Decimals: tenths, hundredths, and comparing
Adding fractions with denominators of ten and a hundred, and comparing decimals to the hundredths
About two to three lessons of 45 to 60 minutes
Decimals are fractions wearing a different outfit
3/10 and 0.3 are exactly the same amount, just written two different ways. Once tenths and hundredths are understood as fractions AND as decimal place values, you can add fractions with different-sized parts by turning them into a matching size first, and compare decimals confidently instead of guessing.
The single trap that catches almost every student here is judging a decimal by how many digits it has. This unit builds the habit of always checking place value, not digit count.
- 3/10 written as a decimal3/10 = 0.3, three tenths
- 3/10 + 4/100rewrite 3/10 as 30/100 first, then add: 30/100 + 4/100 = 34/100 = 0.34
- Comparing 0.5 and 0.450.5 is 0.50, and 50 hundredths is more than 45 hundredths, so 0.5 is greater
What students will be able to do
Students will express tenths as equivalent hundredths, add a fraction with denominator 10 to a fraction with denominator 100 by rewriting the tenths as hundredths, connect tenths and hundredths to decimal notation, and compare two decimals to the hundredths using reasoning about place value.
- I can rewrite a fraction with denominator 10 as an equivalent fraction with denominator 100.
- I can add a tenths fraction and a hundredths fraction by converting to a common denominator first.
- I can write a fraction with denominator 10 or 100 as a decimal, and read it correctly by its place value.
- I can compare two decimals to the hundredths and explain which is greater without just counting digits.
Standards this unit teaches
- 4.NF.C.5Common Core (US)Add tenths and hundredths
Add fractions with denominators of ten and a hundred by rewriting tenths as hundredths.
- 4.NF.C.7Common Core (US)Compare decimals
Compare two decimals to the hundredths by reasoning about their size and using comparison symbols.
- AC9M4N01Australian Curriculum v9 (ACARA)Decimals to hundredths
Extend place value to tenths and hundredths and use decimal notation to name and represent these numbers.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Decimal
- a number written with a decimal point to show tenths, hundredths, and smaller parts
- Tenth
- one of 10 equal parts of a whole, written 1/10 or 0.1
- Hundredth
- one of 100 equal parts of a whole, written 1/100 or 0.01
- Equivalent fractions
- different fractions that name the same amount, such as 3/10 and 30/100
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Tenths and hundredths as fractions and decimals
PictorialA whole split into 10 equal parts gives tenths; a whole split into 100 equal parts gives hundredths. Both can be written as a fraction or as a decimal, and the decimal places have names that match: the first digit after the point is tenths, the second is hundredths.
Write 3/10 and 7/100 as decimals, and read each one by its place value.
- 3/10 has one digit after the decimal point, in the tenths place: 0.3, read as 'three tenths'.
- 7/100 has its digit in the hundredths place, so a zero holds the tenths place: 0.07, read as 'seven hundredths'.
Answer: 3/10 = 0.3 (three tenths); 7/100 = 0.07 (seven hundredths).
- Why does 7/100 need a zero in the tenths place when written as a decimal?
- How would you write 45/100 as a decimal?
2. Adding tenths and hundredths
AbstractTo add a tenths fraction and a hundredths fraction, they must be the same size part first. Rewrite the tenths fraction as an equivalent hundredths fraction by multiplying the top and the bottom by 10, exactly the equivalent-fractions rule from Grade 3, then add the numerators.
Add 3/10 + 4/100.
- Rewrite 3/10 as hundredths: multiply the top and bottom by 10: (3x10)/(10x10) = 30/100.
- Now both fractions are hundredths: 30/100 + 4/100.
- Add the numerators, keep the denominator: 30 + 4 = 34, so 34/100.
- Check against decimals: 0.3 + 0.04 = 0.34, which matches 34/100 = 0.34.
Answer: 3/10 + 4/100 = 34/100 = 0.34.
- Why must 3/10 be rewritten before adding, instead of adding 3/10 and 4/100 directly?
- What is 6/10 rewritten as hundredths?
3. Comparing decimals to the hundredths
AbstractComparing decimals is only safe once both numbers are written with the same number of decimal places. Pad a shorter decimal with a trailing zero so the comparison is fair, then compare place by place from the left.
Compare 0.5 and 0.45. Which is greater?
- Give both numbers the same number of decimal places: 0.5 becomes 0.50.
- Compare hundredths directly: 50 hundredths versus 45 hundredths.
- 50 is greater than 45.
Answer: 0.5 (0.50) is greater than 0.45.
- Compare 0.7 and 0.68. Which is greater, and how do you know?
- Why is it unsafe to compare 0.5 and 0.45 by just comparing '5' and '45' as if they were whole numbers?
Common misconceptions and how to address them
MisconceptionBelieving more digits after the decimal point always makes a bigger number, for example thinking 0.45 is greater than 0.5 because '45 is bigger than 5'.
Why it happens: Whole-number thinking (more digits means a bigger number) gets applied directly to decimals, where digit count after the point does not work the same way.
How to address it: Always pad decimals to the same number of places before comparing (0.50 vs 0.45), and compare place by place, tenths first, then hundredths.
MisconceptionAdding 3/10 and 4/100 by adding numerators and denominators separately without converting first, for example writing 7/110 or 7/100.
Why it happens: Adding straight across is the earliest, simplest fraction-addition rule students meet, and it has to be actively overridden for fractions with different denominators.
How to address it: Rewrite the tenths fraction as hundredths FIRST, exactly like finding a common denominator, before adding any numerators.
MisconceptionReading 0.07 as 'zero point seven', confusing hundredths with tenths because only the digit is noticed, not its place.
Why it happens: Without checking position, the visible digit (7) gets read the same way regardless of whether it sits in the tenths or hundredths place.
How to address it: Say the place name out loud every time a decimal is read: 0.07 is 'seven hundredths', 0.7 is 'seven tenths', never just 'point seven' or 'point oh seven'.
MisconceptionWhen converting 3/10 to hundredths, multiplying only the denominator by 10 and leaving the numerator unchanged, giving 3/100 instead of 30/100.
Why it happens: The denominator is the number being explicitly 'converted' in the student's mind, so it gets all the attention while the numerator is forgotten.
How to address it: Repeat the equivalent-fractions rule from Grade 3: whatever you multiply the bottom by, you must multiply the top by the same number, to keep the value unchanged.
Guided practice (with answers)
1. Write 9/10 as a decimal.
Answer: 0.9 (nine tenths).
2. Write 23/100 as a decimal.
Answer: 0.23 (twenty-three hundredths).
3. Add 6/10 + 21/100.
Answer: 81/100 = 0.81. Rewrite 6/10 as 60/100, then 60/100 + 21/100 = 81/100.
4. Add 2/10 + 9/100.
Answer: 29/100 = 0.29. Rewrite 2/10 as 20/100, then 20/100 + 9/100 = 29/100.
5. Compare 0.36 and 0.4. Which is greater?
Answer: 0.4 (as 0.40), since 40 hundredths is greater than 36 hundredths.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with reading and writing tenths and hundredths, then move to adding and comparing.
Differentiation
- Keep a place-value chart with labelled tenths and hundredths columns visible during every practice question.
- Use the fraction bar diagrams to physically shade tenths and hundredths before writing the matching decimal.
- Always pad decimals to equal length as a first, separate step before attempting any comparison.
- Add two hundredths fractions with different tenths parts, such as 45/100 + 3/10, requiring the conversion in the other direction to check.
- Order three or four decimals from least to greatest, including some with only one decimal place.
- Connect tenths and hundredths to money (dimes and cents) and explain why $0.30 and $0.3 are the same amount.
Assessment: exit ticket
A short exit ticket sampling reading, adding, and comparing tenths and hundredths.
1. Write 5/100 as a decimal, and read it by its place value.
Answer: 0.05, read as 'five hundredths'.
2. Add 4/10 + 15/100.
Answer: 55/100 = 0.55. Rewrite 4/10 as 40/100, then 40/100 + 15/100 = 55/100.
3. Compare 0.6 and 0.58. Which is greater?
Answer: 0.6 (as 0.60), since 60 hundredths is greater than 58 hundredths.
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 tenths and hundredths as fractions and decimals (section 1), Lesson 2 adding tenths and hundredths (section 2), Lesson 3 comparing decimals plus the exit ticket (section 3 and assessment).
- Language to keep saying: say the place name every time, pad to equal length before comparing, convert before adding.
- This unit deliberately reuses the equivalent-fractions rule from Grade 3 (multiply top and bottom by the same number) rather than re-teaching it from scratch; make that connection explicit to save teaching time and reinforce the earlier unit.
- Curriculum note: ACARA's AC9M4N01 covers extending place value to tenths and hundredths at the same Year 4 level as both US standards in this unit, making it a clean, direct crosswalk.
- Present mode and print both work: use Present to build the fraction-bar diagrams live and convert them to decimals on screen, then print the worksheets for independent practice.