Decimals - Place Value to a Thousandths and Ordering Decimals

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

Answer:

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

Answer:

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

Answer:

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 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

Answer:

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

Answer:

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?

Answer a)

1.025 km, 1.089 km, 1.35 km, 1.592 km

Answer b)

John (1.025 km)

Answer c)

Mark (1.592 km)