Last updated 2026-10-24. Written by the TernQuest team. This guide is for parents of 5th graders (and strong 4th graders) who want to teach decimals as an extension of place value, so the rules for comparing, rounding and adding make sense rather than being memorized.
What are 5th graders expected to know about decimals?
Direct answer: By the end of 5th grade, under the California Common Core standards, children are expected to understand the place-value system through thousandths, read and write decimals in standard, word and expanded form, compare decimals to thousandths, round to any place, and add, subtract, multiply and divide decimals to hundredths using models and place-value reasoning. Your school's pacing may differ.
Fourth grade introduced decimal notation for tenths and hundredths as another way to write fractions with denominators of 10 and 100. Fifth grade extends the system one more place and asks children to operate on decimals. If tenths and hundredths are still shaky, the equivalent fractions post covers the 4th grade base, and the 5th grade math checklist shows where decimals sit among the year's other skills.
How do I explain tenths, hundredths and thousandths?
Direct answer: Decimals are the place-value system continued to the right of the ones place. Each place is ten times smaller than the one to its left: ones, then tenths, then hundredths, then thousandths. A child who understands that 10 ones make a ten already has the pattern; decimals just run it the other direction.
Extend the place-value chart
Draw the familiar chart and keep going right:
| Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 1000 | 100 | 10 | 1 | . | 0.1 | 0.01 | 0.001 |
Say it out loud: "ten tenths make one; ten hundredths make one tenth." The decimal point is not a place; it marks where the ones column is. If your child's whole-number place value is unsteady, the place value guide covers the bundling idea decimals depend on.
Read decimals as fractions
The word "and" is the decimal point. 3.45 is "three and forty-five hundredths", which is the same as 3 and 45/100. Reading decimals this way stops children saying "three point four five" as if the digits were unrelated, and it makes 0.45 obviously equal to 45/100.
Build with a hundred grid
A square cut into 100 small squares is the whole. Shade 45 squares: that is 0.45, or 45 hundredths. Shade a full column of ten: that is 0.1, one tenth. Now the child can see that 0.5 (five columns) covers more than 0.45 (four columns and five squares).
Quotable version: "A decimal is just place value continued to the right: each place is ten times smaller than the one before."
How does money help with decimals?
Direct answer: Money is a decimal system children already use. A dollar is the whole, a dime is a tenth of a dollar, a penny is a hundredth. Writing $0.45 as "four dimes and five pennies" connects the two decimal places to coins the child can hold, and it gives them a check for later work: does the answer make sense as money?
| Coins | Amount | Decimal | Read as |
|---|---|---|---|
| 1 dime | 10 cents | 0.10 | one tenth (ten hundredths) |
| 1 penny | 1 cent | 0.01 | one hundredth |
| 4 dimes, 5 pennies | 45 cents | 0.45 | forty-five hundredths |
| 5 dimes | 50 cents | 0.50 | five tenths |
| 3 dollars, 2 dimes | $3.20 | 3.20 | three and two tenths |
Money stops at hundredths; for thousandths, use the hundred grid or the number line. If coin counting is rusty, the counting money post is a quick refresher.
Why do kids think 0.45 is bigger than 0.5, and how do I fix it?
Direct answer: Because 45 is bigger than 5 when the digits are read as whole numbers, which is what a child without decimal place value does. The fix is to compare place by place from the left, the same way whole numbers are compared: 0.5 has five tenths, 0.45 has four tenths, so 0.5 is bigger before the hundredths are even looked at.
Three ways to make it visible
- Pad with zeros. Write 0.5 as 0.50. Now "50 hundredths versus 45 hundredths" is obvious. Adding a zero on the right does not change the value; the hundred grid shows why (five full columns either way).
- Use money. 0.5 is five dimes; 0.45 is four dimes and five pennies. Which would you rather have?
- Use the number line. Draw 0 to 1 in tenths. 0.5 sits on the fifth mark; 0.45 sits just before it.
A comparison routine
Compare 0.7, 0.65 and 0.705:
- Line up the decimal points and pad to the same length: 0.700, 0.650, 0.705.
- Compare tenths: 7, 6, 7. The 0.650 is smallest.
- Compare hundredths for the two with 7 tenths: 0, 0. Tie.
- Compare thousandths: 0, 5. So 0.705 is largest.
Order: 0.65, 0.7, 0.705. Have your child explain each step in place-value words, not "add zeros because the rule says so".
How do I teach rounding decimals?
Direct answer: Rounding a decimal uses the same question as rounding a whole number: which of the two nearest "landmark" numbers is this closer to? To round 3.47 to the nearest tenth, the landmarks are 3.4 and 3.5; 3.47 is closer to 3.5. The number line makes this a question of position rather than a rule about the digit to the right.
The number-line method
- Name the place you are rounding to (tenths).
- Write the two nearest tenths: 3.4 and 3.5.
- Draw a line between them, mark the halfway point (3.45).
- Place the number. 3.47 is past 3.45, so it rounds to 3.5.
Once the child has done this a few times, the shortcut "look at the next digit; 5 or more rounds up" makes sense because they know what it is a shortcut for. The child who only knows the shortcut will round 3.97 to the nearest tenth and write 3.10 instead of 4.0, because they never pictured the landmarks.
How do I teach adding and subtracting decimals?
Direct answer: Line up the decimal points so each place sits under the same place, then add or subtract column by column, regrouping exactly as with whole numbers: ten hundredths make one tenth, ten tenths make one. The single most common error is lining up the right-hand edges, which puts hundredths under tenths.
Worked example: 3.6 + 1.75
Pad and line up:
3.60
+ 1.75
------
5.35
Hundredths: 0 + 5 = 5. Tenths: 6 + 7 = 13 tenths, which is 1 one and 3 tenths; write 3, carry 1. Ones: 3 + 1 + 1 = 5. Answer 5.35. Check with money: $3.60 plus $1.75 is $5.35.
Worked example: 5 − 2.35
The whole number needs its places: 5.00.
5.00
- 2.35
------
2.65
Regroup exactly as in whole-number subtraction; the subtraction with regrouping post covers the mechanics, and they are unchanged here. Check: $5.00 minus $2.35 leaves $2.65.
Estimation as the check
Before every problem, ask for an estimate: "3.6 plus 1.75 is about 4 plus 2, so around 6." If the written answer is 53.5 or 0.535, the estimate catches it. This habit carries into multiplying and dividing decimals later in the year.
What mistakes should I watch for?
Direct answer: Most 5th grade decimal errors come from treating the digits after the point as a whole number: "longer is bigger", right-aligned addition, and rounding without landmarks. Each is a place-value gap, and each is fixed by returning to the hundred grid, the money or the number line rather than by re-explaining the rule.
| Error | Example | Fix |
|---|---|---|
| Longer decimal is bigger | 0.45 > 0.5 | Pad to 0.50; five dimes vs four dimes and five pennies |
| Right-aligned addition | 3.6 + 1.75 written with 6 under 5 | Pad to 3.60; "tenths under tenths" |
| Rounding to the wrong landmark | 3.97 to nearest tenth = 3.10 | Draw 3.9 and 4.0 on a line |
| "Adding a zero makes it bigger" | 0.5 becomes 0.50 "which is more" | Hundred grid: five columns either way |
| Reading digits separately | "three point four five" | "Three and forty-five hundredths" |
Where do practice games fit?
Direct answer: After the grid, the coins and the number line have made the places visible. Then the child needs many short repetitions of comparing, rounding and adding, and a game supplies those. TernQuest's 5th grade decimal skills are tagged to the California Common Core standards, and Pip gives a hint (such as "compare the tenths first") instead of the answer, which is what a child comparing 0.45 and 0.5 needs.
A game is not the place to start. The first week should be at the table with a hundred grid and a handful of coins, and if your child's whole-number place value is not solid, decimal practice of any kind will not stick until it is. If your child is in middle school and working with decimals in ratios and percentages, our content stops at 5th grade and you will need a different resource.
Related reading
- Place value explained for parents — the bundling idea decimals extend to the right.
- 5th grade math skills checklist (2026) — where decimals sit among this year's expectations.
- Equivalent fractions explained for parents (4th grade) — the tenths-and-hundredths fractions decimals rename.
Next step
Tonight, pull out a dime and a penny and ask your child to write each as a decimal, then compare 0.5 and 0.45 with coins. When the places are clear, TernQuest is free to start for one child and its 5th grade decimal games are listed by standard on the public curriculum map.