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CBSE Class 7 · Mathematics

A Peek Beyond the Point

Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “A Peek Beyond the Point” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 7
  • Easy level
  • 8 concepts

1The Need for Smaller Units

When a unit is too big, you need a smaller one: a metre cut into tenths, a rupee into paise. The point is the mark that starts those smaller units.

Calling 3.2 “three point two” without a unit-story is a chant, not a need.

Figure. A leftover shorter than one unit still has size. The tenths house after the decimal point names that leftover as a part of one.

How it works

  1. See a leftover smaller than 1 of the old unitThe need.
  2. Name a tenth or hundredth of that unitThe smaller unit.
  3. Write it after a point3.2 m is 3 m and 2 tenths.

2A Tenth Part

A tenth is 1/10 of the unit. 0.1 and 1/10 name the same part. The first house after the point is tenths.

0.1 is not 1 ten.

Figure. A tenth is one of ten equal parts of one. In 7.6 the digit just after the point is tenths, so it names six tenths, not six.

How it works

  1. Take the unit1.
  2. Cut into 10 equal partsEach is 0.1.
  3. Write 0.1 in the tenths houseFirst after the point.

3A Hundredth Part

A hundredth is 1/100 of the unit. 0.01 lives in the second house after the point. Ten hundredths make one tenth.

0.01 is not 0.1 — that is a house-slide.

Figure. A hundredth is one of ten equal parts of a tenth. The lower bar is that first tenth opened up — not to the same scale as the unit above. The second digit after the point names hundredths.

How it works

  1. Cut the unit into 100 equal partsEach is 0.01.
  2. Park it in the hundredths houseSecond after the point.
  3. Trade 10 hundredths for 1 tenthSame land-of-tens idea.

4Decimal Place Value

Decimal place value is houses: ones | tenths | hundredths | thousandths. The point is the fence, not a plus.

Reading 3.14 as 314 is a fence you ignored.

Figure. 7.25 is 7 ones, 2 tenths, 5 hundredths. The point starts the tenths house. Swapping 2 and 5 writes 7.52 — a different number.

How it works

  1. Write ones left of the pointThe whole units.
  2. Write tenths, then hundredths to the rightThe smaller houses.
  3. Read each digit by its house3 + 1 tenth + 4 hundredths.

5Units of Measurement

The same decimal writing can measure different units: 2.5 m, 2.5 kg. The number is the count of units and tenths; the unit word is required or the number is mute.

2.5 without a unit could be metres or kilograms.

Figure. Metres and money already use houses after the point. 1.5 m is 1 metre and 5 tenths; Rs 6.40 is 6 rupees and 40 paise — two hundredths-houses of a rupee.

How it works

  1. Write the decimal2.5.
  2. Attach the unit you meantm, or kg, or L.
  3. Convert only with a named trade (100 cm = 1 m)Do not invent a trade.

6Locating and Comparing Decimals

On a number line, 3.2 sits past 3, two tenths toward 4. Compare decimals house by house from the left: 3.20 and 3.2 are the same number; 3.2 and 3.02 are not.

More digits does not mean larger — 3.09 < 3.1.

Figure. Locate decimals on the same line as whole numbers. 0.3 sits left of 0.7 because three tenths is less than seven tenths. Compare from the left house first.

How it works

  1. Line up the pointsSame fence.
  2. Compare ones, then tenths, then hundredthsFirst miss wins.
  3. Fill empty houses with 0 if you need a fair look3.2 = 3.20.

3.2 versus 3.02

Which is larger, 3.2 or 3.02?

  • Onesboth 3
  • Tenths2 vs 0
  • Larger3.2

Pro tip. Compare from the left of the fence. Extra zeros on the right do not grow the number.

7Addition and Subtraction of Decimals

Add and subtract decimals by lining up the points. 2.4 + 0.35 is 2.75, not 2.75 only if the houses match. You may write 2.40 to see the hundredths.

Adding 24 + 35 and dropping a point back is a house-slide.

Figure. Line the points up so tenths sit under tenths. 1.4 + 0.8 is 2.2: four tenths and eight tenths make twelve tenths, which trades for one more one and two tenths.

How it works

  1. Line up the pointsOnes under ones.
  2. Add each houseCarry if a house passes 9.
  3. Put the point in the lined-up placeThe sum.

8More on the Decimal System

The decimal system keeps going: thousandths and beyond. This chapter needs tenths and hundredths you can place. A later peek will multiply and divide these writings.

Claiming you finished every decimal house today is too big.

Figure. 2.35 expands as 2 + 3/10 + 5/100. Each digit keeps its house. The houses are powers of ten on both sides of the point.

How it works

  1. Use tenths and hundredths fluentlyThis peek.
  2. Allow thousandths if a measurement needs themA finer house.
  3. Leave × and ÷ of decimals for the later official peekNot this chapter’s whole job.
3.2 compared with 3.02 is
  1. Larger — tenths 2 beats tenths 0
  2. Smaller
  3. The same

Compare from the ones, then tenths.

Notes

  • The official chapter title is “A Peek Beyond the Point”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • 0.1 = 1/10
  • 0.01 = 1/100
  • 10 hundredths = 1 tenth

Recap

Hold these pegs from the official chapter “A Peek Beyond the Point”. The wording is ExamMaster’s teaching, not a textbook recap.

The Need for Smaller Units
When a unit is too big, you need a smaller one: a metre cut into tenths, a rupee into paise.
A Tenth Part
A tenth is 1/10 of the unit. 0.1 and 1/10 name the same part. The first house after the point is tenths.
A Hundredth Part
A hundredth is 1/100 of the unit. 0.01 lives in the second house after the point. Ten hundredths make one tenth.
Decimal Place Value
Decimal place value is houses: ones | tenths | hundredths | thousandths.
Units of Measurement
The same decimal writing can measure different units: 2.5 m, 2.5 kg.
Locating and Comparing Decimals
On a number line, 3.2 sits past 3, two tenths toward 4.

Practise A Peek Beyond the Point

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