1. Decimals

2. Decimals Learning Intentions place decimals in number order
add and subtract decimals
multiply and divide by decimals
round decimals to a specified number of places
convert decimals to fractions and vice versa

3. Number Place Value
Our number system is base 10. Each number written in a column to the left is 10 times bigger
Number to the left of the decimal point are bigger than or equal to 1
Numbers to the right of the decimal point are less than 1
The names of the columns are:
Hundreds
Tens
Units
tenths
hundredths
thousandths

4. The Value of a Digit
Write in words the value of the digit 5 in each of the following numbers:
45.33
61.509

5. Adding Decimals
When adding decimals the decimal points in each number must line up
Add the following decimal numbers:

6. Subtracting Decimals
When subtracting decimals the decimal points in each number must line up
It may be necessary to fill out the number with zeros
Subtract the following decimal numbers:
– 6.4
8 – 0.645

7. Multiplying by 10, 100 and 1000
To multiply a number by 10, 100, 1000, we move the number to the left (by the number of zeros)
Multiply the following numbers:
0.36 x 1000
x 100

8. More Multiplying
When multiplying by 30, 200, 6000, etc we first multiply by 10, 100 or 1000 and then multiply by 3, 2 and 6 respectively
Multiply the following numbers
51.3 x 60
4.5 x 800
0.52 x 3000

9. Dividing by 10, 100, 1000
To divide a number by 10, 100, 1000, we move the number to the right (by the number of zeros)
Divide the following numbers:
7.05 ÷ 1000
1573 ÷ 100

10. More Dividing
When dividing by 30, 200, 6000, etc we first divide by 10, 100 or 1000 and then divide by 3, 2 and 6 respectively
Divide the following numbers
4.75 ÷ 500
0.84 ÷ 200
144 ÷ 3000

11. Multiplying by Decimals
To multiply a decimal by another decimal:
Multiply the numbers ignoring the decimal points
Count the total number of decimal places. This is where the point goes back into the answer.
Multiply the following numbers
0.6 x 15
0.3 x 12.4
0.45 x 0.15

12. Rounding Numbers
Sometimes when numbers are very large or very small we may not write all the digits.
Imagine you have a choice of two jobs, both exactly the same, but one offers £ and the other offers £
The digit 9 and the digit 5 at the end doesn’t really matter.
We sometimes round these to £12K and £22K

13. Small Fractions
Sometimes when we work out the value of a fraction it doesn’t work out as an exact decimal.
For example one third is …
We would still be here next week writing threes.
We need to stop somewhere!

14. Decimal Places
We often round numbers to a set number of decimal places
For example:
= 0.3 (1 decimal place)
Write each of the following numbers to 1 decimal place
0.234
12.456
32.67

15. More decimal places Round each of the numbers to 2 decimal places:
0.238
1.294
2.9994
15.398
6.009
12.23

16. How to Round Numbers Decide which is the last digit to keep
Leave it the same if the next digit is less than 5 (this is called rounding down)
But increase it by 1 if the next digit is 5 or more (this is called rounding up)
Rounding to 1 decimal place
6.214 rounded to 1 dp = 6.2 (next digit is 1)
6.264 rounded to 1 dp = 6.3 (next digit is 6)

17. Dividing by Decimals
We cannot divide by a decimal without a calculator, but we CAN change the calculation to a simpler one that will give the same answer:
Each of the following calculations gives the same answer:
64 ÷ 0.8
6.4 ÷ 0.08
640 ÷ 8
Which calculation is the simplest?

18. Dividing by Decimals When dividing by a decimal number we
decide how we can make the divisor decimal a whole number
multiply BOTH decimals by this number to make the calculation easier
Divide the following numbers:
0.024 ÷ 0.6
64 ÷ 0.008

19. Changing Fractions to Decimals
To convert a fraction into a decimal, we divide the numerator by the denominator
Change the following fractions into decimals

20. Changing Decimals into Fractions
When converting a decimal into a fraction we
find the lowest place value of the number
write the decimal as a whole number over this number
Simplify the result
Change the following decimals into fractions
0.345
0.042