Decimals

C

Put in neat column format if it helps

2.22

22.20

0.20

2.02

a) 0.09

b) 0.05

c) 0.375

If not sure, you can use “reverse bus stop”. So for example, calculate per below:

a) 0.03

b) 7

If 7.50 or above, then rounds to 8. Between 6.500 and 7.499, rounds to 7

c) 0.75

d) 0.07; 0.14; 0.306; 0.35; 0.4

e) 31/100

Remember 1.00 is 100% is 1/1. So 0.5 is 50% is 50/100. Work from there

a)i) 1/4

1. 3/12. In its simplest form, this is 1/4

a)ii) 0.25

1. Convert to a decimal = 0.25

b) i) See below

b) ii) 80%

0.006

1. If not sure, remove the zeros. So make it 20 * 3 = 60 (ie multiply both numbers by the same amount until the zeros are removed. This would be x100)
2. Then , because you removed 3 0s, you need to add these back in.
3. So the 60 because 0.006

a) £102

10metres would be £10.20 * 10 = £102

b) 2.5metres

£10.20 * 2 = £20.40. This leaves £5.10 (£25.50 – £20.40)

£5.10 is exactly half of £10.20. So therefore total is 2.5 metres

1.75kg

1. Convert to grams firstly to make it easier to calculate
2. 2500-750 = 1750
3. Then convert back remembering 1000g = 1kg
4. 1.75kg

2.03; 2.300; 2.302; 2.32

1. If not sure, put numbers in column format

6.9

Make 62.1 to 621 to remove the decimal

Then work through and you 69. Then add the decimal back in to get 6.9

a) See below. 1.52

Convert to the same metric. So in this case, its better to convert to decimals

b) 0.3

For this, you should use reverse bus stop. So 70 goes outside the bus stop with 21 inside.

Then add zeros on so that you can work out the answer to 2 decimal places

Then change the answer by the number of decimal places you added. So if you added 2 zeros, then your answer of eg. 70 would become 0.7

Use proper column format when working through these questions

1.08

1. Sometimes, these questions can be done in 2 parts. First 6/6 and then 0.48/6
2. 6/6 = 1
3. 0.48/6. Treat this is 48/6 = 8.
4. Then move 8 2 decimal places to the right. So 0.08
5. So answer is 1.08

a) 1.32

0.75+0.4+0.17 = 1.32

Convert 2/5 & 17/100 to decimals

b) 16

Use the approach below which is “reverse bus stop”

Change 3.88 to 3 decimal places to make the question easier to answer

a) 0.24

6/25 = 24/100 = 0.24

b) 1.20

Convert all to decimals

So 0.35 + 0.6  + 0.25

1.05

Put into the following format to help (so add a zero onto the 4.6 to make it easier to read):

4.60

– 3.55

a) 0.24

12/50ths = 24/100 = 0.24

b) 12.5%

1/8th = 12.5%.

The way to get to this is “reverse bus stop”. So take the 8 as outside the bus stop and 1 inside. See below….

So 8 into 1 but then add on zeros so you can get to at least 2 digit answer or there is no remainder.

Then take the 125 and move the decimal 3 places to the left to give 0.125. (3 places because you added in 3 zeros)

3/10; 0.305; 1/3; 35%

1. Estimate approximately to the same denominator
2. So , 0.333; 0.305; 0.35; 0.3
3. This makes it easier to rank the numbers

1.5

1. 3 1/4 – 1 3/4 = 1 1/2
2. As a decimal, this is 1.5

1.25

1. 0.012 + 1.238 = 1.250

28%

1. 7/25. To convert to a % you can do reverse bus stop
2. So this would be per below:

five twelfths; 0.65; 0.7; 3/4; 4/5

Can convert all of these to fractions if it helps

7/10 ; 3/4; 4/5; 13/20; 5/12

For first question, use fractions approach remembering to simplify and cross cancel. (See prior question in this paper for illustration)

For second question, its the same as 13/52

Final question convert 15% to 0.15. Then 60/0.15

5.75kg

1. Total weight is best done by converting into common metric. So lets say kg

5.25kg

0.029; 0.23; 0.25; 0.66; 0.667

1. Convert to the same metric if required. This makes the exercise easier
2. So, can convert all of these to decimals
3. 0.23, 0.667, 0.029, 0.66, 0.25

a) 3.7

(3.5+3.9)/2 = 7.4/2

b) 1.55

(1.3+1.8)/2 = 3.1/2

3.44, 4.34, 4.43, 34.4, 43.4, 44.3

C

Value of digit 5 is in tenths

0.07. Put numbers in a column format to help assess if needed

A

1. 0.3 = 3/10

3.55, 5.35, 5.53, 35.5, 53.5, 55.3

D

1. 9 is in the hundredths column
2. So answer is 9 hundredths

B

Way to rank numbers is to put them in Column Format like below:

Go Column by Column

Convert all numbers to the same metric if needed when working through this style of question

0.4

Process:

1. One option is to change 0.08 to 8. So x 100
2. Then multiply 8 by 5
3. This gives 40
4. Then to divide the answer by 100 as you originally multipied the question x 100
5. This gives 0.4

a) 8g

1. If each tea leaves weighs 0.008g, then multiply this by 1000 to get weight of 1000 tea leaves
2. Move the decimal place 3 places (number of zeros after the 1) to the right. 1000x.008g
3. This would give 8

b) 125,000

1. The number of leaves = 125 x 1000

c) 100

1. A tea bag = (250 x 0.008) + 0.5g = 2.5g
2. 250/2.5g = 100

0.2; 1/5; 0.027

1. With these types of questions, its sometimes a good idea to convert all the options to fractions
2. This would give the following:
3. 1/5 ; 1/5; 2/5; 3/8; 27/1000

If not sure, then an alternative approach is to convert all the numbers to the same denominator

Convert all the cards to the same metric if that helps to evaluate

1.009

If not sure, put the numbers in column format like below:

0.092

1. If not sure, put the numbers in a column format like below

11, 12.5

With sequences, its vital to look at the change number on number. So 5 up to 6.5 is +1.5. Then 6.5 to 8 is +1.5 etc

The pattern becomes clear. So 9.5 +1.5 = 11. 11+1.5 = 12.5

3.025    3 1/4    3.34    3 3/4

Try and convert all numbers to the same metric if possible. So in this case, lets convert all the numbers to decimals.

3.25   3.34   3.75   3.025

It becomes far easier to rank smallest to largest then

a) 1224

Will be half of 2448 . So 1224

b) 2496

Will be 48 greater than 2448. So 2496

c) 2.448

The numbers moved by a combined 3 decimal places. So move the decimal place in the original answer by 3 places

d) 51

Do 2448 ÷ 48 = 51. Then move decimal place 1 place to the left. This is because you multiplied 24.48 x 100 and 4.8 x 10. Therefore, the difference is 1 decimal place to adjust the number by

0.603

Ranked smallest to largest below

a)0.569

Move decimal 2 places to the left when going smaller.

b) 2.007

1997 + 10

Write it out as a maths operations question per above

5.02, 5.2,5.202,5.22

Put the numbers in neat Column format and then go through column by column for each digit

0.5

Put them in a Column Format. So….

Add zeros where necessary to ensure all numbers have same number of digits which makes the calculation easier

52.4, 52.402, 52.42

Put in Column format if not sure and pay note to whether your starting with smallest or largest first

52.400

52.420

52.402

a) 31

Reverse Maths. 87 – 56

b) 2

54/6 = 9. Therefore, X + 7 has to be 2

c) 10,000

Question on how many places you have to move the decimal. Its 4 places

1.006

If not sure, put all the numbers in a column format. This is exactly the same requirement if you are ranking numbers

0.993

1.006

1.100 (add zeros on so that all the numbers have the same number of digits)

0.940

0.990

3.08, 3.80. 3.808, 3.88

These are very common questions. The simplest way to do these questions is to write them down in column format with the same number of digits in each number:

3.808

3.800

3.880

3.080

Then to go 1 column at a time left to right. The second column is the first one with a difference. The last number is .0 whereas the others are .8. Therefore it is the smallest. Keep working through in this manner