.0 + 0.03 = 4.03

So, the arrow is pointing to 4.03.

Example 

Ella, Noah, Grace, Ben and Ava all raced one lap around the track. They recorded their times in seconds:

Who drove the quickest?

  1. To find out who was the quickest, we need to look for the shortest time, in other words, the smallest number in the table.

Let’s first look at the tens and units.

  • Noah and Ben have times starting with 49, which is bigger than 48, so we can rule them out.

That leaves Ella, Grace and Ava, who all have times starting with 48.

  1. Now look at the tenths in their times:

  • Ella has 9 tenths (48.9)

  • Grace has 7 tenths (48.7)

  • Ava has 8 tenths (48.8)

Grace has the smallest number of tenths, so her time is the shortest.

Grace was the quickest.

Place Value Example Questions

Question 1: Which of these is the largest number?

6.259     6.314     6.248     6.381     6.298

[1 mark]

Look at the whole number part (the number before the decimal point).

All of the numbers start with 6, so we can’t decide yet, they are all in the 6s.

Now look at the tenths digit (the first number after the decimal point):

6.259 6.314 6.248 6.381 6.298

The tenths digits are:
2, 3, 2, 3, 2

So we can now rule out the numbers starting with 2 tenths, because 3 tenths is bigger.

That leaves us with:
6.314 and 6.381

Next, compare the hundredths digit (the second digit after the decimal):

6.314 6.381

Now we compare 1 and 8. Since 8 is greater, we know:

6.381 is the largest number.

Question 2: What is the value of 6 in 46521?

[1 mark]

The 6 is 4th digit from the right, meaning it’s in the thousands column.

Therefore, the value is

6000 or six thousand

Question 3: What is the value of 3 in 21.638?

[1 mark]

The 3 is the second digit from the right of the decimal point, meaning it is in the hundredths column.

Therefore, the value is

0.03 or three hundredths