Chapter 3 A Peek Beyond the Point (Class 7 - Latest Maths NCERT (Ganita Prakash I) Solutions)

Question . Write the measurements of the objects shown in the picture:

Question. 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) $\frac{4}{10}$

Question. Arrange the following lengths in increasing order:

$4 \frac{1}{10}$, $\frac{4}{10}$, $\frac{41}{10}$, $41 \frac{1}{10}$

Question. 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

Question. 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?

Question. Observe the given sequences of numbers. Identify the change after each term and extend the pattern:

(a) $4, 4 \frac{3}{10}, 4 \frac{6}{10}$, _________, _________, _________, _________

(b) $8 \frac{2}{10}, 8 \frac{7}{10}, 9 \frac{2}{10}$, _________, _________, _________, _________

(c) $7 \frac{6}{10}, 8 \frac{7}{10}$, _________, _________, _________, _________

(d) $5 \frac{7}{10}, 5 \frac{3}{10}$, _________, _________, _________, _________

(e) $13 \frac{5}{10}, 13, 12 \frac{5}{10}$, _________, _________, _________, _________

(f) $11 \frac{5}{10}, 10 \frac{4}{10}, 9 \frac{3}{10}$, _________, _________, _________, _________

Question. How many one-hundredths make one-tenth? Can we also say that the length is 4 units and 45 one-hundredths?

Question. 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.

Question. For the lengths shown below write the measurements and read out the measures in words.

Question. In each group, identify the longest and the shortest lengths. Mark each length on the scale.

(a) $\frac{3}{10}, \frac{3}{100}, \frac{33}{100}$

(b) $3 \frac{1}{10}, \frac{30}{10}, 1 \frac{3}{10}$

(c) $\frac{45}{100}, \frac{54}{100}, \frac{5}{10}, \frac{4}{10}$

(d) $3 \frac{6}{10}, 3 \frac{6}{100}, 3 \frac{6}{10} + \frac{6}{100}$

(e) $\frac{8}{10} + \frac{2}{100}, \frac{9}{100}, 1 \frac{8}{100}$

(f) $7 \frac{3}{10} + \frac{5}{100}, 7 \frac{5}{10}, 7 \frac{41}{100}$

(g) $\frac{65}{10} + \frac{15}{100}, 5 \frac{87}{100}, 5 \frac{7}{100}$

Question. Find the sums and differences:

(a) $\frac{3}{10} + 3 \frac{4}{100}$

(b) $9 \frac{5}{10} \frac{7}{100} + 2 \frac{1}{10} \frac{3}{100}$

(c) $15 \frac{6}{10} \frac{4}{100} + 14 \frac{3}{10} \frac{6}{100}$

(d) $7 \frac{7}{100} - 4 \frac{4}{100}$

(e) $8 \frac{6}{100} - 5 \frac{3}{100}$

(f) $12 \frac{6}{100} \frac{2}{100} - \frac{9}{10} \frac{9}{100}$

Question. 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 $7 \frac{7}{1000}$

Question. Write these quantities in decimal form:

(a) 234 hundredths

(b) 105 tenths

Question. Fill in the blanks below (mm $\leftrightarrow$ cm):

Question. Fill in the blanks below (cm $\leftrightarrow$ m):

Question. How many mm does $1$ meter have?

Question. Can we write $1$ mm = $\frac{1}{1000}$ m?

Question. Fill in the blanks below (g $\leftrightarrow$ kg):

Question. Fill in the blanks below (rupee $\leftrightarrow$ paise):

Question. Name all the divisions between $1$ and $1.1$ on the number line.

Question. Identify and write the decimal numbers against the letters $A$, $B$, $C$, and $D$.

Question. We can figure this out by looking at the quantities these numbers represent using place value.

We can see that $0.2$, $0.20$, and $0.200$ are all equal as they represent the same quantity, i.e., $2$ tenths. But $0.2$, $0.02$, and $0.002$ are different.

Can you tell which of these is the smallest and which is the largest?

Question. Which of these are the same: $4.5$, $4.05$, $0.405$, $4.050$, $4.50$, $4.005$, $04.50$?

Question. Identify the decimal number in the last number line in Figure (b) denoted by ‘?’.

Question. Make such number lines for the decimal numbers:

(a) $9.876$

(b) $0.407$

Question. In the number line shown below, what decimal numbers do the boxes labelled ‘a’, ‘b’, and ‘c’ denote?

Question. Using similar reasoning find out the decimal numbers in the boxes below for labels ‘d’, ‘e’, ‘f’, ‘g’, and ‘h’.

Question. Which decimal number is greater?

(a) $1.23$ or $1.32$

(b) $3.81$ or $13.800$

(c) $1.009$ or $1.090$

Question. Consider the decimal numbers $0.9$, $1.1$, $1.01$, and $1.11$. Which of the above is closest to $1.09$?

Question. Which among these is closest to $4$: $3.56$, $3.65$, $3.099$?

Question. Which among these is closest to $1$: $0.8$, $0.69$, $1.08$?

Question. 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 $25$.

Question 1. Find the sums

(a) $5.3 + 2.6$

(b) $18 + 8.8$

(c) $2.15 + 5.26$

(d) $9.01 + 9.10$

(e) $29.19 + 9.91$

(f) $0.934 + 0.6$

(g) $0.75 + 0.03$

(h) $6.236 + 0.487$

Question 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) $6.236 - 0.487$

Question. Observe this sequence of decimal numbers and identify the change after each term.

$4.4, 4.8, 5.2, 5.6, 6.0, \dots$

We can see that $0.4$ is being added to a term to get the next term. Continue this sequence and write the next $3$ terms.

Question. Similarly, identify the change and write the next $3$ terms for each sequence given below. Try to do this computation mentally.

(a) $4.4, 4.45, 4.5, \dots$

(b) $25.75, 26.25, 26.75, \dots$

(c) $10.56, 10.67, 10.78, \dots$

(d) $13.5, 16, 18.5, \dots$

(e) $8.5, 9.4, 10.3, \dots$

(f) $5, 4.95, 4.90, \dots$

(g) $12.45, 11.95, 11.45, \dots$

(h) $36.5, 33, 29.5, \dots$

Question 1. Convert the following fractions into decimals:

(a) $\frac{5}{100}$

(b) $\frac{16}{1000}$

(c) $\frac{12}{10}$

(d) $\frac{254}{1000}$

Question 2. Convert the following decimals into a sum of tenths, hundredths and thousandths:

(a) $0.34$

(b) $1.02$

(c) $0.8$

(d) $0.362$

Question 3. What decimal number does each letter represent in the number line below?

Question 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

Question 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 $1000$

Question 6. Will a decimal number with more digits be greater than a decimal number with fewer digits?

Question 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.

Question 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.

Question 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?

Question 10. Extend the pattern: $5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, \dots, \dots$

Question 11. How many millimeters make $1$ kilometer?

Question 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?

Question 13. Which is greater?

(a) $\frac{10}{1000}$ or $\frac{1}{10}$?

(b) One-hundredth or $90$ thousandths?

(c) One-thousandth or $90$ hundredths?

Question 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

Question 15. Using each digit $0 - 9$ not more than once, fill the boxes below so that the sum is closest to $10.5$:

Question 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) $\frac{4}{5}$