How to teach decimals

A decimal extends place value to the right of the ones into tenths, hundredths and thousandths. So 0.7 means seven tenths, the same value as 7/10. Decimals let us write in-between amounts, such as 3.5, without using fractions, and money is the everyday example.

Decimals are usually taught from Grade 4 to Grade 6. Students start with tenths and hundredths, anchored to fractions and money, then learn to compare, order, add and subtract decimals, and later to multiply and divide with them.

Because 0.5 is five tenths, which equals 0.50, and 0.50 is larger than 0.45. Reading 0.45 as bigger 'because 45 is more than 5' is the classic longer-is-larger error. Lining up the decimal points and padding with a zero, comparing 0.50 with 0.45, makes it clear.

Money is the everyday decimal model, because a dollar splits into 100 cents, which are hundredths. So $3.45 is 3 ones, 4 tenths of a dollar and 5 hundredths. Using coins and prices gives children a familiar, concrete way into decimal place value.

They are two ways of writing the same in-between amounts. A decimal uses place value to the right of the point, while a fraction uses a numerator over a denominator. So 0.1 and 1/10 are equal, just written differently. Anchoring decimals to fractions first helps the idea land.

Line up the decimal points and pad with zeros so both numbers have the same number of decimal places, then compare digit by digit. To compare 0.5 with 0.45, write 0.50 and 0.45; since 50 hundredths is more than 45 hundredths, 0.5 is larger.

It is the longer-is-larger misconception: the child sees 45 as more than 5 and ignores place value. But 0.5 is five tenths, or 0.50, which is more than 0.45. Naming decimals as tenths and hundredths, not just 'point four five', is what makes place value land.