1. DECIMALS Place Value Ordering Decimals Nearest and significant figures
Money
Adding and Subtracting
Multiplying and dividing by 10,100,1000 etc
Multiplying
Dividing

2. Place Value
Similar to whole numbers the position of the digit indicates how big it is.
If it is in the first column after the decimal it is in the ‘tenths’ column

3. Place Value 0.053 The 5 here means 5 hundredths
The 3 here means 3 thousandths
32.4
The 4 here means 4 tenths

4. Ordering Decimals
Comparing decimal numbers requires looking at the place value of the digits.
Firstly compare the whole number part.
If the whole number part is the same the decimal part must be investigated.
Which is bigger or ?
The whole number parts are both 125 so we must check decimal part.

5. Ordering Decimals
Look at the ‘tenths’ column. Whichever number has the higher digit that is the bigger number.
If they are the same move on to the ‘hundredth’ column
Continue until the order is sorted.
Which is bigger or ?
They both have 3 in the tenths column.
In the hundredths column we have 6 and 7.
This means is bigger even though is longer

6. Nearest Decimal Place Sometimes a decimal number is too long
We need to chop it off after a certain number of places
Lets look at
If we want only 2 numbers after the decimal point we have two choices
The number is either or
Which one?
We must look at the next number
7 is closer to10 than 0
We round up and choose
If the number is 5 or more round up
If it is 4 or less round down

7. Significant figures Significant figures is similar to nearest place
Except we are only interested in the first few digits and the rest we round to zeroes
E.g. When talking about populations we are only interested in millions
What is to 2 significant figures
We are only looking at the first two digits and rounding the rest to zeroes or
The third number is 5 so we round up
Answer is

8. Money Money is represented by numbers to two decimal places
If writing out in pounds DO NOT put in the p sign
Two pounds fifty pence is written £2.50 not £2.50p
When dividing money among people the answer should be rounded up to two decimal places to make sure the money is covered.

9. Adding and subtracting
Adding and subtracting is the same as whole numbers
Just line up the decimal points.

10. Multiplying by 10,100, etc
Multiplying by 10 move the decimal point one place to the right.
Multiplying by 100 move the decimal two places to the left.
Move the decimal as many places to the left as there are zeroes
4.15 x 10 = 41.5
4.15 x 100 = 415
4.15 x 1000 = 4150

11. Dividing by 10, 100,etc
Dividing by 10 move the decimal point one place to the left
Dividing by 100 move the decimal two places to the right
Move the decimal as many places to the right as there are zeroes
4.15 / 10 = 0.415
4.15 / 100 =
4.15 / 1000 =

12. Multiplying (25.6 x 2.67) Multiply as normal ignoring the decimals
Count how many numbers after the decimal points in the two numbers
The answer will have the same number of decimal places
256 x 267 = 68352
25.6 ( One number )
2.67 ( Two numbers )
Three numbers in total
Ans =
2.56 x 2.67 =

13. Dividing decimals by a whole number (542.1 / 3)
When dividing by a whole number place the decimal point in the answer above the point in the question
Divide as normal

14. Dividing decimals by another decimal
It is not a good idea to divide one decimal by another as confusion arises as to where to put the decimal point
Instead we will convert the dividing number to a whole number by moving the decimal
/ 3.75
Move the decimal points two places to the right to change 3.75 to 375
The new division becomes
/ 375
Now divide as normal