How_To_Be_Good_At_Math

12 NUMBERS •^ PLACE VALUE

Place value

In our number system, the amount a digit

is worth depends on where it’s placed in a

number. This amount is called its place value.

The 1 is now in

the tens column,

so it has a place

value of 10

The 1 on its

own has

a place

value of 1

1 1 0 1

The 10 ones

are exchanged

for one ten

The 10 tens are

exchanged for

one hundred

What is place value?

Let’s look at the numbers 1, 10, and 100. They are made of the same

digits, 1 and 0, but the digits have different values in each number.

Ones Tens Ones Hundreds Tens Ones

The zero holds the

ones’ place to show

there are no ones.

The 1 now has a place

value of 100

0 0

We can put up to nine dots

in the ones column. When

we get to 10, we exchange the

10 dots in the ones columns for

one in the new tens column.

Let’s start with the number 1.

We’re going to represent it

by making a ones column and

putting a single dot in it.

We can show up to 99

using two columns. When

we reach 100, we exchange

the 10 tens for one hundred.

When the number 5067 is put into columns,

we find that the same digits as in Step 4 now

have different place values. For example, the 5 is

now in the thousands column, so its value has

gone up from 500 to 5000.

Now let’s put numbers in our columns instead

of dots. We can see that 576 is made up of:

5 groups of 100, or 5 × 100, which is 500

7 groups of 10, or 7 × 10, which is 70

6 groups of 1, or 6 × 1, which is 6.

H

0

T

7

O

6

Th

5

H

5

T

7

O

6

Thousands

The amount a digit is

worth in a number

is called its place value.

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