Lessons · Teaching · decimals, and the operations on them
Decimals are fractions whose denominators are all tens
A decimal is a fraction with a denominator of ten, a hundred, a thousand and so on, written using place value instead of a bar. 0.7 is seven tenths, 0.07 is seven hundredths. Every operation follows from lining up the places, not the digits.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Money hides the difficulty, because two decimal places are always enough and everyone knows what 1.5 pounds means. Then a pupil meets 0.4 plus 0.35 and lines up the right-hand ends, because that is what they do with whole numbers, and gets 0.39.
How to think about it
For adding and subtracting, line up the decimal points and fill empty places with zeros. For multiplying, ignore the points, multiply as whole numbers, then count the total decimal places in both factors and put that many in the answer. For dividing by a decimal, shift both numbers the same number of places until the divisor is whole.
Worked example
0.4 + 0.35: write 0.40 + 0.35, points lined up, giving 0.75The added zero is not decoration, it is the empty hundredths place made visible.
0.3 x 0.4: 3 x 4 = 12, and there are two decimal places in total, so 0.12Two tenths multiplied gives hundredths, which is why the answer is smaller than both.
7.2 divided by 0.8: shift both one place to get 72 divided by 8, which is 9Shifting both by the same amount does not change the quotient.
To convert 3/8 to a decimal, divide 3 by 8, giving 0.375Every fraction is a division, so every fraction has a decimal.
Your turn
Name what must be lined up when decimals are added.
Line up the decimal , not the right-hand ends
Solve one, graded on the server
The trap
Expecting multiplication to make a decimal bigger. 0.3 times 0.4 is 0.12, smaller than either. The whole-number instinct that multiplying grows a number is false everywhere below one.