A Peek Beyond the Point — Mastery

Q1. Why a unit is divided into 10 parts rather than 4 or 8. The reason is

• A. Ten is easier to remember than four
• B. Ten matches the special role of 10 in the Indian place value system
• C. Four parts cannot give accurate measurements
• D. Eight parts give fractions that cannot be added

Q2. Following the rule the mixed number 4 1/10 written as an improper fraction with denominator 10 is

• A. 5/10
• B. 41/10
• C. 14/10
• D. 40/10

Q3. Identify the pattern in the sequence 4, 4 3/10, 4 6/10,.... What is the next term?

• A. 4 9/10
• B. 5
• C. 5 1/10
• D. 4 8/10

Q4. Each one-hundredth is obtained by

• A. Splitting a whole unit directly into 50 equal parts
• B. Splitting each one-tenth into 10 equal parts
• C. Splitting each one-thousandth into 10 equal parts
• D. Folding a one-tenth strip in half

Q5. On, a length is written as 1 14/100. How is it read aloud?

• A. One and fourteen one-tenths
• B. One and fourteen-hundredths
• C. One hundred and fourteen-hundredths
• D. One point fourteen

Q6. Using the place-value table the place value of the digit 5 in the decimal 7.05 is

• A. 5 hundredths
• B. 5 tenths
• C. 5 ones
• D. 5 thousandths

Q7. Asks: what fraction is obtained when 1/100 is split into 10 equal parts?

• A. 1/10
• B. 1/100
• C. 1/1000
• D. 1/10000

Q8. The table asks: 99 paise = Rs ____. Which value goes in the blank?

• A. Rs 9.9
• B. Rs 0.099
• C. Rs 99.0
• D. Rs 0.99

Q9. The conversion ___ paise = Rs 0.05. The missing value is

• A. 0.5 paise
• B. 5 paise
• C. 50 paise
• D. 500 paise

Q10. On a number line is drawn with 1 and 2 marked. To locate 1.4 between them, the segment from 1 to 2 should be divided into

• A. 100 equal parts; take the 14th
• B. 4 equal parts; take the 1st
• C. 10 equal parts; take the 4th
• D. 10 equal parts; take the 1st

Q11. Asks: name all divisions between 1 and 1.1 on a number line where the unit is divided into 100 parts. The marks between 1 and 1.1 are

• A. 1.1, 1.2, ..., 1.9
• B. 1.01, 1.02, ..., 1.09
• C. 1.001, 1.002, ..., 1.009
• D. 1.10, 1.20, ..., 1.90

Q12. Question 4(a) asks to arrange in descending order: 11.01, 1.011, 1.101, 11.10, 1.01. The correct descending order is

• A. 11.10, 11.01, 1.101, 1.011, 1.01
• B. 11.10, 11.01, 1.101, 1.01, 1.011
• C. 11.01, 11.10, 1.101, 1.011, 1.01
• D. 1.011, 1.01, 1.101, 11.01, 11.10

Q13. Find the sum 9.01 + 9.10 from the Figure it Out exercise on

• A. 18.11
• B. 9.11
• C. 18.20
• D. 18.01

Q14. Reasoning along Sonu's lines the difference of two decimals A and B (with A > B) lies between which pair of whole-number expressions?

• A. (int A - int B) - 1 and (int A - int B) + 1
• B. (int A - int B) and (int A - int B) + 1
• C. (int A + int B) and (int A + int B) + 1
• D. 0 and int A - int B

Q15. Traces the history of decimal fractions. They were used in the works of which 8th-century Indian mathematician on arithmetic and algebra?

• A. Brahmagupta
• B. Aryabhata
• C. Shridharacharya
• D. Bhaskara II

Q16. Using 1 cm = 0.01 m write 36 cm as a decimal fraction of a metre.

• A. 3.6 m
• B. 0.036 m
• C. 36.00 m
• D. 0.36 m

Q17. Question 4(d) asks to arrange in descending order: 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m. The correct order is

• A. 33.331, 33.31, 33.313, 33.133, 33.13
• B. 33.31, 33.331, 33.313, 33.13, 33.133
• C. 33.331, 33.313, 33.133, 33.31, 33.13
• D. 33.331, 33.313, 33.31, 33.133, 33.13

Q18. Question 10 asks to extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ___, ___. The next two terms are

• A. 5.07 and 5.06
• B. 5.17 and 5.16
• C. 7.07 and 6.06
• D. 7.07 and 7.06

Q19. Question 1(a) of the Figure it Out asks to convert 5/100 into a decimal. The correct decimal is

• A. 0.5
• B. 0.05
• C. 0.005
• D. 5.00

Q20. Question 1(b) asks to convert 16/1000 into a decimal. The correct value is

• A. 1.6
• B. 0.16
• C. 16.00
• D. 0.016

Q21. Question 1(c) asks to convert 12/10 into a decimal. The correct value is

• A. 1.2
• B. 0.12
• C. 12.10
• D. 0.012

Q22. Question 1(d) asks to convert 254/1000 into a decimal. already shows 254 g = 0.254 kg. The correct decimal is

• A. 2.54
• B. 25.4
• C. 0.0254
• D. 0.254

Q23. Question 7 Mahi buys 0.25 kg beans, 0.3 kg carrots, 0.5 kg potatoes, 0.2 kg capsicums and 0.05 kg ginger. The total weight of her items is

• A. 1.05 kg
• B. 1.25 kg
• C. 1.50 kg
• D. 1.30 kg

Q24. Records the 2013 Amsterdam City Council mishap: a program processed payments in euro-cents instead of euros, sending out 188 million euros instead of 1.8 million. By what factor was the amount sent over the intended one?

• A. 10 times
• B. 1000 times
• C. Same amount, only the unit changed
• D. About 100 times

Q25. A 1983 Air Canada Boeing 767 fuel mishap where ground staff loaded 22,300 pounds instead of kilograms (1 pound is about 0.453 kg). The fuel actually loaded was approximately

• A. Twice what was needed
• B. About one-tenth of what was needed
• C. Exactly the right amount
• D. About half of what was needed

Q26. A girl measures the door opening as 2 ft 5 inches but tells the carpenter to make a door 2.5 ft wide. The carpenter makes a 2 ft 6 inches door (since 0.5 ft = 6 inches) which does not close fully. The mistake was

• A. Reading the decimal 2.5 ft as if the digit after the point meant inches instead of tenths of a foot
• B. Confusing feet with metres
• C. Forgetting that 1 ft = 10 inches
• D. Rounding 2 ft 5 inches up to the next foot

Q27. Rohit in Class 7 writes that 3.099 > 3.65 because 3.099 has more digits after the decimal point. Question 6 directly addresses this. The best diagnostic comment a teacher in Rampur can make is

• A. Rohit is correct; longer decimals are always greater.
• B. Rohit is wrong because all decimals less than 4 are equal.
• C. The question cannot be decided without a calculator.
• D. Rohit is wrong; comparison goes place by place from the left, and 3.65 has 6 tenths versus 3.099's 0 tenths, so 3.65 > 3.099.

Q28. A student says 0.2 ≠ 0.20 because the second number has an extra zero. The 'zero dilemma' resolves this. The most effective teacher response is

• A. Tell the student to ignore zeros after the decimal point and move on.
• B. Mark the wrong answer with a red cross and write the correct answer above it.
• C. Tell the student that decimals cannot be compared when the number of digits differs.
• D. Show on a 10-part number line that 0.2 = 2 tenths = 20 hundredths = 0.20, but warn that 0.2 ≠ 0.02 because the zero now sits between the point and the 2.

Q29. A Class 7 teacher in Pune wants to introduce decimals for the first time, following the approach of Ganita Prakash Chapter 3. The best first activity is

• A. Write the symbol 0.1 on the board and ask the class to memorise that it equals one-tenth.
• B. Drill the rule 'shift the decimal point one place right when multiplying by 10' on the board.
• C. Hand out scales (rulers) marked in cm and mm, and let students measure pencils, books and small objects whose length is not a whole cm.
• D. Ask the class to recite the place-value table up to the thousandths place.

Q30. Examine the order in which Chapter 3 develops a child's understanding of decimals: I. Place-value table for 7.05 and decimal notation with the decimal point. II. Folding a paper strip into 10 equal parts and naming each part one-tenth. III. Sonu's screw problem showing why whole-cm marks are not accurate enough. Which sequence of teaching mirrors the chapter's order?

• A. I, II, III
• B. II, III, I
• C. III, I, II
• D. III, II, I