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Many Class 7 students can add 2.7 and 3.5 but freeze when asked whether 0.45 or 0.5 is bigger. The trouble is rarely the adding. It is not yet seeing what each digit after the point is worth. This post explains place value for decimals the way the new NCERT book does, works through comparing, adding and subtracting, and lists the slips to watch for.
Where are decimals in the new Class 7 maths book?
NCERT's new Class 7 book is Ganita Prakash, in two parts. The Part 1 contents page lists Chapter 3, "A Peek Beyond the Point", and the book's note says the chapter "introduces the usage of the decimal point and additions and subtractions involving decimal numbers". Multiplying and dividing decimals come later, in Chapter 4 of Part 2, "Another Peek Beyond the Point". If your school uses a different book, check with your teacher which chapter you are on.
The chapter itself is free as a PDF: Chapter 3, A Peek Beyond the Point. It starts with a screw that is "between 2 cm and 3 cm" and asks how to say exactly how long it is.
What do the digits after the point mean?
Split one unit into 10 equal parts and each part is one tenth. Split each tenth into 10 again and each tiny part is one hundredth, so 100 of them make a unit. The chapter shows the same length written three ways:
1 and 1 tenth and 4 hundredths
1 and 14 hundredths
114 hundredths
All three are 1.14. In the same way, 4.45 is 4 + 4/10 + 5/100, which is 445/100. Each place to the right is worth one tenth of the place before it, just as with whole numbers.
Why do so many students think 0.45 is bigger than 0.5?
Because 45 is bigger than 5. Lauren Resnick and colleagues studied exactly this in Conceptual bases of arithmetic errors: the case of decimal fractions (1989). They found two families of errors. "Whole number errors" come from applying rules for ordinary multidigit numbers, such as "more digits means bigger". "Fraction errors" come from trying to read decimals as fractions in a muddled way. They argue such errors are a natural part of learning and are useful clues for a teacher.
A later study by Kelley Durkin and Bethany Rittle-Johnson, The effectiveness of using incorrect examples to support learning about decimal magnitude (2012), tutored 74 students in Grades 4 and 5. Students who compared a wrong worked example with a correct one learned the procedures and concepts better, and held fewer misconceptions, than students who compared two correct examples.
How do you compare two decimals? A worked example
Which is greater, 6.456 or 6.465? The book's method is to compare place by place, starting from the left.
Units: both have 6. Move right.
Tenths: both have 4. Move right.
Hundredths: 5 against 6. The second number has more.
So 6.465 > 6.456. You can stop at the first place where the digits differ, because everything after it is worth less than one unit of that place.
Now try one from the chapter: which of 0.9, 1.01, 1.1 and 1.11 is closest to 1? In order, 0.9 < 1 < 1.01 < 1.1 < 1.11. The number 1.01 is 1/100 away from 1, while 0.9 is 10/100 away, so 1.01 is closest.
How do you add and subtract decimals?
Line up the decimal points, so tenths sit under tenths, then add as you would whole numbers.
2.7 + 3.5: 7 tenths + 5 tenths = 12 tenths, which is 1 unit and 2 tenths. Write 2, carry 1. Then 2 + 3 + 1 = 6. Answer: 6.2.
3.5 − 2.7: you cannot take 7 tenths from 5 tenths, so turn 1 unit into 10 tenths: 15 − 7 = 8 tenths, and 2 − 2 = 0. Answer: 0.8.
34.505 − 18.1: write 18.1 as 18.100 so the places match. 34.505 − 18.100 = 16.405.
17 − 0.05: write 17 as 17.00. 17.00 − 0.05 = 16.95.
Estimate first. The chapter points out that 25.936 + 8.202 must be more than 25 + 8 = 33 and less than 26 + 9 = 35. The real sum is 34.138, which fits.
What mistakes should you watch for?
Longer is larger. 0.125 is less than 0.5. Compare tenths first.
Lining up the last digit instead of the point. In 34.505 − 18.1, the digit after the point in 18.1 is in the tenths place, so it goes under the 5 tenths, not the last 5.
Reading time as a decimal. The book's example: "4.5 hours after noon" is 4:30, not 4:50, because 0.5 of an hour is 30 minutes.
Mixing units. A width of 2 ft 5 in is not 2.5 ft. Since 1 ft is 12 inches, 2.5 ft is 2 ft 6 in.
Moving the point by one place. The chapter warns that reading 0.05 mg of a medicine as 0.5 mg means a dose 10 times too large.
A 15-minute practice routine
Two minutes of place value. Write three decimals as sums, such as 3.07 = 3 + 0/10 + 7/100.
Five comparisons. Order sets like 0.3, 0.03, 0.33 and say which place decided each one.
Find the wrong one. Take a worked answer with a slip (from a friend, your old homework, or one you make up) and explain what went wrong. That is the comparison Durkin and Rittle-Johnson studied.
Mixed sums. Do four additions or subtractions mixed with two questions from earlier chapters. Mixing topics helped learning a week later in Rohrer and Taylor's experiments (2007).
If place value itself still feels shaky, the Fermi Concept Library covers every concept in mathematics, each with its own lesson and its place in the map, so you can step back to tenths and hundredths before moving on. For the order of operations that the next chapters build on, see our guide to arithmetic expressions in Class 7.
Tonight, measure three things at home with a ruler, write each length in centimetres as a decimal, and put them in order.
