Exercises: place value chart

How well do you know your place value charts? With these tasks you will practice drawing place value charts and comparing numbers.

1
Explain (e.g., by drawing on a place value chart) why $2.7$ is greater than $2.08$ .
Which number lies exactly in the middle between these two numbers?

For this task you need the following basic knowledge: Place value chart
Enter the number 2.7 in the place value table:
Th
H
T
O
.
t
h
th
0
0
0
2
.
7
0
0
Compare this with the number 2.08 on the place value chart:
Th
H
T
O
.
t
h
th
0
0
0
2
.
0
8
0
The two numbers have the same entry in the ones place, but in the tenths place, for $2.7$ we have a $7$ , and for $2.08$ , we have a $0$ .
Now, $7$ is greater than $0$ , so $2.7$ is greater than $2.08$ .
The difference (i.e., the distance) between the two numbers is $0.62$ . Half the distance is thus $0.31$ . So the exact middle between $2.7$ and $2.08$ , we have the number $2.08 + 0.31 = 2.39$ .
Alternatively, you could also take the arithmetic mean of $2.7$ and $2.08$ and find $\frac{2.7 + 2.08}{2} = \frac{4.78}{2} = 2.39$ as the number in the exact middle
2
Enter the following numbers into a place value chart.
0.75

For this task you need the following basic knowledge: Place value chart
Th
H
T
O
.
t
h
th
0
.
7
5

$12.598$

For this task you need the following basic knowledge: Place value chart
Th
H
T
O
.
t
h
th
1
2
.
5
9
8

0.005

For this task you need the following basic knowledge: Place value chart
Th
H
T
O
.
t
h
th
0
.
0
0
5
3
$1 µm$ is $\frac{1}{1 000 000} m$ , that is, a millionth of a meter. Now, if you write $25 µm$ in $m$ , how many places behind the decimal point do you have to put the digit 2?

For this task you need the following basic knowledge: Decimal numbers
$25 μ m$ $=$ $\frac{25}{1 000 000}$
↓
Shift the decimal point six places to the left.
$=$ $0.000025$
$\Rightarrow$ You have to put the digit 2 five places behind the decimal point, i.e., in the hundred-thousandths positon.

$25 μ m$	$=$	$\frac{25}{1 000 000}$
	↓	Shift the decimal point six places to the left.
	$=$	$0.000025$