Chapter-8 decimals

1. Decimalize each of the following:

Seven tenths

(b) 2 tenths and 9 tenths

(c) Fourteen and a half

(d) A total of 102 ones

(e)638 is the number in

Explanation:

(a) 7/10 = 0.7 is the decimal representation of seven tenths.

(b) Two tens and nine tenths are expressed in decimal notation as 20 + 9 / 10 = 20.9 (c) The decimal equivalent of sixteen is 14.6

(d) The decimal representation of 102 is 100 + 2 = 102.0.

(e) The decimal representation of 600 is 600.8


2. These decimals should be expressed as fractions. To the lowest form, reduce the fraction.

(a) 0.6

(b) 2.5

(c) 1.0

(d) 3.8

(e) 13.7

(f) 21.2

(g) 6.4

Explanation:

(a) 0.6 = 6 / 10

= 3 / 5

(b) 2.5 = 25 / 10

= 5 / 2

(c) 1.0 = 1

(d) 3.8 = 38 / 10

= 19 / 5

(e) 13. 7 = 137 / 10

(f) 21.2 = 212 / 10

= 106 / 5

(g) 6.4 = 64 / 10

= 32 / 5


3. On the number line, display the following numbers.

(a) 0.2

 (b) 1.9

Explanation:

(a)0.2

On the number line, point (a) is halfway between 0 and 1. Ten equally sized segments make up the area between 0 and 1. Each equal component will therefore equal one tenth. The second point between 0 and 1 is therefore 0.2.





(b) 1.9

(b) On the number line, 1.9 lies between positions 1 and 2. 10 equally sized sections make up the area between numbers one and two. Each equal component will therefore equal one tenth. 1.9 is the ninth number between 1 and 2, so.




4. The number line should show the numbers below.

(c) 1.1

(d) 2.5

Explanation:

The distance between points 1 and 2 on the number line is divided into 10 equally sized parts by the number 1.1, which is located between them. A tenth will therefore be equivalent to each equal piece. Hence, the beginning point between 1 and 2 is 1.1.



(d) The number line's point 2.5 divides the space between points 2 and 3 into 10 pieces of equal length. A tenth will therefore be equivalent to each equal piece. Hence, 2.5 is the sixth point between 2 and 3.



5. On the given number line, write the decimal number that corresponds to the points A, B, C, and D.



Explanation:

(a) On the provided number line, Point A corresponds to 0.8 cm.

(b) On the given number line, Point B corresponds to 1.3 cm.

(c) On the given number line, Point C equals 2.2 cm.

(d) On the provided number line, Point D equals 2.9 cm.


6. (A) Ramesh's notepad measures 9 cm 5 mm in length. How long will it be in centimetres?

(a) A young gramme plant measures 65 mm in length. Provide the measurement in centimetres.

Explanation:

(a) Ramesh's notepad is 9 cm and 5 mm long.


[(9 + 5/10)] cm is the length. cm


= 9.5 cm


(c) The gramme plant measures 65 mm in length.


So, 65/10 cm is the length in cm.


= 6.5 cm


7. The following decimal numbers should be written in words.

(a) 0.03

(b) 1.20

(c) 108.56

(d) 10.07

(e) 0.032

(f) 5.008

Explanation:

The decimals in words are as follows:

(a) 0.03 is equal to three zeros.

(b) 1.20 equals one minus two.

(c) 108.56 = 108 rounded to the next whole number

(d) 10.07 is equal to ten zero seven.

(e) 0.032 = zero three two zero

(f) 5.008. That is, five zero eight.


8. Who is superior?

(a) 0.3 or 0.4

(b) 0.07 or 0.02

(c) 3 or 0.8

(d) 0.5 or 0.05

(e) 1.23 or 1.20

Explanation:

(a) 0.3 or 0.4

These integers have the same whole parts. We are aware that 0.4's tenth part is larger than 0.3's.

∴ 0.4 > 0.3.

(b) 0.07 or 0.02

The first tenths of both numbers are the same, but 0.07 has a larger hundredth part than 0.02 does.

∴ 0.07 > 0.02.

(c) 3 or 0.8

The entirety of three is greater than the fraction of 0.8.

∴ 3 > 0.8

(d) 0.5 or 0.05

These integers have the same whole parts. The tenth part of 0.5 in this case is greater than the 0.05.


9. Who is superior?

(f) 0.099 or 0.19

(g) 1.5 or 1.50

(h) 1.431 or 1.490

I 3.3 or 3.300

(j) 5.64 or 5.603

Explanation:

(f) 0.099 or 0.19


These integers have the same whole parts. In this case, the tenth component of 0.19 exceeds that of 0.099.


∴ 0.099 < 0.19.


(g) 1.5 or 1.50


It's possible that, up until the tenth place, both numbers share the same parts. In this case, 1.5 has an empty hundredth spot. It indicates that this digit is 0, which is equivalent to the number 1.50 in the hundredth place.


These two sums are equivalent.


(h) 1.431 or 1.490


In this case, the first 10 parts of both integers are the same, but the hundredth part of 1.490 is larger than that of 1.431.


∴ 1.431 < 1.490.


I 3.3 or 3.300


Up until the tenth place, the numbers have the same parts. At the hundredth and thousandth places of 3.3, there are no digits. It indicates that these numbers are zero, which is equivalent to the 100th and 1000th digits of 3.300.


These two sums are equivalent.


(j) 5.64 or 5.603


In this case, the first 10 parts of both integers are the same, but the hundredth part of 5.64 is larger than that of 5.603


∴ 5.64 > 5.603


10. Find the greater number from the following five examples.

Explanation:

The following five examples are provided:


(a) 32.55 or 32.5


These integers have the same whole parts. The hundredth part of 32.55 is greater than that of 32.5, but the tenth part is also equal.


Therefore, 32.55 > 32.5.32.5, but the tenth part is also equal.


Hence, 32.55 > 32.5.


(b) 1 or 0.99


The entirety of 1 is larger than the fraction of 0.99.


∴ 1 > 0.99.


(c) 1.09 or 1.093


Up to the hundredth, the numbers in this situation share the same elements. Nonetheless, 1.093 has a thousandth part greater than 1.09,


∴ 1.093 > 1.09,


(d) 2 or 1.99


The entire portion of 2 is bigger than the portion of 1.99,


∴ 2 > 1.99,


(e) 2.08 or 2.085


Up to the hundredth, the numbers in this situation share the same elements. However, 2.085's thousandth part is greater than 2.08's.


∴ 2.085 > 2.08,


11. Decimalize and represent as rupees.

(a) 5 rupees

(c) 75 rupees

(c) 20 rupees

d) 50 rupees and 90 cents

(e) 725 rupees

Explanation:

We are aware that one rupee is divided into 100 paise.


5 paise equals 5/100 rupees (a).


= 0.05 rupees


(b) 75 paise equals 1/75 of a rupee.


0.75 rupees


(c) 20 paise is equal to 20/100 rupees.


0.20 rupees


d) Fifty rupees 90 paise = [(50 + 90 / 100)] rupees


= 50.90 rupees


(e) 725 paise is equal to 725/100 rupees.


7.25 rupees

12. Rashid paid $35.75 and $32.60 respectively for his maths and science textbooks. Determine Rashid's overall spending total.

Explanation:

Math textbook cost is 35.75.

Science book costs 32.60.

The entire amount Rashid spent is

35.75

+ 32.60

68.35

The entire sum of money Rashid spent was 68.35.


13. Radhika received 15.80 from her father and 10.50 from her mother. The total amount Radhika's parents provided her should be calculated.

Explanation:

Her mother gave Radhika around $10.50.

Radhika's father contributed $15.80.

Total gift from her parents was $.

10.50

+ 15.80

26.30

Radhika's parents contributed a total of $26.30


14. In the morning, Naresh walked 2 km 35 m, and in the evening, he walked 1 km 7 m. How far did he travel overall?

Explanation:

Naresh walked 2 km, 35 metres in the morning.


= [(2 + 35 /1000)] km


= 2.035 km


He walked 1 km 7 metres in the evening.


= [(1 + 7 / 1000)] km


= 1.007 km


The distance Naresh covered overall was


2.035


+ 1.007


3.042


3.042 km is the total distance covered.


15. Sunita walked 500 metres to go to her school after travelling 15 km 268 m by bus, 7 km 7 m by automobile, and 500 m on foot. What distance separates her home and school?

Explanation:

Around 15 kilometres 268 metres were covered by bus.


= [(15 + 268 / 1000)] km


= 15.268 km


7 km 7 m is the distance a car travels.


= [(7 + 7 / 1000)] km


= 7.007 km


Sunita covered a 500 m distance.


= 500 / 1000


= 0.500 km


Her home is located a total of 1.6 miles from the school.


15.268


7.007


+ 0.500


22.775


It is 22.775 kilometres from her home to the school overall.


16. Ravi bought 2 kilogrammes 20 g of sugar, 5 kg 400 g of rice, and 10 kg 850 g of flour. Find out how much weight he spent overall.

Explanation:

Rice weighs 5 kg and 400 g.


= [(5 + 400 / 1000)] kg


= 5.400 kg


Sugar weighs 2 kilogramme 20 g.


= [(2 + 20 / 1000)] kg


= 2.020 kg


Flour weighs 10 kg 850 g.


= [(10 + 850 / 1000)] kg


= 10.850 kg


The weight of his acquisitions as a whole is


5.400


2.020


+ 10.850


18.270


His purchases weigh a total of 18.270 kg


17. Raju spent 35.65 on a book. He gave the shopkeeper 50 yen. What much of cash did he receive back from the shop owner?

Explanation:

50.00 was provided to the shop owner.


The cost of the book is 35.65.


The difference between these two will be the money Raju receives back from the merchant.


The sum of money Raju received is


50.00


– 35.65


14.35


Raju has so been left with 14.35


18. Rani possessed 18.50. She spent 11.75 on one ice cream. How much cash does she currently have?

Explanation:

18.50 in Rani's pocket


A cone of ice cream costs $11.75.


The difference between these two will now be determined by the money that Rani has left.


Hence, the money she has left is


18.50


– 11.75


6.75


There are 6.75 dollars left with Rani


19. Tina had a 20 m (55 cm) piece of cloth. She uses this to cut a 4 m 50 cm length of fabric for a curtain. How much clothing is still on her?

Explanation:

Cloth length is 20 m 5 cm.


= 20.05 m


Curtain material must be 4 m 50 cm long.


= 4.50 m


The distinction between these two will be determined by the amount of cloth Tina has left.


Thus, the amount of fabric she has left is


20.05


– 4.50


15.55


The length of the fabric still with Tina is 15.55 metres


20. Every day, Namita travels 20 km and 50 m. She travels the first 10 km and 200 m by bus and the remaining distance by car. How far does she drive in her car?

Explanation:

Namita travelled a total of 20 km 50 m.


= 20.050 km


Bus travel distance is 10 km and 200 m.


= 10.200 km


Total distance travelled - Bus distance equals the distance driven by car.


The distance that must be driven by car is


20.050


– 10.200



9.850


Namita drove 9.850 kilometres.