UNIT 5 : DECIMAL NUMBERS
5.1 Decimal numbers
Decimal numbers such as 3,762 are used in situations in which we look for
more precision than whole numbers provide.
As with whole numbers, a digit in a decimal number has a value which
depends on the place of the digit. The places to the left of the decimal pointare ones, tens, hundreds, and so on. This tableshows the decimal place value for various positions:
ONES / TENTHS / HUNDREDTHS / THOUSANDTHS / ……. / ……. / ……(Units)
Place (underlined) Name of Position Complete:
1,234567 Ones (units) position 1 Unit=….. Tenths
1,234567 Tenths (décimas) 1 Unit= 100 ……….
1,234567 Hundredths ( centésimas) 1 Unit=……..Thousandths
1,234567 Thousandths (………………………)
1,234567 Ten thousandths(………………………………)
1,234567 Hundred Thousandths(……………………………..)
1,234567 Millionths (……………………………..)
Note that adding extra zeros to the right of the last decimal digit does not
change the value of the decimal number.
5.2 Reading and writing Decimal numbers
We have to read the whole number, then the word “point” and the decimal numbers one by one.
Example:
The number 2,34 two point three four
Or we can read it using the table above:
2,34 Two ones and thirty four hundredths
Exercise
1.Draw a line to match each number to its equivalent value in words:
0,324 Fourteen point nine six
106,7 Thirty-two units and four tenths
14,96 One hundred and six point seven
5,09 Five hundred and sixty seven hundredths
32,4 Three hundred and twenty-four thousands
500,67 Five units and nine hundredths.
2.Write each number as digits, putting in decimal points where needed:
a) One hundred and sixty five point two four.
b) Fifty-seven ones and ninety-two hundredths.
c) Three ones and eighteen hundred thousandths
d) Nineteen point zero one seven
3.Write how these numbers are read:
a) 23,589 e) 7,805
b) 456,77 f) 20,11
c) 0,0008 g) 0,00009
d) 18,025 h) 48,012
5.3 Comparing Decimal numbers:
To compare two decimal numbers:
We compare the integer number:
Example: 3,75 and 4,2
3 is less than 4. So 3,75 is less than 4,2 3,75 4,2
Example: 8,64 and 6,78
8 is greaterthan 6.So 8,64 is greater than 6,78 8,646,78
If the integer numbers are the same, we add zeros into the decimal part, until they both have the same amount of decimal numbers.
Example: 3,75 and 3,8 3,75 and 3,80 3,753,80
Example: 0,045 and 0,0458
Exercise:
a) Put these numbers in order from least to greatest:
5,9 6 6,6 6,1 5,4 6,13 5,95
b) Write down these numbers in order from greatest to least:
3,03 3,17 2,98 3,1 2,9 3,3
5.4 Rounding Decimal Numbers
The rule is:
1. Look at the digit which is one place on the right to the required approximation.
2. If the digit is less than 5, cut the number (change the digits on the right tozeros)
3. If the digit is 5 or more than 5, add one unit to the digit of the roundingposition and change the others to zeros
Round:
1,17 to the nearest tenth
2,375 to the nearest hundredth
0,7084 to the nearest thousandth
12,87 to the nearest unit
5.5 Adding and Subtracting Decimal numbers
To add or subtract decimals, line up the decimal points and then follow therules for adding or subtracting whole numbers, placing the decimal point inthe same column as above.
When one number has more decimal places than another, use zeros(0) to givethem the same number of decimal places.
Example:
Add 43.67 + 2.3
1) Line up the decimal points and adds a 0 on the right of the second:
2) Then add.
43.67
2.30
Exercise: Add or subtract the following:
a)0,8 + 0,4 c) 1,2 + 1,8 e) 2,5 – 0,75 g) 3 - 0,15
b)2,4 – 0,6 d) 3,25 + 1,75 f) 0,12 + 4,8 h) 1- 0,3
5.6Multiplying decimal numbers
Multiplying decimals is just like multiplying whole numbers. The only extrastep is to decide how many digits to leave to the right of the decimal point. Todo that, add the numbers of digits to the right of the decimal point in bothfactors.
Example:
Multiply 23,56 x 34,1
23.56
x 34.1
2356
9424
Exercise:Calculate a) 5,6 x 6,9 b) 12,37 x 76,78
5.7.Dividing decimals by decimals
Multiply the divisor by a power of 10 great enough to obtain a whole number. Multiply the dividend by that same power of 10.
Then the problem becomes one involving division by a whole number instead
of division by a decimal.
Note: “Calculate each quotient to …….decimal places “( Saca …..decimales)
Example:
a) 56,7 : 2,34 b) 1.432,3 : 0,42
c) – 12,34: 3,5 d) 1: 1,2
Exercises:
1.Complete:
ONES/ UNITSunidades / décimas
2. Write each number:
a) One hundred and one point three. g) Forty hundredths
b) Ten units and two tenths. h) One point one eight
c) Zero point five six. i) Twenty two ten thousandths
d) Ninety four thousandths. j)Two ones and seven tenths
e) One and three ten thousandths. k) Twelve point zero eight
f) Six millionths. l) Thirty eight hundredths
3.Write in words the following numbers:
a) 45,8765 c) 1200, 89
b) 0,007 d) 38,09
4.The number 9,162 is greater than 9,17. True or false?
5. The number 0,175 is greater than 0,2. True or false?
6. Which is the greatest: 96,145 ; 96,2 or 96,19?
7. Which is the lowest: 25,62 ; 96,2 or 25,6?
9. Writ these number in order, starting with the greatest:
75,1 25,7 75,06 25,008
10.Write these numbers in order, starting with the lowest:
0,17 0,8 0,072 0,06 0,064
11. Answer True(T) or False(F)
a) 0,7 is less than 0,71 e) 0,09 is more than 0,1
b) 0,08 is more than 0,008 f) 0,802 is less than 0,8027
c) 8 is equal to 8,00 g) 8,67 is equal to 8,670
d) 0,07 is less than 0,1 h) 0,1 is equal to
12. Fill in the empty space with an amount containing a decimal number:
a)3,5 3,7 b) a)3,5 3,7 c) 6,9109 6,91092
13. Put these numbers in order from greatest to least:
a) 1,4 1,390 1,39 1,399 1,41
b) 0,6 - 0,9 - 0,8 2,07 –1,0
c) 5,83 5,51 5,09 5,511 5,47
d) 0,1 0,09 0,099 0,11 0,029
14. Write the value that corresponds to each letter:
15.Calculate:
a)175,4 – 86,9207 c) 12,8 – 1,937 e) 124,75 + 86,287 + 5,3408
b)68,529 – 7,88 d) 132- 26, 53 f) 6,12 + 0,87 +1,342
16. Calculate:
a) 0,5 - 0,75 b) 0,25 – 1 c) 1,2 – 1,5 d) 2 – 1, 95 e) 0,4 + 0,8 – 1,6 f) 2,7 – 0,95 – 1,04
16 Work out:
a) 12,4 – ( 18,365 – 7,62 ) c) 17,28 – 12,54 – 4,665
b)12, 4 – 18,365 + 7,62 d) 17,28 – ( 12,54 - 4,665)
17. Calculate:
a)8 · 0,3 d) 5 · ( 0,5) g) ( - 0,1) · ( - 0,2) j) 0,6 · 0,4
b)0,75 · 2 e) 0,25 · 4 h) 0,25 · 5 k) 1,3 · 0,08
c)( - 0,1) · ( +6) f) (- 0,4) · 0,2 i) 0,4 · 0,3 l) 0,25 · 0,16
18 Calculate:
a) ( 5,2 – 3,17 ) – ( 0, 48 + 0,6 ) c) 5 – ( 0,8 + 0,6 )
b) 2, 7 – ( 1,6 – 0,85 ) d) ( 3,21 + 2,4 ) – ( 2,8 – 1,75 )
19. Multiply:
a) 3,26 · 100 c) 35,29 · 10 e) 4,7 · 1000 g)0,002 · 1000 i) 1,499 · 10
b) 9,47 · 1000 d) – 6,24 · 100 f)( -10) · 0,475 h) 1,125 · 100 j) 0.086 · 10000
20.work out:
a)47: 3 c) 169 : 11 e) 14, 3 : 9 g) 526 : 23 i) 6321 : 145
b)9 : 7 d) 7,7 : 6 f) 96,7 : 22 h) 82,93 : 36 j) 1245,4 : 263
21. :Work out:
a) 123 : 1000 c) 57,28 : 100 e) 2 : 1000 g) 5 : 10 i) 8 : 100
b) 2,54 : 10 d) 2,8 : 10000 f) 0,3 : 1000 h) 8,4 : 10 j) 3,8 : 10
22. Complete:
a) 78 : = 7,8 b) 3,8 : = 0,0038 c) : 1000 = 0,05 d) : 100 = 2,3
23 Work out and pay attention to the results.:
a) 6. 0,5 b) 10 · 0,5 c) 22 · 0,5 d) 1,4 · 0,5 e) 4,2 · 0,5 f) 0,8 · 0,5
24. Work out and pay attention to the results:
a) 3: 0,5 b) 5 : 0,5 c) 11 : 0,5 d) 0,4 : 0,5 e ) 0,7 : 0,5 f) 2,1 : 0,5
25.Jackie bought a goldfish for 2,95 €, a bowl for 5,59€ and a bottle of water for 0,60€a)What was the total prize?
b) How much change did she get back if she paid with a twenty euro note?
26. Jack spent 5,25€ in the supermarket and 10,99 € in the music shop. How much change did he get from 20 €?
27.An electrician has 8 m of cable and then cut off 45cm. How long was the remaining cable?
28.Peter was 1,52 m tall and a year later he had grown 9 cm. How tall was he then?
29. Three friends contribute the same amount of money to buy a birthday present that costs 17,40 €. How much money does each friend give?
30. Carlos went around the circuit four times, covering a total distance of 11,2 Km. How long is the circuit?
31.We paid 17,50€ for 10 kilos of peaches. How much does one Kilo cost?
32. Francisco goes forward 0,8m with each step he takes. How many steps does he take if he covers a distance of 40 metres?
33.One melon that weighs two and a half Kilos costs 3,25 €.How much does one Kilo cost?
34. A box of 100 pairs of disposable latex gloves costs 20€. How much does one pair cost?
35.Pablo has 40,25€ in his moneybox. He can save 2,75€ each week. How long will it take until he has all the money he needs to buy a jersey that costs 54€?
36. Andrea weighs 72,4 Kilos and goes on a diet intending to lose 1,20 Kilos every month. How much does she hope to weigh in six months?
37. A can of fizzy drink contains 0,33 litres. How many litres are needed to fill 100 cans?
38. How much do I have to pay for:
- 5 boxes of milk ( 1,05 € each box)
-0,920 kg of ham (13,25 € a Kilo)
- 2 packets of cookies ( 2,85 € each packet)
Check yourself
1.Write down with numbers or words
- Six units and four tenths. - 5,184
- Fiftythree units and one hundredth - 0,002
- Two units and seventy four hundredths. - 12,56
2. Round to the nearest tenth, hundredth and thousandth:
3,8885,376,1283
4,3576,2935,2412
3. Put in order from least to greatest:
a) 5,4 5,235 5,25 5,45 5,2
b) 4,3 4,5 4,35 4,214 4,45
4. Fill in the empty space:
a) 4< < 4,05 b) 0,35< <0,36 c)2,8< <2’83
5. Calculate::
(Calculate the exact quotient)
7. In a restaurant 7 friends are having a meal, the bill is £173,6 and each
person contributes £25,50. What tip does the waiter receive?
8. I buy 7 mugs and pay 53,55 €. How much does each mug cost?