Lesson 16 · Fractions and Decimals

Decimals and Simplification

MathematicsSubject
13 minEstimated read
A decimal is a fraction with the bottom already chosen

A decimal is a fraction whose bottom is always a power of ten, agreed in advance so nobody has to write it.

Place value after the point

After the point, the same rule keeps going: tenths, hundredths, thousandths. The pattern has just been carried on past the units column.

Place Worth In 3.482
Units13 units
Tenths1/104 tenths
Hundredths1/1008 hundredths
Thousandths1/10002 thousandths
More digits does not mean bigger

Is 0.7 or 0.65 larger? 0.7 is seven tenths while 0.65 is six tenths and a bit. Writing 0.7 as 0.70 makes it obvious.

Adding and subtracting

Line up the decimal POINTS, not the right hand ends, and fill short columns with zeros.

Why multiplying moves the point

Tenths times tenths gives hundredths, exactly as multiplying the bottoms of two fractions gives a bigger bottom.

0.3 times 0.4 is not 1.2

Both numbers are less than 1, so the answer must be less than either. 0.12 is right while 1.2 is ten times too big.

Dividing by a decimal

Shift the point in both numbers by the same amount: 4.8 ÷ 0.6 becomes 48 ÷ 6, which is 8.

Rounding is a decision, not a mistake

Look at the next digit only. Round at the END of a calculation, never in the middle.

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