### Overview

It’s easy to get fazed by decimal points. There are few simple techniques that make sums involving decimal points easy to do. Also I think there are potential relatively easy Grade A questions about converting recurring decimals to fractions (sounds scary but there is a neat trick to make it straightforward).

### Decimals Questions

**1.** Van Persie played 44 games and averaged 0.75 goals per game. Walcott played 64 games and averaged 0.5625 goals per game. Who scored the most goals?

**2.** A local newspaper charges 10.6p per word to place an advert. John’s advert costs £6.89. How many words are in John’s advert?

**3.** Hernandez averages 0.72 goals per game. In what fraction of games played does Hernandez score?

**4.** Convert these fractions to decimals:-

a) 2/9

b) 11/18

c) 4/7

**5.** Convert theses recurring decimals to fractions in their simplest forms;

a) 0.77777…

b) 0.030303…

c) 0.58555…

d) 0.73929292… NB this involves a lot of arithmetic– I’m not sure actual exam question would be this awkward.

### Decimals Approach

**1.** To multiply by decimal numbers

a) Ignore the decimal points and multiply the numbers.

b) Add the decimal places in all the numbers

c) Put the number of decimal places found in b) in your answer.

So, for example, if you are multiplying 2 x 0.5:

a) Ignore the decimal points and multiply = 2 x 5 = 10

b) Add the decimal places = 1 (just o.5)

c) Put 1 decimal place in the answer = 1.0

Another example 0.5 x 0.5

a) Ignore the decimal points and multiply = 5 x 5 = 25

b) Add the decimal places = 2 (o.5 and o.5)

c) Put 2 decimal places in the answer = 0.25

**2.** When dividing by decimal points. Multiply both numbers by a factor of 10 to eliminate the decimal point. Then just use normal division rules to complete the sum.

For example 12/0.4 = 120/4 (multiply both numbers by 10) = 30.

**3.** To convert a decimal to a fraction remember that

One decimal place will convert to tenths

Two decimal places will convert to hundredths

Three decimal places will convert to thousandths etc etc

Once you have converted to tenths or hundredths or thousandths… then simplify the fraction as much as possible using your knowledge of fractions and factors.

**4.** To convert a fraction into a decimal divide the top (numerator) of the fraction by the bottom (denominator) of the fraction. The resulting answer could be a recurring decimal or a terminating decimal. You can predict hat type of decimal you will get:-

Denominator (bottom) has ONLY prime factors of 2 and/or 5, answer = Terminating

Denominator (top) has ANY prime factors other than 2 and 5 = Recurring

**5.** Recurring decimals can be converted to fractions using the method outlined in this example:

Convert 0.333333.. to a fraction.

10 x 0.333333… = 3.33333333

Subtract 1 x 0.3333… 0.33333333

Gives 9 x o.33333 = 3.0000000

Therefore 0.33333 = 3/9 = 1/3.

You can use a similar method for any recurring fraction. This was a simple example involving one recurring digit. For 2 recurring digits you would multiply by 100 and 3 recurring digits you would multiply by 1,000 etc etc.

Having done a few of these, I can see why they are Grade A. It seems that calculating the first part is ok if you remember the method outlined above. However you often left with fractions with 3 or 4 digits which you then have to simplify. This needs to be done with care and you often have to use factor trees to find common factors to simplify the initial fraction. Definitely requires practice (well it does for me!)

### Decimals Answers

**1.** Van Persie = 44 x 0.75 = (44 x 75)/100 = 33.

Walcott = 64 x .5625 = (64 x 5625)/10000 = 35.

Walcott scored the most goals.

**2.** £6.89/10.6p = 6.89÷0.106 = 6890/106 = 65 words in the advert.

**3.** 0.72 = 72/100 = 36/50 = 18/25

**4.** 2÷9− This will be recurring as denominator has a prime factor that is not 2 or 5.

= 0.22222…

11/18 will also be recurring

= 0.61111.…..

4/7 = 0.57142857142857…

**5 a)** 0.7777 x 10 = 7.77777

0.7777 x 1 = 0.77777

9 x 0.777777 = 7.000

0.77777 = 7/9

**5 b)** 0.030303 x 100 = 3.030303

0.030303 x 1 = 0.030303

99 x 0.030303 = 3.000

0.0303030 = 3/99 = 1/33

**5 c) ** 0.585555 x 1,000 = 585.55555

0.5855555 x 1 = 0.58555

999 x 0.58555 = 584.970

0.585555÷999 = 584.970 = 58497/99900 = 19499/33300

Using factor tree 33,300 = 2² x 3² x 5² x 37 and 37 is a factor of 19499.

Therefore 0.585555… = 527/2700

**5 d)** 0.73929292.. x 10,000 = 7392.929292

0.73929292.. x 1 = 0.739292

0.73929292..x 9,999 = 7392.19000

0.73929292 = 7392.19000÷9999 = 739219/999900 = 7319/9900