Decimals and Percentages · Grade 6

What do the digits after the decimal point mean?

Each place to the right of the point is worth a tenth of the one before it: first tenths, then hundredths, then thousandths. A decimal is therefore a fraction written without a fraction bar, and it can always be converted to a fraction with a denominator of ten, a hundred or a thousand.

Learning objectives

The same table, continued

In a place value table, each place to the left is worth ten times the one before: ones, tens, hundreds. The decimal point does not begin something new — it simply marks where the ones end.

To the right of it the same logic continues in reverse. The first place is tenths, the second hundredths, the third thousandths, and each is worth a tenth of the one before it.

So the digit three means different things in those two places. In the tenths place it is three tenths; in the hundredths place it is three hundredths — ten times less.

One number, two ways of writing it

A decimal is a fraction in disguise. Seven tenths can be written as seven over ten, and twenty-five hundredths as twenty-five over a hundred, which cancels down to a quarter.

The denominator is set by how many digits follow the point: one digit means tenths, two means hundredths, three means thousandths. That is the whole conversion rule.

Read it the way you say it

Reading digit by digit hides the size. The number 3.07 is not 'three point oh seven' in any useful sense — it is three and seven hundredths, and saying that aloud makes it obvious the number is close to three.

This reading habit doubles as a sanity check. A student who says 'seven hundredths' out loud will not write them in the tenths place, and that is the error the whole rest of this topic rests on.

Worked examples

  1. What is the place value of the digit 4 in 2.354?

    1. After the point: 3 is in the tenths place, 5 in the hundredths
    2. The third place is thousandths
    3. So 4 is in the thousandths place

    Answer: Four thousandths

  2. Write 0.25 as a fraction in lowest terms

    1. Two digits after the point, so the denominator is a hundred
    2. This gives 25 over 100
    3. Divide numerator and denominator by 25

    Answer: One quarter

  3. How do you read 6.08 aloud?

    1. The whole part is 6
    2. There are two digits after the point, so these are hundredths
    3. The digits 0 and 8 make eight hundredths

    Answer: Six and eight hundredths

Common mistakes

Reading the number digit by digit
That loses the place value entirely. Someone who says 'three point oh seven' does not hear that the number is close to three, while someone who says 'three and seven hundredths' hears it immediately.
Treating a zero after the point as unnecessary
The zero in a number like 0.07 is what pushes the seven into the hundredths place. Deleting it makes it seven tenths, which is ten times larger.
Choosing the denominator from the digit rather than the count of digits
The denominator depends on how many digits follow the point, not on their value. 0.5 has a denominator of ten and 0.05 a denominator of a hundred, even though the digit is the same.

What to remember

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