Decimals: Tenths, Hundredths and Thousandths
1 Whole
1 =
=
=
Or,
1 whole = 10 tenths
1 whole = 100 hundredths
1 whole = 1000 thousandths
1 tenth = 0.1
1 hundredth = 0.01
1 thousandth = 0.001
| 10 |
| 10 |
| 100 |
| 100 |
| 1000 |
| 1000 |
Or,
1 whole = 10 tenths
1 whole = 100 hundredths
1 whole = 1000 thousandths
1 tenth = 0.1
1 hundredth = 0.01
1 thousandth = 0.001
Understanding Tenths
0.5, 0.7 and 0.2 are decimals or decimal numbers.
Divide 1 whole into 10 equal parts.
In the fraction form, each part has a value equal to
| 1 |
| 10 |
In the decimal form, each part has a value equal to 0.1 (read as zero point one).
Two parts are
or 2 tenths or 0.2.
Two parts are
| 2 |
| 10 |
The dot in a decimal number is called a decimal point.
1. What decimals do the following shaded parts represent?
a)
4 tenths
= 0.4
4 tenths
| 4 |
| 10 |
b)
3 tenths
= 0.3
3 tenths
| 3 |
| 10 |
c)
10 tenths
10 tenths = 1 whole
= 1
10 tenths
10 tenths = 1 whole
= 1
10 tenths make 1 whole.
d)
= 2 +
= 2 + 0.3
= 2.3
| 2 | 3 |
| 10 |
| 3 |
| 10 |
= 2 + 0.3
= 2.3
e)
2 fifths
=
= 0.4
2 fifths
| 2 |
| 5 |
| 4 |
| 10 |
= 0.4
2 fifths = 4 tenths
2. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.
a) 0.3
0.3 =
0.3 =
| 3 |
| 10 |
b) 0.5
0.5 =
=
0.5 =
| 5 |
| 10 |
=
| 1 |
| 2 |
c) 1.6
1.6 =
=
1.6 =
| 1 | 6 |
| 10 |
=
| 1 | 3 |
| 5 |
3. What is the value of each digit in 736.5?
In 736.5,
- the digit 7 is in the hundreds place, its value is 7 × 100 or 700
- the digit 3 is in the tens place, its value is 3 × 10 or 30
- the digit 6 is in the ones place, its value is 6 × 1 or 6
- the digit 5 is in the tenths place, its value is 5 × 0.1 or 0.5
Understanding Hundredths
Divide 1 whole into 100 equal parts.
In the fraction form, each part has a value equal to
or 1 hundredth.
In the decimal form, each part has a value equal to 0.01 (read as zero point zero one).
In the fraction form, each part has a value equal to
| 1 |
| 100 |
In the decimal form, each part has a value equal to 0.01 (read as zero point zero one).
4. What decimals do the following shaded parts represent?
a)
4 hundredths
= 0.04
4 hundredths
| 4 |
| 100 |
b)
10 hundredths
10 hundredths = 1 tenth
= 0.1
10 hundredths = 1 tenth
= 0.1
10 hundredths make 1 tenth.
c)
50 hundredths
= 0.50
Or,
=
= 0.5
The decimals 0.5 and 0.50 have the same value.
50 hundredths
| 50 |
| 100 |
Or,
| 50 |
| 100 |
| 5 |
| 10 |
= 0.5
The decimals 0.5 and 0.50 have the same value.
d)
= 1 +
= 1 + 0.23
= 1.23
| 1 | 23 |
| 100 |
| 23 |
| 100 |
= 1 + 0.23
= 1.23
e)
| 3 | 12 |
| 25 |
| 12 |
| 25 |
= 3 +
| 48 |
| 100 |
= 3 + 0.48
= 3.48
Change the denominator to a multiple of 10.
25 × 4 = 100
25 × 4 = 100
5. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.
a) 0.03
0.03 =
0.03 =
| 3 |
| 100 |
b) 0.5
0.25 =
=
0.25 =
| 25 |
| 100 |
=
| 1 |
| 4 |
c) 1.55
1.55 =
=
1.55 =
| 1 | 55 |
| 100 |
=
| 1 | 11 |
| 20 |
6. What is the value of each digit in 73.65?
In 73.65,
- the digit 7 is in the tens place, its value is 7 × 10 or 70
- the digit 3 is in the ones place, its value is 3 × 1 or 3
- the digit 6 is in the tenths place, its value is 6 × 0.1 or 0.6
- the digit 5 is in the hundredths place, its value is 5 × 0.01 or 0.05
7. What is the value of each digit in 73.65?
A = 2.82
B = 2.95
C = 3.03
8. Do the following.
a) Change $10 and 35 ¢ to dollars.
$10 and 35 ¢ = $10 + $0.35
= $10.35
$10 and 35 ¢ = $10 + $0.35
= $10.35
100 ¢ = $1
1 ¢ =
of $1
= $0.01
1 ¢ =
| 1 |
| 100 |
= $0.01
b) Write 4 m 65 cm in m.
4 m 65 cm = 4 m + 65 cm
= 4.65 m
4 m 65 cm = 4 m + 65 cm
= 4.65 m
100 cm = 1 m
1 cm =
m
= 0.01 m
1 cm =
| 1 |
| 100 |
= 0.01 m
c) Express
litres in decimal.
L = 9 L +
L
= 9 L + 0.03 L
= 9.03 L
| 9 | 3 |
| 100 |
| 9 | 3 |
| 100 |
| 3 |
| 100 |
= 9 L + 0.03 L
= 9.03 L
Understanding Thousandths
Divide 1 whole into 1000 equal parts.
In the fraction form, each part has a value equal to
or 1 thousandth.
In the decimal form, each part has a value equal to 0.001 (read as zero point zero zero one).
In the fraction form, each part has a value equal to
| 1 |
| 1000 |
In the decimal form, each part has a value equal to 0.001 (read as zero point zero zero one).
9. What decimals do the following fractions or mixed numbers represent?
a) 8 thousandths
8 thousandths =
= 0.008
8 thousandths =
| 8 |
| 1000 |
b)
=
+
= 2 + 0.607
= 2.607
| 2607 |
| 1000 |
| 2607 |
| 1000 |
| 2000 |
| 1000 |
| 607 |
| 1000 |
= 2 + 0.607
= 2.607
c)
= 5 +
= 5 + 0.300
= 5.300
Or,
= 5 +
= 5 +
= 5 + 0.3
= 5.3
The decimals 5.300 and 5.3 have the same value.
| 5 | 300 |
| 1000 |
| 5 | 300 |
| 1000 |
| 300 |
| 1000 |
= 5 + 0.300
= 5.300
Or,
| 5 | 300 |
| 1000 |
| 300 |
| 1000 |
= 5 +
| 3 |
| 10 |
= 5 + 0.3
= 5.3
The decimals 5.300 and 5.3 have the same value.
10. What fractions or mixed numbers do the following decimals represent? Express in the simplest form.
a) 0.003
0.003 =
0.003 =
| 3 |
| 1000 |
b) 0.250
0.250 =
=
=
0.250 =
| 250 |
| 1000 |
=
| 25 |
| 100 |
=
| 1 |
| 4 |
c) 1.775
1.775 =
=
1.775 =
| 1 | 775 |
| 1000 |
=
| 1 | 33 |
| 40 |
11. What is the value of each digit in 7.365?
In 7.365,
- the digit 7 is in the ones place, its value is 7 × 1 or 7
- the digit 3 is in the tenths place, its value is 3 × 0.1 or 0.3
- the digit 6 is in the hundredths place, its value is 6 × 0.01 or 0.06
- the digit 5 is in the thousandths place, its value is 5 × 0.001 or 0.005
12. Write a decimal for each letter on the number line below.
A = 2.973
B = 2.988
C = 2.995
D = 3
13. Compare the numbers 3.687, 3.678 and 3.876 and 3.786.
a) Which number is the smallest?
b) Which number is the greatest?
c) Arrange the numbers in increasing order.
d) Arrange the numbers in decreasing order.
a) 3.678 is the smallest number.
b) 3.876 is the greatest number.
c) Increasing order:
3.678, 3.687, 3.786, 3.876
d) Decreasing order:
3.876, 3.786, 3.687, 3.678
b) 3.876 is the greatest number.
c) Increasing order:
3.678, 3.687, 3.786, 3.876
d) Decreasing order:
3.876, 3.786, 3.687, 3.678
Compare the numbers digit by digit starting with the digit in the highest place value.
14. Complete the number patterns below.
a) 3.591, 3.594, ______, 3.6, ______
Rule: Add 0.003 to get the next decimal number.
b) 14.72, 13.62, ______, 11.42, ______, 9.22
Rule: Subtract 1.1 to get the next decimal.