DECIMALS
When a number is in decimal form it consists of whole numbers and a
fraction part (parts of that number).
The fraction part is to the right of the decimal point. If this is zero, it means
that there is no fraction part.
7 = 7.0 = 7.00 = 7.000 = 7.000
13 = 13.0 = 13.00 = 13.000 , and so on.
The zeroAFTER a decimal point can be knocked off, as long as there are NO
NON-ZERO NUMBERS after the zero.
Examples1.5700 = 1.57 - these 0s can go since there’s nothing after them.
The 0 in 1.206 CAN NOT be removed, because there is a 6 after the 0.
4.00230 = 4.0023 - There is a 2 and 3 after the first 0s, so those 0s stay.
Q1. Put these decimal numbers into the correct order, from the lowest to
the highest value.
7.6, 8.1, 6.9, 7.3, 7.9
• Look at the whole numbers first:
- There is one decimal that begins with 6 so this will be the lowest
value decimal 6.9
- There are three decimals begining with a 7 ( 7.6, 7.3 and 7.9). As
there are several decimals begining with a 7 you then need to look
at the fraction part and put them into order from low to high. This
will give you an order of 7.3, 7.6, 7.9.
- The final decimal in the list begins with an 8 and is therefore the
highest decimal, 8.1.
• The answer to this question is therefore:
• 6.9, 7.3, 7.6, 7.9, 8.1
HOW TO DIVIDE AND MULTIPLY DECIMALS BY 10, 100 OR
1000.
• When multiplying decimal numbers the decimal point should be
moved to the right to make the number bigger.
• When dividing decimal numbers the decimal point should be moved to
the left to make the number smaller.
• You should move the decimal points as many times as there are zeros
in the number you are multiplying by.
- So
by 10 – move once
By 100 – move twice
By 1000 – move three times
Q1. Show how to divide and multiply the decimal 24.31
• Move the decimal point to
the left
• Move the decimal point to
the right
DECIMAL
24.31
÷ 10
2.431
÷ 100
.2431
÷ 1000
.02431
DECIMAL
24.31
× 𝟏𝟏𝟏𝟏
243.1
× 𝟏𝟏𝟏𝟏𝟏𝟏
2431.00
× 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
24310.00
MULTIPLYING WITH DECIMALS
Decimals are best treated as whole numbers when multiplying. We keep
count of how many digits the decimal point(s) is in front of, then put the
decimal back in at the end when we have our answer.
Q1. What is 6 x 1.8?
Here there is only one decimal – 6 does not have a decimal.
The decimal point is in front of ONE DIGIT – the 8.
Now, imagine any decimal numbers are WHOLE NUMBERS. 1.8 becomes 18.
The question is transformed by doing this: 6 x 1.8 6 x 18
We now do 6 x 18 in the usual way:
Now, we PUT THE DECIMAL POINT BACK IN.
There was one decimal point which was in front of one digit, so in our final
answer, we need to put the decimal back in front of one digit:
So 6 x 1.8 = 10.8
Q2. What is 11 x 0.0015?
Again there is only one decimal, but this time it is in front of FOUR DIGITS –
0015
Again, we imagine any decimal numbers are whole numbers.
0.0015 becomes 15.
11 stays the same – it is already a whole number.
11 x 0.0015 11 x 15
Now we do 11 x 15 in the usual way:
Now, we PUT THE DECIMAL POINT BACK IN.
There was one decimal point which was in front of fourdigits, so in our final
answer, we need to put the decimal back in front of fourdigits.
The decimal “jumps over” the 5, the 6, the 1, thenJUMPS OVER NOTHING for
the fourth digit. “Nothing” in maths is written as 0.
So, the answer to 11 x 0.0015 is 0.0165
Q3. What is 0.16 x 10.5?
Here we have two decimal numbers.
One decimal is in front of TWO DIGITS (The 1 and 6 in 0.16)
One decimal is in front of ONE DIGIT (The 5 in 10.5 )
IN TOTAL, THIS IS 2 + 1 = 3 DIGITS.
Now we think of the numbers as whole numbers, without any decimals.
0.16 x 10.5 16 x 105
Again, we now do 16 x 105 in the usual way:
The decimal points were in front of a total of three digits,so in
our final answer, we need to put the decimal back in front of threedigits.
So the answer to 0.16 x 10.5 is 1.680
Because the last digit is a 0 and it comes after the decimal, we can knock it
off if we want to.
The answer is 1.680 , or if we like, 1.68
FRACTIONS TO DECIMALS, AND DIVIDING WITH DECIMALS
The best bet is to remember that fractions and divisions are closely linked.
𝟏𝟏
Q1. What is 𝟒𝟒 as a decimal?
𝟏𝟏
The first thing to remember is that means 1 split into 4; it means 1 ÷ 4.
𝟒𝟒
If the question was something like 4 ÷ 2 it would be much easier!
With 1 ÷ 4, though, there will be remainders.
We solve this by adding extra 0s to the number we are dividing:
1 = 1.0 = 1.00 = 1.000 = 1.0000 and so on. Just as many 0s as we need!
We then carry out the division, being sure to LINE UP THE DECIMAL POINTS:
𝟏𝟏
So (which is the same as 1 ÷ 4) = 0.25 as a decimal.
𝟒𝟒
Q2. What is 4.2 ÷ 0.08 ?
𝟔𝟔
Remember that things like 6 ÷ 2is the same as𝟐𝟐 (six halves, which is three.)
So 4.2 ÷ 0.08 can be written as
𝟒𝟒.𝟐𝟐
𝟎𝟎.𝟎𝟎𝟎𝟎
.
Now, we can use equivalent fractions to get rid of awkward decimals.
Multiplying by 10, 100, 1 000 and so on is an easy way to get rid of decimals.
This tells us that 4.2 ÷ 0.08 is the same thing as 420 ÷ 8.
We can now do this division in the usual way. The bottom number goes on
the outside:
So 4.2 ÷ 0.08 = 52.5 as a decimal.
Q3. What is 8 ÷ 0.25 ?
𝟖𝟖
Similar to before, we can write 8 ÷ 0.25as 𝟎𝟎.𝟐𝟐𝟐𝟐, then use the rules of
equivalent fractions to change it into a “nicer” fraction:
So 8 ÷ 0.25 is the same as 32 ÷ 1 , which is 32.
It is much easier to divide by a whole number than a decimal.
So, as a general rule:
WHEN DIVIDING BY A DECIMAL, REWRITE THE DIVISION QUESTION AS A
FRACTION, AND CHANGE THE FRACTION INTO A FRACTION WITH WHOLE
NUMBERS
Q4. What is two thirds as a decimal?
𝟐𝟐
Two thirds written as a fraction is 𝟑𝟑 . This means 2 ÷ 3.
Again, we can write 2 as 2.0000 ... if we need.
This would go on forever!
𝟐𝟐
𝟑𝟑
= 0.6666666...
We can ROUND our answer to make a reasonable approximation.
𝟐𝟐
𝟑𝟑
= 0.67 to the nearest hundredth.
We round the 6 hundredths up to 7 hundredths, because the number to the
right of it was 5 or bigger.
𝟒𝟒
Q5. Find 𝟓𝟓 of 27.
𝟏𝟏
The best start would be to find 𝟓𝟓 of 27, which is the same as 27 ÷ 5:
𝟏𝟏
So 𝟓𝟓 of 27 = 5.4
𝟒𝟒
But we want 𝟓𝟓ths which is four times as much, so we need to multiply by 4:
5.4 x 4  54 x 4
(Remember from before, first take the decimal point out, then replace it):
There was only one decimal point which was in front of 1 number (the 4).
We now put the decimal point back in front of one number:
𝟒𝟒
So 𝟓𝟓 of 27 =21.6