By using Ganita Prakash Class 7 Solutions and Part 1 Chapter 3 A Peek Beyond the Point Class 7 Question Answer, students can improve their problem-solving skills.
Class 7 Maths Chapter 3 A Peek Beyond the Point Solutions
Ganita Prakash Class 7 Chapter 3 Solutions
Class 7 Maths Ganita Prakash Chapter 3 Solutions A Peek Beyond the Point
3.1. The Need for Smaller Units
Page: 47
Question 1.
Which scale helped you measure the length of the screws accurately? Why?
Answer:
As obvious from the above figures, the bottom figures helped us to measure the length of the screws accurately. It is because we have considered the smaller units in the bottom figures.
Question 2.
What is the meaning of 2 \(\frac{7}{10}\) cm (the length of the first screw)?
Answer:
The meaning of 2 \(\frac{7}{10}\) is two complete centimetres and seven tenth centimetres.
Note: The Length of the second screw = 3 centimetres and two-tenth centimetres.
It can also be written as 3.2 cm.
Question 3.
Can you explain why the unit was divided into smaller parts to measure the screws?
Answer:
The unit was divided into smaller parts to measure the exact length of screws.
In the absence of smaller units we can only find between which two bigger units the length will lie.
Question 4.
Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.
Answer:
| Object | Length |
| 1. Pen | 14 centimetres and sixtenth Centimetres |
| 2. Pencil | 15 Centimetres and fivetenth Centimetres. |
| 3. Remote | 14 centimetres and fivetenth Centimetres. |
| 4. Sharpener | 1 centimetre and sevententh centimetres. |
| 5. Ganita Prakash Book VII | 27 centimetres and fivetenth centimetres. |
Question 5.
Write the measurements of the objects shown in the picture.
Answer:
Sharpener = 2 \(\frac{4}{10}\) cm
Pencil = 4 \(\frac{5}{10}\) cm
Cap = 1 \(\frac{4}{10}\) cm
3.2. A tenth part
Page:49
Question 6.
Arrange these lengths in increasing order:
(a) \(\frac{9}{10}\)
(b) 1 \(\frac{7}{10}\)
(c) \(\frac{130}{10}\)
(d) 13 \(\frac{1}{10}\)
(e) 10 \(\frac{5}{10}\)
(f) 7 \(\frac{6}{10}\)
(g) 6 \(\frac{7}{10}\)
(h) \(\frac{4}{10}\)
Answer:
(h) \(\frac{4}{10}\) < (a) \(\frac{9}{10}\) < (b) 1 \(\frac{7}{10}\) < (g) 6 \(\frac{7}{10}\) < (f) 7 \(\frac{6}{10}\) < (e) 10 \(\frac{5}{10}\) < (c) \(\frac{130}{10}\) < (d) 13 \(\frac{1}{10}\)
Page: 50
Question 7.
Arrange the following lengths in increasing order: 4\(\frac{1}{10}\), \(\frac{4}{10}\), \(\frac{41}{10}\), 41 \(\frac{1}{10}\).
Answer:
\(\frac{4}{10}\) < (4 \(\frac{1}{10}\). and.\(\frac{41}{10}\)) < 41 \(\frac{1}{10}\)
Here, 4 \(\frac{1}{10}\) and \(\frac{41}{10}\) are same lengths.
Question 8.
Sonu is measuring some of his body parts. The length of Sonu’s lower arm is 2 \(\frac{7}{10}\) units, and that of his upper arm is 3 \(\frac{6}{10}\) units. What is the total length of his arm?
Answer:
The length of Sonu’s Lower arm = 2 \(\frac{7}{10}\) units The length of Sonu’s upper arm = 3 \(\frac{6}{10}\) units ∴ Total Length of his arm
= 2 \(\frac{7}{10}\) + 3 \(\frac{6}{10}\)
= (2 + 3) + (\(\frac{7}{10}\) + \(\frac{6}{10}\))
= 5 + \(\frac{7 + 6}{10}\)
= 5 + \(\frac{13}{10}\)
= 5 + 1 + \(\frac{3}{10}\)
= 6 + \(\frac{3}{10}\)
= 6 \(\frac{3}{10}\) units
Note: We can use different methods to get the total length of his arm.
(i) we can add them as :
(ii) We can convert mixed fractions to improper fractions and then add them as:
Page: 51
Question 9.
The lengths of the body parts of a honeybee are given. Find its total length.
Head: 2 \(\frac{3}{10}\) units
Thorax: 5 \(\frac{4}{10}\) units
Abdomen: 7 \(\frac{5}{10}\) units
Answer:
The lengths
Head = 2 \(\frac{3}{10}\) Units
Thorax = 5 \(\frac{4}{10}\) units
Abdomen = 7 \(\frac{5}{10}\) units.
So, total length of the honeybee = Length of its head + Length of its Thorax + Length of its Abdomen
= 2 \(\frac{3}{10}\) + 5 \(\frac{4}{10}\) + 7 \(\frac{5}{10}\)
= (2 + 5 + 7) + (\(\frac{3}{10}\) + \(\frac{4}{10}\) + \(\frac{5}{10}\))
= 14 + (\(\frac{3 + 4 + 5}{10}\))
= 14 + \(\frac{12}{10}\)
= 14 + 1 + \(\frac{2}{10}\)
= 
= 15 + \(\frac{1}{5}\)
= 15 \(\frac{1}{5}\) units
Question 10.
The length of Shylaja’s hand is 12 \(\frac{4}{10}\) units, and her palm is 6 \(\frac{7}{10}\) units, as shown in the picture. What is the length of the longest (middle) finger?
Answer:
The length of Shylaja’s hand = 12 \(\frac{4}{10}\) units
The length of her palm = 6 \(\frac{7}{10}\) units
The Length of the longest (middle) finger can be got by subtracting length of her palm from the length of her hand.
∴ , the length of the longest (middle) finger =
Note: We can do it in the following way :
12 \(\frac{4}{10}\) – 6 \(\frac{7}{10}\) = 11 \(\frac{14}{10}\) – 6 \(\frac{7}{10}\) = 5 \(\frac{7}{10}\) units
Page: 52
Question 11.
Try computing the difference by converting both lengths to tenths.
Answer:
Question 12.
A Celestial Pearl Danio’s length is 2 \(\frac{4}{10}\) cm, and the length of a Philippine
Goby is \(\frac{9}{10}\) cm. What is the difference in their lengths?
Answer:
Length of a celestial Pearl Danio = 2 \(\frac{4}{10}\) cm
Length of a Philippine Goby = \(\frac{9}{10}\) cm
∴ Difference of their lengths = 2 \(\frac{4}{10}\) – \(\frac{9}{10}\)
= \(\frac{20+4}{10}\) – \(\frac{9}{10}\) = \(\frac{24}{10}\) – \(\frac{9}{10}\) = \(\frac{15}{10}\) cm
Question 13.
How big are these fish compared to your finger?
Answer:
Length of my finger = 8 \(\frac{2}{10}\) cm
Length of Celestial Pearl Danio = 2 \(\frac{4}{10}\) cm
So, my finger is bigger than a celestial Pearl Danio by
Length of a Philippine Goby = \(\frac{9}{10}\) cm
∴ , my finger is bigger than a Philippine Goby by
Question 14.
Observe the given sequences of numbers. Identify the change after each term and extend the pattern:
Answer:
3.3. A Hundredth Part
Page: 53
Question 15.
What is the length of this smaller part? How many such smaller parts make a unit length?
Answer:
Here, each one-tenth has 10 smaller parts and there are 10 one-tenths in a unit.
Hence, there will be 100 smaller parts in a unit.
So, the length of one part = \(\frac{1}{100}\) of a unit.
Hence, 100 smaller parts will make a unit length.
Question 16.
How many one-hundredths make one-tenth? Can we also say that the length is 4 units and 45 one-hundredths?
Answer:
Ten one-hundredths make one-tenth.
i.e. 10 × \(\frac{1}{100}\) = \(\frac{1}{10}\)
Length = 4 units + 45 one-hundredths
= 4 + \(\frac{45}{100}\)
= 4 \(\frac{45}{100}\) units
Page: 54
Question 17.
Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.
Answer:
Page: 54, 55, 56
Question 18.
For the lengths shown below write the measurements and read out the measures in words.
Answer:
I – 5 \(\frac{37}{100}\)
II -15 \(\frac{3}{100}\)
III – 7 \(\frac{52}{100}\)
IV – 9 \(\frac{8}{100}\)
Question 19.
What will be the sum of 15 \(\frac{3}{10}\) \(\frac{4}{100}\) and 2 \(\frac{6}{10}\) \(\frac{8}{100}\) ?
Answer:
Note: We can get the sum by another method as:
Page 57
Question 20.
Are both these methods different?
Answer:
These methods are same.
Question 21.
Observe the addition done below for 483 + 268. Do you see any similarities between the methods shown above?
Answer:
483 + 268 = (400 + 200) + (80 + 60) + (3 + 8)
= 600 + 140 + 11
= 740 + 11
= 751
This is the same as the method shown above.
Question 22.
What is the difference: 25 \(\frac{9}{10}\) – 6 \(\frac{4}{10}\) \(\frac{7}{100}\) ?
Answer:
25 \(\frac{9}{10}\) – 6 \(\frac{4}{10}\) \(\frac{7}{100}\)
Page: 58
Question 23.
Solve this by converting to hundredths. What is the difference 15 \(\frac{3}{10}\) \(\frac{4}{100}\) – 2 \(\frac{6}{10}\) \(\frac{8}{100}\) ?
Answer:
Page: 58
Question 24.
Figure it Out :
1. Find the sums and differences:
(a) \(\frac{3}{10}\)+3 \(\frac{4}{100}\)
Answer:
(b) 9 \(\frac{5}{10}\) \(\frac{7}{100}\)+2 \(\frac{1}{10}\) \(\frac{3}{100}\)
Answer:
(c) 15 \(\frac{6}{10}\) \(\frac{4}{100}\)+14 \(\frac{3}{10}\) \(\frac{6}{100}\)
Answer:
(d) 7 \(\frac{7}{100}\)-4 \(\frac{4}{100}\)
Answer:
= 3 + \(\frac{3}{100}\)
= 3 \(\frac{3}{100}\)
(e) 8 \(\frac{6}{100}\)-5 \(\frac{3}{100}\)
Answer:
= 3 + \(\frac{3}{100}\) = 3 \(\frac{3}{100}\)
(f) 12 \(\frac{6}{100}\) \(\frac{2}{100}\)–\(\frac{9}{10}\) \(\frac{9}{100}\)
Answer:
3.4. Decimal Place Value
Page: 59
Question 25.
Can we not split a unit into 4 equal parts, 5 equal parts, 8 equal parts, or any other number of equal parts instead?
Answer:
Yes, we can split a unit into 4 equal parts.
We can split a unit into 5 equal parts,
We can split a unit into 8 equal parts,
We can split a unit into 10 equal parts,
By the above illustrations, we can conclude that we can split a unit into any number of equal parts.
Question 26.
Then why split a unit into 10 parts every time?
Answer:
We prefer to split a unit 10 parts every time because of the special role 10 plays in the Indian place value system.
For example, for a whole number 425, written in a Indian place value system – the place value of 4 is hundred (100), that of 2 is tens (10) and that of 5 is one (1). Each place value is 10 times bigger than the one immediately to its right. Equivalently. Each place value is 10 times smaller than the one immediately to its left:
10 ones make 1 ten,
10 tens make 1 hundred,
10 hundreds make 1 thousand, and so on.
In order to extend this system of writing numbers to quantities smaller than one, we divide one into 10 equal parts.
Page: 60
Question 27.
Can we extend this further?
Answer:
Yes we can extend this notion further. We can 1,00,000,10,00,000,1,00,00,000, etc. towards the left side and \(\frac{1}{1000}\), \(\frac{1}{10000}\), \(\frac{1}{100000}\), …….towards the right side.
Question 28.
What will the fraction be when \(\frac{1}{100}\) is split into 10 equal parts?
Answer:
We have the fraction \(\frac{1}{100}\).
If we split this further into 10 equal parts, the fraction will become \(\frac{1}{1000}\).
In this case 1000 parts will make up one unit.
Note: In this similar manner we can split given fractions into smaller units. We can split \(\frac{1}{1,000}\), into \(\frac{1}{10,000}\) and again \(\frac{1}{10,000}\) into 1,00,000, every time dividing the fraction in hand by 10.
Page: 61
Question 29.
We can ask similar questions about fractional parts:
(a) How many thousandths make one unit?
(b) How many thousandths make one tenth?
(c) How many thousandths make one hundredth?
(d) How many tenths make one ten?
(e) How many hundredths make one ten?
Answer:
(a) 1,000
(c) 10
(d) 100
(e) 1,000
Question 30.
Make a few more questions of this kind and answer them.
Answer:
Question 1.
How many ten-thousandths make one unit?
Answer:
10,000 ten-thousandths make one unit.
Question 2.
How many ten-thousandths make one-tenth?
Answer:
1000 ten-thousandths make one-tenth.
Question 3.
How many ten-thousandths make one-hundredth?
Answer:
100 ten-thousandths make one hundredth.
Question 4.
How many 10 -thousandths make one thousandth?
Answer:
10 ten-thousandths make one thousandth.
Question 5.
How many 1 lakhth make 10units?
Answer:
10,00,000 one-lakhths make 10 units.
Page: 63
Question 31.
Make a place value table similar to the one above. Write each quantity in decimal form and in terms of place value, and read the number:
(a) 2 ones, 3 tenths and 5 hundredths
(b) 1 ten and 5 tenths
(c) 4 ones and 6 hundredths
(d) 1 hundred, 1 one and 1 hundredth
(e) \(\frac{8}{100}\) and \(\frac{9}{10}\)
(f) \(\frac{5}{100}\)
(g) \(\frac{1}{10}\)
(h) 2 \(\frac{1}{100}\), 4 \(\frac{1}{10}\) and 7 \(\frac{7}{1000}\)
Answer:
Note: In (h) above, 2 \(\frac{1}{100}\), 4 \(\frac{1}{10}\) and 7 \(\frac{7}{1000}\)
= (2 + 4 + 7) + (\(\frac{1}{100}\) + \(\frac{1}{10}\) + \(\frac{7}{1000}\))
= (13) + (0.01 + 0.1 + 0.007)
= 13 + 0.117
= 13.117
Page: 64
Question 32.
How can we write 234 tenths in decimal form?
Answer:
Given number is 234 tenths.
To write it in decimal from, we write
\(\frac{234}{10}\) = \(\frac{200}{10}\) + \(\frac{30}{10}\) + \(\frac{4}{10}\)
= 20 + 3 + 0.4
= 23.4
Question 33.
Write these quantities in decimal form: (a) 234 hundredths, (b) 105 tenths.
Answer:
(a) 234 hundredths can be written as
\(\frac{234}{100}\) = \(\frac{200}{100}\) + \(\frac{30}{100}\) + \(\frac{4}{100}\)
= 2 + 0.3 + 0.04
= 0.34
(b) 105 tenths = \(\frac{100}{10}\) + \(\frac{0}{10}\) + \(\frac{5}{10}\)
= 10 + 0 + 0.5
= 10.5
3.5. Units of Measurement
Question 34.
How many cm is 1 mm?
Answer:
Since 10 mm make 1 cm
Question 35.
How many cm is (a) 5 mm? (b) 12 mm?
Answer:
We know that 10 mm make 1 cm.
5 mm = \(\frac{1}{10}\) × 5 cm=\(\frac{1}{2}\) cm
12 mm = \(\frac{1}{10}\) × 12 cm
= \(\frac{12}{10}\) cm=(\(\frac{10}{10}\) + \(\frac{2}{10}\)) cm
= 1.2 cm
Page 65
Question 36.
Fill in the blanks below ( mm<->cm)
Answer:
Page: 66
Question 37.
How many m is (a) 10 cm? (b) 15 cm?
Answer:
(a) We know that 100 cm=1 m
So, 1 cm = \(\frac{1}{100}\) m
10 cm = \(\frac{1}{100}\) × 10 m
= \(\frac{10}{100}\) m = 0.1 m
(b) 15 cm = \(\frac{1}{100}\) × 15 m
= \(\frac{15}{100}\) m = 0.15 m
Page: 66
Question 38.
Fill in the blanks below (cm <-> m):
Answer:
Question 39.
How many mm does 1 meter have?
Answer:
We know that 10 mm = 1 cm
And 100 cm = 1 m
arrow 1000 mm = 1 m
So, 1000 mm is contained in 1 meter or 1 meter has 1000 mm.
Question 40.
Can we write 1 mm = \(\frac{1}{1000}\) m ?
Answer:
We know that 1000 mm=1 meter
So, 1 mm = \(\frac{1}{1000}\) meter
Hence, we can write 1 mm=\(\frac{1}{1000}\) m
Page: 67
Question 41.
How many kilograms is 5 g?
Answer:
We know that 1 kilo = 1000
∴ 1 kilogram = 1000 gram
arrow \(\frac{1}{1000}\) kilogram = 1 gram
arrow 5 × \(\frac{1}{1000}\) kilogram = 5 gram
arrow \(\frac{5}{1000}\) kilogram = 5 gram
So, \(\frac{5}{1000}\) kilogram is 5 g.
Question 42.
How many kilograms is 10 g?
Answer:
We know that 1000 g = 1 kg
arrow 1 g = \(\frac{1}{1000}\) kg
arrow 10 g = 10 × \(\frac{1}{1000}\) kg = \(\frac{1}{100}\) kg
Therefore, \(\frac{1}{100}\) kg is 10g.
Question 43.
Fill in the blanks below (g rightarrow kg)
Answer:
3.6. Locating and Comparing Decimals
Page: 69
Question 44.
Fill in the blanks below (rupee <-> paise)
Answer:
Page: 70
Question 45.
Name all the divisions between 1 and 1.1 on the number line.
Answer:
Question 46.
Identify and write the decimal numbers against the letters.
Answer:
A → 5.09
B → 5.13
C → 5.20 or 5.2
D → 5.31
Question 47.
Sonu says that 0.2 can also be written as 0.20,0.200; Zara thinks that putting zeros on the right side may alter the value of the decimal number. What do you think?
Answer:
I think Zara is not right as I know that putting zeroes on the extreme right of a decimal does not alter the value of the decimal number. For example: 12.34 can also be written as 12.340 or 12.3400 or 12.34000, etc. Note: Putting zeroes at the right of a decimal number helps us to get equal number of digits after decimal so that we can calculate the sum or difference easily and without error. And, or example – Let us suppose we have to add 1.7 and 22.0324, then we write 1.7 as 1.7000 so that we get equal number of digits after decimals in both of the numbers and then
This makes our work easier! Is not it?
Page 71
Consider the decimal numbers 0.2, 0.02 and 0.002.
Question 48.
Can you tell which of these is the smallest and which is the largest?
Answer:
Among 0.2, 0.02 and 0.002, 0.002 is the smallest and 0.2 is the largest. This can be understood by writing these numbers as 0.200, 0.020 and 0.002, respectively.
Question 49.
Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
Answer:
4.05 and 4.050 are same.
4.5, 4.50 and 04.50 are same.
Observe the number lines in Figure (a) below. At each level, a particular segment of the number line is magnified to locate the number 4.185.
Question 50.
Identify the decimal number in the last number line in Figure (b) denoted by ‘?’.
Answer:
Question 51.
Make such number lines for the decimal numbers: (a) 9.876 (b) 0.407.
Answer:
(a) 9.876
(b) 0.407
Question 52.
In the number line shown below, what decimal numbers do the boxes labelled ‘a’, ‘b’, and ‘c’ denote?
Answer:
A – [6]
B – [7.5]
C – [9.5]
There are 10 divisions between 5 and 10.
arrow 10 divisions =5 units
arrow 2 divisions =1 unit.
arrow 1 division =\(\frac{1}{2}\) unit.
Page 72
Question 53.
Using similar reasoning, find out the decimal numbers in the boxes below.
Answer:
There are 10 divisions between 8 and 8.1. So, each division represents \(\frac{0.1}{10}\) = 0.01
Hence, d = 8.01
and e = 8.05
Here, there are 10 divisions between 4.3 and 4.8.
So, each division represents
\(\frac{4.8-4.3}{10}\) = \(\frac{0.5}{10}\) =0.05 units
∴, f = 4.35, g = 4.5, h = 4.85
Question 54.
Which is larger: 6.456 or 6.465?
Answer:
Here we compare the highest place value digits first.
Here one’s digit is the digit having highest place value.
We notice both are same and they are equal to 6.
Now we move on to tenths digit. Here again both the tenths digit are same and equal to 4.
Now we move little right to find the hundredth’s digit, which are 5 and 6, respectively
So, the second number is greater as 6 is greater than 5.
Hence, 6.465 > 6.456
Note: By using the above method we can compare any two numbers.
Page 73
Question 55.
Why can we stop comparing at this point? Can we be sure that whatever digits are there after this will not affect our conclusion?
Which decimal number is greater?
(a) 1.23 or 1.32
(b) 3.81 or 13.800
(c) 1.009 or 1.090
Answer:
We can stop comparing at this point as lower place value digits do not make up for the heigher place value digits. For example – 5.678 cannot be made greater than 5.7 by placing digit of any value.
(a) 1.32 is greater than 1.23
(b) 3.81 is greater than 13.800
(c) 1.090 is greater than 1.009
Now consider: 0.9,1.1,1.01 and 1.11.
Question 56.
Which of the above is closest to 1.09?
Answer:
In the above 1.11 is closest to 1.09.
Page 73
Question 57.
Which among these is closest to 4: 3.56, 3.65,3.099?
Answer:
Here, 3.65 is closest to 4.
Question 58.
Which among these is closest to 1: 0.8, 0.69, 1.08?
Answer:
1.08 is closest to 1.
Question 59.
In each case below use the digits 4, 1, 8, 2, and 5 exactly once and try to make a decimal number as close as possible to 25.
Answer:
3.7. Addition and Subtraction of Decimals
Page 74
Question 60.
Priya requires 2.7 m of cloth for her skirt, and Shylaja requires 3.5 m for her kurti. What is the total quantity of cloth needed?
Answer:
Cloth required by Priya for her skirt = 2.7 m. Cloth required by Shylaja for her kurti
= 3.5 m
So, the total quantity of cloth needed
= 2.7 m + 3.5 m=6.2 m
Question 61.
How much longer is Shylaja’s cloth compared to Priya’s?
Answer:
Length of Shylaja’s cloth = 3.5 m
Length of Priya’s cloth = 2.7 m
To know how much longer Shylaja’s cloth is compared to Priya’s,
We find the difference
Now, 0.8 m = 80 cm.
Therefore, Shylaja’s cloth is 80 cm longer than Priya’s cloth.
Page 75
Question 62.
Write the detailed place value
computation for 84.691-77.345, and its compact form.
Answer:
84.691-77.345
Detailed place value computation:
Page 75
Question 63.
Figure it Out :
1. Find the sums
(a) 5.3 + 2.6
Answer:
5.3 + 2.6 = 7.9
(b) 18 + 8.8
Answer:
18 + 8.8 = 26.8
(c) 2.15 + 5.26
Answer:
(d) 9.01 + 9.10
Answer:
(e) 29.19 + 9.91
Answer:
(f) 0.934 + 0.6
Answer:
(g) 0.75 + 0.03
Answer:
(h) 6.236 + 0.487
Answer:
2. Find the differences
(a) 5.6-2.3
(b) 18-8.8
(c) 10.4-4.5
(d) 17-16.198
(e) 17-0.05
(f) 34.505-18.1
(g) 9.9-9.09
(h) 6.236-0.487
Answer:
Page: 75
Consider the sequence:
4.4, 4.8, 5.2, 5.6, 6.0,…
Question 64.
Continue this sequence and write the next 3 terms.
Answer:
4.4, 4.8, 5.2, 5.6, 6.0, 6.4, 6.8, 7.2
3.8. More on the Decimal System
Page 76
Question 14.
Similarly, identify the change and write the next 3 terms for each sequence given below. Try to do this computation mentally.
(a) 4.4,4.45,4.5, ……
(b) 25.75, 26.25, 26.75,…
(c) 10.56, 10.67, 10.78,…
(d) 13.5, 16, 18.5,…
(e) 8.5, 9.4, 10.3,…
(f) 5, 4.95, 4.90,…
(g) 12.45, 11.95, 11.45,…
(h) 36.5, 33, 29.5,…
Answer:
(a) 4.4, 4.45, 4.5, 4.55, 4.6, 4.65
(b) 25.75,26.25,26.75, 27.25, 27.75, 28.25
(c) 10.56, 10.67, 10.78, 10.89, 11, 11.11
(d) 13.5, 16, 18.5, 21, 23.5, 26
(e) 8.5, 9.4, 10.3, 11.2, 12.1, 13
(f) 5, 4.95, 4.90, 4.85, 4.8, 4.75
(g) 12.45, 11.95, 11.45, 10.95, 10.45, 9.95
(h) 36.5, 33, 29.5, 26, 22.5, 19
Question 65.
Make your own sequences and challenge your classmates to extend the pattern.
Answer:
(i) 100, 90, 80, ______, ______, ______.
arrow 70,60,50.
(ii) 100, 90, 70, 40, ______, ______, ______.
arrow 0,-50,-110
(iii) 10.5, 10.25, 10, ______, ______, ______.
arrow 9.75,9.50,9.25.
(iv) 22.5, 22.65, 22.8, ______, ______, ______.
arrow 22.95,23.1,23.25.
(v) 6.25, 6.06, 5.81, ______, ______, ______.
arrow 5.68,5.49,5.3.
(vi) 7.21, 7.44, 7.67, ______, ______, ______.
arrow 7.9,8.13,8.36.
Sonu has observed sums and differences of decimal numbers and says, “If we add two decimal numbers, then the sum will always be greater than the sum of their whole number parts. Also, the sum will always be less than 2 more than the sum of their whole number parts.”
Let us use an example to understand what his claim means:
If the two numbers to be added are 25.936 and 8.202, the claim is that their sum will be greater than 25 + 8 (whole number parts) and will be less than 25 + 1 + 8 + 1.
Question 66.
What do you think about this claim? Verify if this is true for these numbers. Will it work for any 2 decimal numbers?
Answer:
Yes, Sonu’s claim is correct.
Since,
Clearly, 34:138 is greater than the sum of their whole number parts which is 33 and less than 35 which is 2 more than the sum of their whole number parts.
Yes, it will work for any two decimal number as “sum of decimal parts can never be greater than 2”.
Question 67.
What about for the sum of 25.93603259 and 8.202?
Answer:
Sum of 25.93603259 and 8.202
Here the sum of whole parts of the numbers = 33 and hence 2 more than their sum = 35 So, we can easily verify that the obtained sum is greater than 33 but less than 35.
Question 68.
Similarly, come up with a way to narrow down the range of whole numbers within which the difference of two decimal numbers will lie.
Answer:
The difference of any two decimal numbers will be greater than the difference of their whole number parts and less than one more than their difference of whole number parts.
For example:
Consider 7.8632 and 4.2121
Here, difference is;
The difference of whole number parts = 7-4 = 3 and one more than 3 is 4. Here, we can notice that 3.6511 is more than 3 but less than 4.
Page 78
Question 69.
Where else can we see such ‘non’decimals’ with a decimal-like notation?
Answer:
Yes, in a cricket match 10.5 overs does mean 10 overs and 5 balls. We know an over is equal to 6 balls.
Page: 78, 79, 80
Question 70.
Figure it Out :
1. Convert the…
(a) \(\frac{5}{100}\)
(b) \(\frac{16}{1000}\)
(c) \(\frac{12}{10}\)
(d) \(\frac{254}{1000}\)
Answer:
(a) \(\frac{5}{100}\) = 0.05
(b) \(\frac{16}{1000}\) = 0.016
(c) \(\frac{12}{10}\) = 1.2
(d) \(\frac{254}{1000}\) = 0.254
2. Convert the following decimals into a sum of tenths, hundredths and thousandths:
(a) 0.34
(b) 1.02
(c) 0.8
(d) 0.362
Answer:
(a) 0.34 = 3 × \(\frac{1}{10}\) + 4 × \(\frac{1}{100}\)
(b) 1.02 = 1 + 2 × \(\frac{1}{100}\)
(c) 0.8 = 0 + 8 × \(\frac{1}{10}\)
(d) 0.362 = 3 × \(\frac{1}{10}\) + 6 × \(\frac{1}{100}\) + 2 × \(\frac{1}{1000}\)
3. What decimal number does each letter represent in the number line below?
Answer:
(a) 6.45 (b) 6.55 (c) 6.525
4. Arrange the following quantities in descending order:
(a) 11.01, 1.011, 1.101, 11.10, 1.01
(b) 2.567,2.675,2.768,2.499,2.698
(c) 4.678 g, 4.595 g}, 4.600 g, 4.656 g, 4.666 g
(d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m
Answer:
(a) 11.10>11.01>1.101>1.011>1.01
(b) 2.768>2.698>2.675>2.567>2.499
(c) 4.678 g}>4.666 g}>4.656 g}>4.600 g}> 4.595 g
(d) 33.331 m>33.313 m>33.31 m>33.133 m > 33.13 m
5. Using the digits 1, 4, 0, 8, and 6 make:
(a) the decimal number closest to 30
(b) the smallest possible decimal number between 100 and 1000.
Answer:
(a) 40.168
(b) 104.68
6. Will a decimal number with more digits be greater than a decimal number with fewer digits?
Answer:
Not always. As 40.3 is greater than 39.6789, while number of digits in 40.3 is less than the number of digits in 39.6789.
7. Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums, and 0.05 kg of ginger. Calculate the total weight of the items she bought.
Answer:
Weight of various items purchased by
So, the total weight of the items Mahi bought = 1.30 kg.
8. Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk to a milk dairy in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity of milk supplied to the dairy in the last three days.
Answer:
Quantity of milk supplied in first three days = 3.79 L, 4.2 L, 4.25 L
∴ Total quantity supplied in these three days
In 6 days, Pinto supplies 25 litres of milk.
To get the total quantity of milk supplied to the dairy in the last three days subtract quantity supplied in 3 days from those supplied in 3 days.
∴ , we get
Thus, Pinto supplied 12.76 L of milk in last 3 days.
9. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
Answer:
Weight of Tinku in January = 35.75 kg
Weight of Tinku in February = 34.50 kg.
Since, 34.50 kg is less than 35.75 kg.
Hence, Tinku has lost weight.
To get the change in weight we subtract February’s weight from January’s weight.
We get
So, Tinku has lost 1.25 kg.
10. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ______, ______.
Answer:
5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ______, ______.
Here,
5.5 + (0.9) = 6.4
6.4-(0.01) = 6.39
6.39 + (0.9) = 7.29
7.29-(0.01) = 7.28
7.28 + (0.9) = 8.18
8.18-(0.01) = 8.17
So, the next number will be,
8.17 + (0.9) = 9.07
and second next number will be,
9.07-(0,01) = 9.06
11. How many millimeters make 1 kilometer?
Answer:
1 kilometer = 1000 meter
1 meter = 100 cm
1 cm = 10 mm
So, 1 kilometer = 10,00,000 mm
Therefore, 10,00,000mm make 1 km.
12. Indian Railways offers optional travel insurance for passengers who book e-tickets. It costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
Answer:
Cost of optional travel insurance = 45 paise Number of passengers who opt for insurance = 100,000
Hence, the total insurance fee paid
= 45 × 100000 paise
= 4500000 paise
= ₹ 45000.
So, total insurance fee paid
= ₹ 45,000.
13. Which is greater?
(a) \(\frac{10}{1000}\) or \(\frac{1}{10}\) ?
(b) One-hundredth or 90 thousandths?
(c) One-thousandth or 90 hundredths?
Answer:
(a) \(\frac{1}{10}\) is greater than \(\frac{10}{1000}\) as 10 units of \(\frac{1}{10}\) make one complete unit while 100 units of \(\frac{10}{1000}\) make one complete unit.
(b) One-hundredth or 90 thousandths 90 thousandths is greater than one-hundredth, as 90 thousand = \(\frac{90}{1000}\) = \(\frac{9}{100}\) = 9 one-hundredths.
(c) One-thousandths or 90 hundredths
90 hundredths = 90 × \(\frac{1}{100}\)
= 9 × \(\frac{1}{10}\)
One-thousandth = \(\frac{1}{1000}\)
Clearly 9 × \(\frac{1}{10}\) > \(\frac{1}{1000}\)
So, 90 hundredths is greater than one thousandth.
14. Write the decimal forms of the quantities mentioned (an example is given):
(a) 87 ones, 5 tenths and 60 hundredths = 88.10
(b) 12 tens and 12 tenths
(c) 10 tens, 10 ones, 10 tenths, and 10 hundredths
(d) 25 tens, 25 ones, 25 tenths, and 25 hundredths
Answer:
(a) 87 ones, 5 tenths and 60 hunderdths
= 88.01(87 × 1 + 5 × \(\frac{1}{10}\) + 60 × \(\frac{1}{100}\))
(b) 12 tens and 12 tenths
= 12 × 10 + 12 × \(\frac{1}{10}\)
= 120 + 1.2
= 121.2
(c) 10 tens, 10 ones, 10 tenths and 10 hundredths
= 10 × 10 + 10 × 1 + 10 × \(\frac{1}{10}\) + 10
× \(\frac{1}{100}\)
= 100 + 10 + 1 + 0.1
= 111.1
(d) 25 tens, 25 ones, 25 tenths and 25 hundredths
= 25 × 10 + 25 × 1 + 25 × \(\frac{1}{10}\) + 25
× \(\frac{1}{100}\)
= 250 + 25 + 2.5 + 0.25
= 277.75
15. Using each digit 0-9 not more than once, fill the boxes below so that the sum is closest to 10.5:
Answer:
16. Write the following fractions in decimal form:
(a) \(\frac{1}{2}\)
(b) \(\frac{3}{2}\)
(c) \(\frac{1}{4}\)
(d) \(\frac{3}{4}\)
(e) \(\frac{1}{5}\)
(f) \(\frac{4}{5}\)
Answer:
(a) \(\frac{1}{2}\) = 0.5
(b) \(\frac{3}{2}\) = 1.5
(c) \(\frac{1}{4}\) = 0.25
(d) \(\frac{3}{4}\) = 0.75
(e) \(\frac{1}{5}\) = 0.20
(f) \(\frac{4}{5}\) = 0.8