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3 Decimals
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Australia
Year 7

3.01 Decimals and place value

Lesson
Worksheet
Practice
Worksheet
Place value
1

Write down the place value represented by the digit 7 in the following numbers:

a
48.07
b
0.487
c
47.008
d
40.708
2

How do you say the following numbers?

a

59.412

b

6.026

3

Write the number 'sixty five and six hundred and eighty nine thousandths' as a decimal.

4

Write the following numbers in decimal form:

a

Four tenths

b

Seventy hundredths

c

Seventy six hundredths

d

Two and three tenths

e

Six and seven hundredths

f

Twelve and twenty-two thousandths

5

Write the following fractions as decimals:

a
\dfrac{7}{10}
b
\dfrac{94}{100}
c
\dfrac{61}{1000}
d
\dfrac{689}{1000}
e
\dfrac{2}{10}
f
\dfrac{9}{100}
g
\dfrac{7}{1000}
h
\dfrac{63}{1000}
6

For each of the following, fill in the boxes with the missing numbers:

a
8.43 = 8 + ⬚ + 0.03
b
29.65 = 20 + 9 + ⬚ + 0.05
c
8.52 = 8 + ⬚
d
31.305 = 30 + 1 + ⬚ + ⬚
Expanded form
7

Convert the following numbers from expanded form to decimal form:

a
2 \times 10 + 5 \times 1 + 7 \times \dfrac{1}{10} + 3 \times \dfrac{1}{100} + 2 \times \dfrac{1}{1000}
b
1 \times 10 + 0 \times 1 + 2 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 1 \times \dfrac{1}{1000}
c
3 \times 100 + 0 \times 10 + 3 \times 1 + 0 \times \dfrac{1}{10} + 1 \times \dfrac{1}{100} + 4 \times \dfrac{1}{1000}
d
4 \times 1 + 0 \times \dfrac{1}{10} + 0 \times \dfrac{1}{100} + 1 \times \dfrac{1}{1000}
8

Consider the number read as " 34 and 695 thousandths":

a

Write the number in expanded form.

b

Write the number in decimal form.

9

Write the following numbers in decimal form:

a
7 + \dfrac{4}{10} + \dfrac{2}{100}
b
75 + \dfrac{8}{10} + \dfrac{2}{100}
c
500 + 2 + \dfrac{8}{10} + \dfrac{3}{1000}
d
12 + \dfrac{2}{100} + \dfrac{3}{10000}
Compare decimals
10

For each of the following, choose the larger decimal number:

a

0.71 or 0.7

b

0.39 or 0.4

c

2.305 or 2.503

d

4.9999 or 4.8

11

Which is the smaller decimal: 0.76 or 0.67?

12

Write the following numbers in ascending order:

a
0.24, 0.204, 2.4, 0.024, 0.0024
b
3.68, 3.86, 3.068, 3.681, 3.1
13

Write the following numbers in descending order:

a
0.54, 0.504, 0.5, 0.054, 0.0054
b
7.28, 7.82, 7.078, 7.168, 7.8
14

For each of the following, insert the symbol \gt or \lt to make the expression true:

a

0.71 \, ⬚ \, 0.7

b

0.39 \, ⬚ \, 0.389

c

2.305 \, ⬚ \, 2.309

d

4.9998 \, ⬚ \, 4.9999

e

0.001 \, ⬚ \, 0.0009

f

2.189 \, ⬚ \, 2.19

g

0.035 \, ⬚ \, 0.0043

h

0.999\,99 \, ⬚ \, 1

Multiply and divide by powers of 10
15

Consider the product 0.973 \times 100.

a

State in which direction the decimal point must be moved to calculate the answer.

b

State the number of places the decimal point must be moved. Explain your answer.

c

Hence calculate the product.

16

Consider the fraction \dfrac{452}{1000}.

a

Write the fraction as a quotient using a '\div' sign.

b

452 is equivalent to 452.0. State in which direction the decimal point in 452.0 must be moved to calculate the answer to part (a).

c

State the number of places the decimal point must be moved. Explain your answer.

d

Hence write the quotient as a decimal number.

17

Evaluate, writing your answer in decimal form:

a
0.7 \times 10
b
0.0098 \times 10
c
0.02 \times 10
d
0.65 \times 10
e
0.093 \times 10
f
0.3784 \times 10
g
5.2 \times 10
h
0.003 \times 10
i
0.35 \times 100
j
9.3 \times 100
k
6.74 \times 100
l
59.43 \times 100
m
0.035 \times 100
n
0.007 \times 100
o
0.4 \times 100
p
0.0046 \times 100
q
0.204 \times 100
r
0.6489 \times 1000
s
0.04 \times 1000
t
5.761 \times 1000
u
0.008 \times 1000
v
0.0043 \times 1000
w
0.408 \times 1000
x
0.934 \times 1000
18

Evaluate, writing your answer in decimal form:

a
0.3 \div 10
b
4.707 \div 10
c
34 \div 10
d
0.57 \div 10
e
0.832 \div 10
f
3.9 \div 10
g
6.75 \div 10
h
7.651 \div 10
i
95.71 \div 10
j
79.66 \div 100
k
8.4 \div 100
l
0.2 \div 100
m
56 \div 100
n
423 \div 1000
o
953.5 \div 100
p
423.3 \div 1000
q
5.6 \div 100
r
0.42 \div 100
s
7583.5 \div 100
t
2.2 \div 1000
u
\dfrac{52}{100}
v
\dfrac{104}{100}
w
\dfrac{203}{1000}
x
\dfrac{2}{100}
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ACMNA156

Round decimals to a specified number of decimal places

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