Grade 6

Decimals and Percentages

The grade six decimal, from the place value just right of the point through to the percentage on a price tag, with every step resting on the one before it.

8 lessons

  1. 1What do the digits after the decimal point mean?Each place to the right of the point is worth a tenth of the one before it: first tenths, then hundredths, then thousandths. A decimal is therefore a fraction written without a fraction bar, and it can always be converted to a fraction with a denominator of ten, a hundred or a thousand.30m
  2. 2How do you compare two decimal numbers?Compare place by place from left to right and stop at the first place where the digits differ. A longer number is not necessarily a larger one, because length is not size: 0.5 is greater than 0.45 even though it has fewer digits. You may add zeros at the end to line the two up.30m
  3. 3How do you add and subtract decimal numbers?Write one under the other with the decimal points lined up, not with the last digits lined up. Then tenths add to tenths and hundredths to hundredths, just as ones add to ones. If one number has fewer digits, add zeros at the end to fill the columns.30m
  4. 4What happens when you multiply a decimal by ten or a hundred?Every digit moves up one place for each multiplication by ten, and down one place for each division. In writing it looks as though the point moves, but what actually moves is the digits: multiplying by ten turns tenths into ones. This is why you do not add a zero to a decimal when multiplying by ten.30m
  5. 5How do you multiply two decimals and where does the point go?Multiply the digits as though there were no decimal point at all, then count how many digits follow the point in the two factors together. That total is how many digits follow the point in the answer. When dividing by a whole number, carry the division past the point and add zeros as needed.35m
  6. 6What is a percentage and how do you convert between percentages, fractions and decimals?Per cent means out of a hundred, so one per cent is one hundredth. Twenty-five per cent, twenty-five hundredths and a quarter are three ways of writing the same amount. To go from a percentage to a decimal divide by a hundred, and to go the other way multiply by it.30m
  7. 7How do you find a percentage of an amount and how do you find the whole?There are three questions, not one. To find a percentage of an amount, multiply the amount by the percentage as a decimal. To find the whole when you know a part and what percentage it is, divide the part by that percentage. And to find what percentage one number is of another, divide and multiply by a hundred.35m
  8. 8How do you work out a price after a discount or a price rise?Work out the discount and subtract it, or multiply directly by what is left: a thirty per cent discount means paying seventy per cent. A price rise works the same way with a hundred and ten per cent. A rise and a fall of the same percentage do not cancel out, because each is calculated from a different whole.40m