# Decimals - Place Value to a Thousandths and Ordering Decimals

## Decimals: Place Value up to Thousandths

1/10 can be written as 0.1. This is known as Tenth
1/100 can be written as 0.01. This is known as Hundredths
1/1000 can be written as 0.001. This is known as Thousandths
1/10, 1/100, 1/1000 are fractions.

0.1, 0.01, 0.001 are decimals.

#### Practice Question 1

What is the place value of each of the following numbers?
a) 0.089
b) 0.518
c) 9.713
For this question, let us draw a place value chart.
Number Ones Decimal
Point
Tenths Hundredths Thousandths
0.089 0 . 0 8 9
0.518 0 . 5 1 8
9.713 9 . 7 1 3
0.089 0.518 9.713
Ones 0 0 9
Decimal
Point
. . .
Tenths 0 5 7
Hundredths 8 1 1
Thousandths 9 8 3

Look at the last number, 9.713. We can state the place values of all the numbers as:
1. 9 → Ones
2. 7 → Tenths
3. 1 → Hundredths
4. 3 → Thousandths

For the number 0.518, can you tell the place value of 1 from the chart?
If you have said Hundredths, you are correct.

#### Practice Question 2

Let's go a step further.
What is the place value of each of the following numbers?
a) 45.089
b) 192.931
For this question, let us draw a place value chart.
Number Hundreds Tens Ones Decimal
Point
Tenths Hundredths Thousandths
45.089 4 5 . 0 8 9
192.931 1 9 2 . 9 3 1
45.089 192.931
Hundreds 1
Tens 4 9
Ones 5 2
Decimal
Point
. .
Tenths 0 9
Hundredths 8 3
Thousandths 9 1

#### Practice Question 3

What is the place value of the underlined and red digit the following numbers?
a) 20.041
b) 9.21
For this question, let us draw a place value chart.
Number Tens Ones Decimal
Point
Tenths Hundredths Thousandths
20.041 2 0 . 0 4 1
9.21 9 . 2 1

20.041 9.21
Tens 2
Ones 0 9
Decimal
Point
. .
Tenths 0 2
Hundredths 4 1
Thousandths 1
Hence,
The place value of 4 in 20.041 is Hundredths
The place value of 2 in 9.21 is Tenths

## Decimals: Ordering Decimals

Decimals can be order from:
a) Smallest to Largest (Ascending order)
b) Largest to Smallest (Descending order)

#### Practice Question 1 (Ascending order)

Arrange the following numbers in ascending order:
0.049, 0.591, 0.87, 0.348
0.049, 0.348, 0.591, 0.87

#### Practice Question 2 (Descending order)

Arrange the following numbers in descending order:
0.128, 0.069, 0.598, 0.285
0.598, 0.285, 0.128, 0.069

#### Practice Question 3

A group of Grade 5 pupils walked from their homes to the market. Mary walked 1.35 km, John walked 1.025 km, Stacey walked 1.089 km, and Mark walked 1.592 km.
a) Arrange the distances in ascending order.
b) Which student walked the least distance?
c) Which student walked the most distance?
1.025 km, 1.089 km, 1.35 km, 1.592 km

John (1.025 km)

Mark (1.592 km)