Decimals guide

Hi... I am Dec.

I am a Dalmation with ten spots!

I would love to learn more about decimals. Will you help me?

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What are decimals?Decimals are parts of whole things.

They are a little like fractions,but we write them in a different way.

Decimal numbers have a decimal point.This separates the whole numbers (on the left)

from the part numbers (on the right).

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Decimal Points

Whole Numbers Part Numbers

.

.

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It is important toremember what each digit

stands for in a number.This is called place value.

Whole NumbersWhole NumbersWhole NumbersWhole Numbers Part NumbersPart NumbersPart Numbers

Th H T U . t h thThousands Hundreds Tens Units Decimal

Point tenths hundredths thousandths

8 5 6 1 . 9 3 21 Thousand =

1 Hundred =1 Ten =1 Unit =

1 Tenth =1 Hundredth =

10 Hundreds10 Tens10 Units10 Tenths10 Hundredths10 Thousandths

Each place is 10 times bigger than the place on its right.


What dodecimals look like?If a large

square shows one whole, this is what

some decimals

might look like...

One tenthOne out of ten

0.1

One hundredthOne out of a hundred

0.01

Two tenths andseven hundredths

Twenty-seven hundredths0.27

What decimal does this picture show?


Number lines can help usto compare decimals.

0 1 2 3 4 50.3 0.8 ? 2.4 3.2 ? ?

What decimal numbers are the red arrows pointing to?

1.3 1.4 1.5 1.6 1.7 1.81.32 ? 1.47 1.55 ? 1.73 ?

This number line shows units, tenths and hundredths.

The number line below shows units and tenths.

If the numbers don’t all have the same number of digits, it might help to put a zero on the end.

Never put a zero before the decimal point though!

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Putting decimals in order is like putting whole

numbers in order.Remember to

line up the decimal points

though!

3.87 2.41 1.07 2.9 3.3

3.5 3.50 5.71 5.710

Let’s put these numbers in order of size,from smallest to largest.

Write them out, one under the other, with the decimal points in a line.

Next, look at the digits on the left of the list and and choose the smallest.

1.07 2.41 2.9 3.3 3.87

3 . 8 72 . 4 11 . 0 72 . 9 03 . 3 0

1.07

Then, choose the next largest.If the digits are the same,

compare the digit to the right.2.41 2.9

Keep going until you have put all of the numbers in order.


We can also compare the size of decimals using the greater than

and less than symbols.

7.8 7.517 . 8 07 . 5 1

Let’s compare these numbers...< >Write the numbers, one under the other,

with the decimal points in a line.

Write the two numbers againwith < or > between them,

to show which is smaller and which is larger.

If the digits are the same,compare the digit to the right.

In our example, 7.8 has eight tenths.7.51 has five tenths so that is smaller.

Next, look at the digits on the left ofthe list and and choose the smallest.

Both of our numbers have seven units.

7 . 8 07 . 5 1

7.51 < 7.8

7 . 8 07 . 5 1

Remember...The small end of the sign always

points to the smaller number.

Did you notice that7.8 is bigger than 7.51, even thoughit has fewer digits?

Can youexplain why?

Rounding a decimal means changing it to one with

a similar (but simpler) value.This makes it easier to work with.

3.5 3.6 3.7 3.8 3.9 4.03.0 3.1 3.2 3.3 3.4

3.4 rounded to the nearest whole number is 3.0

If you have a number that is half-way betweentwo whole numbers (like 3.5), we round it UP.

3.8 rounded to the nearest whole number is 4.0

Let’s round these decimals to the nearest whole number...


7.615 8

7.615 7.6

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To round to the nearest whole number...

7.615Let’s try rounding...

To round to the nearest tenth...

To round to the nearest hundredth...

Look at the digit to the right of the units.We have six tenths,

so we round the units up to eight.

Look at the digit to the right of the tenths.We only have one hundredth,so the tenths stays the same.

We don t always need to draw a number line when

we are rounding decimals.

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Look at the digit to theright of the hundredths.

Here, we have five thousandths,so we round the hundredths up to two.

If the next digit is0, 1, 2, 3 or 4,round down.

If the next digit is5, 6, 7, 8 or 9,round up.


Some decimals have digits that repeat. These are called

recurring decimals(or repeating decimals).

3.333333...8.010101...5.182182...

3.38.015.182

3.38.015.182

Here are some examples...

To save time, we use a dot over the first and last digits

of the repeating pattern.

Sometimes we use a line to show the repeating pattern.

The repeating patterns could go on forever!


Adding and subtracting decimals is just like

adding and subtracting whole numbers.

Just remember to line up the decimal points...

... and don’t forget to write the decimal point in your answer!

5 . 63 . 72+

1

5 . 63 . 72+

8 . 732 . 52-

9 . 32 6 . 21?


How do we multiply or

divide decimals by 10 or 100?

Multiplying by 10

T U . t h

3 . 50 . 3 5

Dividing by 10

T U . t h

0 . 3 53 5 . 0 0

Multiplying by 100

U . t h th

3 . 50 . 0 3 5

Dividing by 100

T U . t h

0 . 3 53 . 5 0

To multiply by 10, move the digits one space to the left.To multiply by 100, move the digits two spaces to the left.

To divide by 10, move the digits one space to the right.To divide by 100, move the digits two spaces to the right.

0.35 x 10 = 3.5

3.5 ÷ 10 = 0.35

0.35 x 100 = 35

3.5 ÷ 100 = 0.035 Remember...1) The decimal point

doesn’t move.2) You might need to

fill in any blank places with a zero.


We multiply and divide decimals in the same way as we do for whole numbers.But it is easier to change the decimals

into whole numbers first...

2.3 x 7We can change the decimal (2.3) into a whole number by multiplying it by 10...

Now, let’s multiply 23 by 7...2. 3x 1 0= 2 3

2 3 x 7= 1 6 1

2. 3x 7= 1 6. 1You might use different methods to multiply and divide whole numbers. Just remember to change decimals to whole

numbers when you are multiplying and dividing them... and change the final answer back into a decimal!

Finally, we need to change the answer back into a decimal by dividing it by 10 (because we multiplied by 10 earlier). So...

16.5 ÷ 3Let’s change the decimal (16.5) into a whole number by multiplying it by 10...

Now, let’s divide 165 by 3...1 6. 5x 1 0= 1 6 5

166 5 ÷ 3= 5 5

1 6. 5÷ 3= 5. 5

We need to change the answer back into a decimal by dividing it by 10 (because we multiplied by 10 earlier). So...

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17100

0.17 17%To convert a decimal to a percentage,

multiply the decimal by 100.Don’t forget to write the % sign!

To convert a percentageto a fraction,

write the numberas the numerator and

100 as the denominator.

How do we convert fractions, decimals and percentages?

To convert a fractionto a decimal,

divide the numeratorby the denominator

(divide the top numberby the bottom number).

Fractions, decimals and percentages are different ways of describing the same amounts.

Can you remember these?


Fraction Decimal Percentage1 1 100%

3/4 0.75 75%2/3 0.6 66.6%1/2 0.5 50%1/3 0.3 33.3%1/4 0.25 25%1/5 0.2 20%1/8 0.125 12.5%

1/10 0.1 10%1/100 0.01 1%

Answering money problems will usually involve working with decimals. Here are some things to remember...

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Remember...Calculators might give an answer with only one decimal place.However, answers to money questions will usually need to be written with two decimal places.So... 3.9 = $3.90

3.9

Tens(of dollars) Dollars Decimal

PointTens

(of cents)Cents

$ 1 5 . 9 3 $1.00 = 100¢$0.10 = 10¢$0.01 = 1¢

Education

Decimals guide