Tenths and hundredths

The decimal point does not start a new system. It marks where the whole numbers end. Each place to the left of the point is worth ten times the place on its right, and that rule keeps going straight through the point without a break.

The places after the point

So 3.47 is three wholes, four tenths and seven hundredths. Said aloud in school it is three and forty seven hundredths, where the word and marks the point.

Seeing tenths and hundredths

A strip cut into ten equal parts shows tenths. A square cut into a hundred small squares shows hundredths, and a full column of ten of those small squares is one tenth. That picture is why 0.4 and 0.40 are the same amount: four columns and forty small squares cover exactly the same area.

The money version

Dimes are tenths of a dollar and pennies are hundredths, which makes money the easiest first model for decimals. 0.35 of a dollar is three dimes and five pennies. A student who can count change already understands hundredths.

Decimals on a number line

Between 0 and 1, mark ten equal steps and you have the tenths. Between any two of those, mark ten more and you have the hundredths. Drawing it once answers a lot of questions that a rule alone does not.

Beyond hundredths

The pattern keeps going. The next place is thousandths, worth 1/1000 each. Money stops at hundredths because the cent is the smallest coin, but measurement does not: a runner's time of 10.482 seconds uses thousandths, and a millimetre is a thousandth of a metre.

Common mistakes

Thinking a longer decimal is a bigger number

0.5 is larger than 0.47, even though 47 is larger than 5. Compare place by place, starting from the tenths.

Reading the digits one at a time

Saying three point four seven is fine in conversation and hides the place value. Three and forty seven hundredths is what tells you the size.

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