Dividing Decimals Worksheets – Tenths by Tenths
Keep the quotient unchanged by scaling the dividend and divisor together. Use the group model, then print eight problems with room for written division and a multiplication check.
Keep the size of a group in view
Leo sees 0.6 ÷ 0.2 and writes 0.3. He remembers moving decimal points, but he is not sure what the quotient represents. Ask him to imagine a strip that is six tenths of a unit long. How many pieces of length two tenths fit into it?
Group six tenths into pairs. Each small section below represents one tenth. Each outlined pair has a total length of two tenths.
There are three groups of two tenths. Therefore 0.6 ÷ 0.2 = 3. The quotient counts the groups; it is not a length of three tenths. Check by putting the groups back together: 3 × 0.2 = 0.6.
Why multiply both numbers by ten?
Six tenths divided into groups of two tenths has the same group count as six whole units divided into groups of two whole units. Both the total amount and the size of each group become ten times as large. The number of groups stays the same.
In symbols, 0.6 ÷ 0.2 = 6 ÷ 2 = 3. For another example, 9.1 ÷ 2.6 becomes 91 ÷ 26. Because 26 × 3.5 = 91, the original quotient is also 3.5. Multiplying both numbers by ten changes the units used to describe them, but preserves their ratio.
A quotient can include part of a group
Consider 0.9 ÷ 1.2. Nine tenths is smaller than one full group of twelve tenths, so the answer must be less than one. Scaling both numbers gives 9 ÷ 12. Nine is three quarters of twelve, and three quarters is 0.75. Thus 0.9 ÷ 1.2 = 0.75.
This is a number relationship, not a claim that every real-life situation allows a fraction of an object. A length can be part of another length; a question about buying full packages might require a different interpretation. These worksheets ask for exact numerical quotients without a story context.
Continue the division when the whole-number step is not enough
For 1.4 ÷ 2.5, rewrite both numbers as 14 ÷ 25. Twenty-five does not fit into fourteen a whole number of times, so the quotient begins with 0. Write 14 as 14.00 to keep working: 25 × 0.5 = 12.5, leaving 1.5. Then 25 × 0.06 = 1.5. Together, 0.5 + 0.06 = 0.56.
Writing zeros after the decimal point does not change 14. It lets you describe the remaining amount in tenths and hundredths. In the work area, a child may use partial quotients, a written long-division method, or multiplication facts to find the missing factor.
Dividing can give a larger number
Compare 3.8 ÷ 0.2 with 3.8 ÷ 2. Small groups of two tenths fit into 3.8 nineteen times. Groups of two fit 1.9 times. Making the group smaller allows more groups to fit into the same amount.
For a positive dividend, division by a positive number below one gives a quotient larger than the dividend. Division by a number greater than one gives a smaller quotient. Ask which situation applies before calculating; this helps catch a decimal point placed on the wrong scale.
Multiply to check the exact quotient
Check 1.4 ÷ 2.5 = 0.56 by multiplying: 2.5 × 0.56 = 1.40. The result matches the original dividend. If a child instead writes 5.6, the check gives 14, showing a factor-of-ten error.
The answer key may show 3.5 where a child writes 3.50, or 4 where the child writes 4.00. These are equivalent values. Accept the added final zeros. A zero inside a decimal has a different role and cannot simply be removed.
Each set has eight problems. The dividend is positive and below 20; the divisor is positive and below 10. Both have one decimal place. Every quotient ends exactly at a whole number, tenths, or hundredths: no rounding is needed. This set does not include division by zero, repeating decimals, whole-number divisors, or answers requiring three decimal places. Use New numbers for a fresh set with the same scope.
Make a practice set
Choose what to print. Selecting both shows the answer key on screen and prints the questions followed by the answers.
After the practice
Multiply each quotient by its original divisor to check the dividend. Ask the child to explain why both numbers must be scaled together, and accept equivalent final-zero forms.
Calculation practiceSubtracting Decimals to Hundredths Worksheets
Align decimal points and rename tenths and hundredths before subtracting.
15 problems · Answer key included
Calculation practiceMultiplying Decimals Worksheets – Tenths by Tenths
Use tenths and hundredths to explain the product, then show your work.
8 problems · Answer key included
More about division · Grade 5 worksheets
Grade 5 selected skill connection: 5.NBT.B.7 (selected exact decimal division using models and place-value reasoning). See the Common Core grade guidance. This worksheet does not cover every requirement in the standard.