More on the Decimal System

Class 7 Maths · Chapter 3: A Peek Beyond the Point · NCERT Ganita Prakash section 3.8

Learn

When a point slips: a decimal or unit mistake can be serious. A city office once paid out money counted in cents instead of euros, sending about 100 times too much. An aeroplane was loaded with fuel in pounds instead of kilograms and ran short in the air. Reading 0.05 mg of medicine as 0.5 mg gives 10 times the dose!

0.5 = 10 × 0.05

Decimal-looking, but not decimal: "4.5 hours after noon" is 4:30 p.m., because 0.5 hour = 30 minutes (not 4:50!). A door "2.5 ft" wide is 2 ft 6 inches, since 1 ft = 12 inches. In cricket, "5.5 overs" means 5 overs and 5 balls, because an over has 6 balls: here the point is not a decimal point at all.

0.5 hour = 30 min · 0.5 ft = 6 in

A pinch of history: fractions with denominators 10, 100, 1000 appear in the works of Indian mathematicians such as Śhrīdharāchārya (8th century). Around 950 CE, al-Uqlīdisī described decimal notation in his "Book of Chapters on Indian Arithmetic". The point (·) became common in the 16th century; some countries still use a comma instead (1 000,5).

Fractions as decimals: 1/2 = 5/10 = 0.5, 3/2 = 1.5, 1/4 = 25/100 = 0.25, 3/4 = 0.75, 1/5 = 2/10 = 0.2, 4/5 = 0.8. Make the denominator 10, 100 or 1000 first, then write the decimal.

1/4 = 25/100 = 0.25

Explore: a real decimal or not?

1. Sort each: is the point a decimal point?

Remember

• Watch the point and the unit: 0.5 mg is 10 times 0.05 mg.
• Not every point is a decimal point: 0.5 hour = 30 min, 5.5 overs = 5 overs and 5 balls.

Quick check

A train leaves "2.5 hours after 10 a.m." When is that?

1. 12:30 p.m.
2. 12:50 p.m.
3. 12:05 p.m.
4. 12:25 p.m.

Think about it

If 1 lakh people each pay 45 paise for travel insurance, how much is that in rupees?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.