Download CONNECT: Decimals

CONNECT: Decimals
OPERATIONS: + and –
To be able to perform the usual operations (+, –, x and ÷) using decimals, we
need to remember what decimals are. To review this, please refer to
CONNECT:
Fractions – Fractions 4 – FRACTIONS, DECIMALS,
PERCENTAGES – how do they relate?
The digits of a number which are after (to the right of) a decimal point are
called decimal places. Each of those digits represents a value just as those
digits that are before (to the left of) the decimal point do.
millions hundred
ten
thousands hundreds
thousands thousands
tens
units . tenths hundredths thousandths
This is vitally important to remember, especially when adding and subtracting
decimals. We always need to line up the digits of the numbers involved
according to where they are in our decimal system (which uses the columns in
the table above).
So, for example, if we are asked to add the following numbers: 17.4, 5.86,
and 0.107, we must line them up. You can use the decimal point as a
reference for the numbers, so we would get this:
17.4
5.86
0.107
Notice that it is only the last number that has three decimal places, that is, it
has 7 in the thousandths column. In other words, both 17.4 and 5.86 do not
have any thousandths. Another way to say this is that they both have 0
thousandths. 17.4 also has 0 hundredths. So we could also write our
problem like this:
17.400
5.860
0.107
1
Now that we have columns, the addition is just like any other addition, without
a decimal point. We really just ignore the point, but insert it in the answer
under the others. So, my solution would start like this:
17.400
5.860
0.107
.
Now we can add the digits column by column, starting from the right as usual.
So my answer would be
17.400
5.860
0.107
23.367
Putting the 0s in is particularly important with subtraction.
An example: Take 5.98 from 12.1
It is also important to have the order correct – remember we are taking the
bottom number from the top one! So
12.1
–5.98
Again, we need to put in the 0 hundredths in the 12.1, and start the solution
with a decimal point, so:
12.10
–5.98
.
Now, subtract as if the decimal points are invisible.
12.10
–5.98
6.12
2
Two more examples.
1.
Add the following numbers: 589.123, 30.8, 9.04, 0.2
589.123
30.800
9.040
0.200
629.163
2.
Take 5.9 from 16
Where is the decimal point in the 16? As 16 is a whole number, we can put a
point to its right and attach 0s without changing its value. So,
16.0
–5.9
10.1
Now here are some for you to try.
solutions at the end of this resource.
Add these:
You can check your results with the
0.1, 15.23, 7.6;
123.456, 78.9, 0.01
Subtract the smaller from the larger:
15.2, 2.15
3.08, 0.456
If you need help with any of the Maths covered in this resource (or any other Maths
topics), you can make an appointment with Learning Development through
Reception: phone (02) 4221 3977, or Level 3 (top floor), Building 11, or through your
campus.
3
Solutions
0.1, 15.23, 7.6
0.10
15.23
7.60
22.93
15.2, 2.15
15.20
–2.15
13.05
4
123.456, 78.9, 0.01
123.456
78.900
0.010
202.366
3.08, 0.456
3.080
–0.456
2.624