Chapter 3: A Peek Beyond the Point
When whole units are too big to measure exactly, we split them into tenths, hundredths and thousandths. In this chapter we see how this extends our place value system to the decimal point, convert between units, locate and compare decimals, add and subtract them, and spot notations that only look like decimals.
In this chapter you will
- read and write tenths, hundredths and thousandths as decimals
- convert mm, cm, m, g, kg and paise using decimals
- place decimals on a number line and compare them
- add, subtract and estimate with decimals
Topics
- A Tenth Part NCERT 3.1–3.2
Split a unit into 10 equal parts: each is one-tenth (1/10).
- A Hundredth Part and Decimal Place Value NCERT 3.3–3.4
Each place is 10 times the place on its right: … 10, 1, 1/10, 1/100, 1/1000.
- Units of Measurement NCERT 3.5
1 mm = 0.1 cm; 1 cm = 0.01 m; 1 g = 0.001 kg; 1 paisa = ₹0.01.
- Locating and Comparing Decimals NCERT 3.6
Zeros at the end of a decimal don't change it (0.2 = 0.20); zeros right after the point do (0.02).
- Addition and Subtraction of Decimals NCERT 3.7
Line up the decimal points (fill with zeros), then add or subtract as with whole numbers.
- More on the Decimal System NCERT 3.8
Watch the point and the unit: 0.5 mg is 10 times 0.05 mg.
Key words
- Tenth
- one of 10 equal parts of a unit: 1/10 = 0.1
- Hundredth
- 1/100 = 0.01
- Thousandth
- 1/1000 = 0.001
- Decimal point
- the dot that separates the whole part from the fractional part
- Decimal system
- place value based on 10, going on to tenths, hundredths …
- Place value
- what a digit is worth because of its place
Summary
- 10 tenths = 1 unit; 10 hundredths = 1 tenth; 100 hundredths = 1 unit.
- 7.05 = 7 units and 5 hundredths; 0.2 = 0.20, but 0.02 is different.
- 1 mm = 0.1 cm, 1 cm = 0.01 m, 1 g = 0.001 kg, 1 paisa = ₹0.01.
- Line up the points to add or subtract; compare digit by digit from the left.