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 |
|---|---|---|
| Units | 1 | 3 units |
| Tenths | 1/10 | 4 tenths |
| Hundredths | 1/100 | 8 hundredths |
| Thousandths | 1/1000 | 2 thousandths |
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.
Tenths times tenths gives hundredths, exactly as multiplying the bottoms of two fractions gives a bigger bottom.
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.
Look at the next digit only. Round at the END of a calculation, never in the middle.
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