Head office, Rana Pratap Bagh, Delhi011 2721 1512+91 97116 99511

Decimals and percentages

Understand tenths and hundredths, change between fractions, decimals and percentages, and work out discounts.

Get the whole book: Maths for classes 6 to 8 (4 lessons, free to print)

Let us begin

The big idea

Prices, marks and discounts all use decimals and percentages. They are just other ways of writing fractions, and you can move between them easily.

A decimal uses a point to show parts smaller than one. In 2.35 the 2 is ones, the 3 is tenths and the 5 is hundredths. So 2.35 is 2 + 3/10 + 5/100. Each place to the right is ten times smaller.

To compare decimals, compare the whole parts first, then tenths, then hundredths. 0.6 is the same as 0.60, which is bigger than 0.58. To add or subtract decimals, line up the decimal points.

Per cent means per hundred. 35% means 35 out of 100, which is 35/100 = 0.35. To change a fraction to a percentage, make the denominator 100 or multiply by 100. For example 3/4 = 75/100 = 75%.

To find a percentage of an amount, multiply by the percentage and divide by 100. 10% of an amount is that amount divided by 10. Discounts and marks use this.

35 out of 100 as a gridA square made of 100 small boxes in 10 rows of 10. The first 35 boxes are shaded. Beside it, the same amount is written as 35 out of 100, 35 per cent, 0.35 and 7 over 20. 35 out of 100 35% 0.35 35/100 = 7/20 Same amount, three ways.
35 shaded boxes out of 100 can be written as 35%, 0.35 or 35/100, which simplifies to 7/20.

Worked examples

See how it works

  1. Fraction, decimal and percentage: 3/4

    3 ÷ 4 = 0.75. And 0.75 = 75/100 = 75%. So 3/4 = 0.75 = 75%.

  2. Percentage of an amount

    Find 20% of Rs 450. 450 × 20 ÷ 100 = 9000 ÷ 100 = 90. So 20% of Rs 450 is Rs 90.

  3. Comparing decimals

    Which is bigger, 0.6 or 0.58? Write 0.6 as 0.60. Compare 60 hundredths with 58 hundredths. 0.60 is bigger. So 0.6 > 0.58.

  4. A discount

    A shirt costs Rs 600. There is a 15% discount. Discount = 600 × 15 ÷ 100 = 90. Price to pay = 600 − 90 = Rs 510.

Try it at home

Discount detective

You will need

  • An old shop bill, a newspaper advertisement or a list of prices you write yourself
  • A pencil and paper

What to do

  1. Choose three prices, for example Rs 80, Rs 250 and Rs 400.
  2. Find 10% of each by dividing by 10.
  3. Find 50% of each by halving. Then find 25% by halving again.
  4. Work out the price after a 10% discount for each item.
  5. Check one answer by working it out a different way.

Ask a grown-up: An adult can show a real shop bill. No money needs to be handled.

Fun fact

The word per cent comes from the Latin words per centum, which mean by the hundred.

Practice sheet

Check what you learned

Write your answers in a notebook, or print this sheet and write on it. When you finish, mark your work with the answer key.

Practice sheet: Decimals and percentages (Classes 6-8, Maths)

  1. Write 7/10 as a decimal.
  2. Write 0.25 as a fraction in its simplest form.
  3. Which is greater, 0.4 or 0.39?
  4. Find 2.5 + 1.75.
  5. Find 5.0 − 2.35.
  6. Write 1/2 as a percentage.
  7. What is 40% of 250?
  8. A student scores 45 out of 50. What is the percentage?
  9. A book costs Rs 250. There is a 10% discount. What do you pay?
  10. Write 0.08 as a percentage.
  11. Put in order, smallest first: 0.5, 0.05, 0.55.

Answer key

Answers: Decimals and percentages

Do the practice sheet first, then check here. If an answer is different from yours, read the lesson again and try once more.

  1. 0.7
  2. 1/4 (25/100 divided top and bottom by 25).
  3. 0.4 (0.40 is more than 0.39).
  4. 4.25
  5. 2.65 (5.00 − 2.35).
  6. 50%
  7. 100 (250 × 40 ÷ 100).
  8. 90% (45/50 = 90/100).
  9. Rs 225 (10% of 250 is 25, and 250 − 25 = 225).
  10. 8%
  11. 0.05, 0.5, 0.55.

What next

Keep learning

Get the whole book

All 4 maths lessons for classes 6 to 8 on one page, with every practice sheet and answer key, ready to print.

Maths for classes 6 to 8

All 136 lessonsAll printable books

WhatsApp us