ACARA v9 CONTENT DESCRIPTION “recognise, represent and order decimals to hundredths, compare their size using place value, and make connections between decimals and fractions”
A decimal extends place value past the ones into parts of a whole. The first place after the point is tenths, the second is hundredths, so 0.25 is two tenths and five hundredths. Each place is ten times smaller than the one before, exactly as the whole-number places are ten times larger. This is the foundation for everything else about decimals: knowing which place a digit sits in tells you its value. Year 4 builds on the first look at tenths and hundredths to compare, order and convert decimals, all of which rest on reading these two places correctly.
Tenths and hundredths
The first decimal place is tenths, the second is hundredths of one whole.
3 tenths and 0 hundredths make 0.30: the first decimal place is tenths, the second is hundredths of one whole.
The value of each place
In a decimal, the same digit means different amounts depending on its place. The 2 in 0.25 is two tenths, but the 2 in 0.02 is two hundredths, ten times smaller. Reading a decimal means naming the place of each digit: tenths first, hundredths second. This place value is what makes 0.7 and 0.07 so different, even though both use a 7. Getting the place right is the single most important decimal skill, because every comparison and conversion that follows depends on knowing whether a digit counts tenths or hundredths.
Decimal place value
Each decimal digit has a place: tenths first, hundredths second.
In 0.25, which place is the circled digit in?
Comparing by place value
To compare two decimals, line up the decimal points and compare place by place, starting with the tenths. 0.7 beats 0.07 because seven tenths is far more than zero tenths; 0.45 beats 0.4 because the tenths tie and then five hundredths beats none. A common trap is thinking 0.07 is bigger because it has more digits, but a longer decimal is not always larger — the places decide. Comparing tenths first, then hundredths, gives the right answer every time, and it is the same left-to-right comparison used for whole numbers.
Compare decimals
Compare decimals place by place: tenths first, then hundredths.
Which is larger, 0.7 or 0.07? Compare place by place.
Putting decimals in order
Ordering several decimals uses the same place-value comparison, applied across the whole list. To order 0.4, 0.04 and 0.44 from smallest, look at the tenths: 0.04 has zero tenths so it is smallest, then 0.4 and 0.44 both have four tenths, and 0.44 is larger by its hundredths. Lining the numbers up by their decimal points makes the tenths and hundredths columns clear. Ordering decimals is a practical skill — arranging measurements, scores or prices — and it always comes down to comparing the highest place first and working down.
Order decimals
To order decimals, compare the tenths place first, then the hundredths.
Which of these is the smallest? Compare the tenths place first.
A decimal is a fraction
Every decimal is a fraction in disguise, written in tenths or hundredths. One decimal place means tenths, so 0.6 is 6/10; two places means hundredths, so 0.07 is 7/100. This connection runs both ways: a fraction with denominator 10 or 100 can be written as a decimal, and a decimal can always be read back as such a fraction. Seeing decimals and fractions as two notations for the same parts of a whole is a central Year 4 idea, because it links the new decimal place value to the fractions already understood.
Decimal to fraction
One decimal place means tenths; two places means hundredths.
Write 0.6 as a fraction.
Two ways to write a part
Pulling the unit together, a decimal and its fraction are two ways of writing the same amount. A table makes the pairs plain: 0.1 is 1/10, 0.25 is 25/100, 0.5 is 5/10. Reading across, the decimal place value and the fraction denominator say the same thing — tenths over ten, hundredths over a hundred. With decimal places named, values compared and ordered by place, and every decimal linked to its fraction, a child can work confidently with decimals to hundredths, the foundation for decimal addition, money and measurement in the years to come.
Decimals and fractions
Every decimal is a fraction in tenths or hundredths, written another way.
Each decimal equals a fraction. Reveal each to pair them.
Quick self-check
1. Which is larger, 0.7 or 0.07?
2. The decimal 0.3 written as a fraction is...
3. In 0.25, the digit 2 is in the...
4. Ordered smallest first, which comes first: 0.4, 0.04, 0.44?