What does it mean?
Multiplication can make a positive quantity larger or smaller. Taking three lots of 0.4 gives 1.2, while taking 0.2 of 0.3 gives only 0.06. An area model explains the second result: tenths in one direction and tenths in the other form hundredths.
Multiplying decimals scales a quantity. Four tenths taken three times is twelve tenths, or 1.2. Tenths times tenths make hundredths: 0.3 × 0.2 = 0.06. Multiply whole-number digits, then use the total decimal places to name the product. Check its size against the factors.
Learning goal: Multiply decimals with place-value reasoning. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Decimal place value: tenths and hundredths if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Calculate the product of the whole-number digits, then use place value to name its size. In 1.2 × 0.3, think 12 tenths × 3 tenths = 36 hundredths = 0.36. A total-of-decimal-places rule is a compact record of that unit reasoning. Estimate first: 0.3 of 1.2 must be less than 1.2.
Notation: 3 tenths × 2 tenths = 6 hundredths
Key rule and when to use it
Tenths × tenths gives hundredths. Whole-number multiplication finds the digits; the place values of both factors determine the product’s size.
Three multiplication cases to recognise
Decimal × whole number: 1.25 × 4 = 5. Four groups of 125 hundredths make 500 hundredths. Decimal × decimal: 0.12 × 0.3 = 36 thousandths = 0.036. When the whole-number digit product is 36 but three decimal places are needed, insert a zero before 36.
Powers of ten change place value: 0.047 × 100 = 4.7. Every digit moves to a place worth one hundred times as much. These are exact calculations, not rounding. A final zero can be removed only when it leaves the value unchanged.
Worked examples, step by step
Example 1: Calculate 0.4 × 3.
- Four tenths taken 3 times make 12 tenths.
- Rename 12 tenths as 1 whole and 2 tenths.
Answer: 1.2
Example 2: Calculate 0.3 × 0.2.
- Multiply 3 × 2.
- Tenths times tenths make hundredths.
- Write 6 hundredths.
Answer: 0.06
Example 3: Calculate 2.4 × 0.15.
- 24 × 15 = 360. The factors are 24/10 and 15/100.
- The product is 360/1,000 = 0.360 = 0.36.
- Since 0.15 is less than 1, the answer should be less than 2.4.
Common mistakes and important boundaries
Zeros are placeholders, not spare digits to discard before interpreting value. 0.06 and 0.6 differ by a factor of ten. A product with a positive factor between 0 and 1 is smaller than the other positive factor. This gives a useful size check even before doing the exact arithmetic.
A point to explain
Multiplying two numbers below 1 makes a smaller product.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Multiplying Decimals: Place Value and Scaling — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
0.5 × 0.4 = ?
Answer and a way to check
0.2
Use place value and estimate the size before placing the decimal point.
1.2 × 0.3 = ?
Answer and a way to check
0.36
Use place value and estimate the size before placing the decimal point.
0.6 × 0.5 = ?
Answer and a way to check
0.3
Use place value and estimate the size before placing the decimal point.
2.5 × 0.2 = ?
Answer and a way to check
0.5
Use place value and estimate the size before placing the decimal point.
You buy 4 pens at ₹2.50 each. What is the total cost in rupees?
Answer and a way to check
10
Use place value and estimate the size before placing the decimal point.
Calculate 0.08 × 0.5.
Answer and a way to check
0.04
Half of eight hundredths is four hundredths. Numerically 8 × 5 = 40 thousandths = 0.040.
Calculate 1.25 × 4.
Answer and a way to check
5
125 hundredths × 4 = 500 hundredths = 5 wholes.
A learner writes 0.3 × 0.2 = 0.6. Explain and correct it.
Answer and a way to check
0.06
Tenths × tenths make hundredths, so 3 × 2 gives six hundredths. The proposed 0.6 is also larger than both positive factors below one.
Multiplying Decimals: Place Value and Scaling — answer key
0.2 Use place value and estimate the size before placing the decimal point.
0.36 Use place value and estimate the size before placing the decimal point.
0.3 Use place value and estimate the size before placing the decimal point.
0.5 Use place value and estimate the size before placing the decimal point.
10 Use place value and estimate the size before placing the decimal point.
0.04 Half of eight hundredths is four hundredths. Numerically 8 × 5 = 40 thousandths = 0.040.
5 125 hundredths × 4 = 500 hundredths = 5 wholes.
0.06 Tenths × tenths make hundredths, so 3 × 2 gives six hundredths. The proposed 0.6 is also larger than both positive factors below one.
Questions students and parents ask
What happens when a decimal is multiplied by 10, 100 or 1,000?
Each digit takes a place worth 10, 100 or 1,000 times as much. Thus 2.47 × 10 = 24.7, × 100 = 247 and × 1,000 = 2,470. The number of printed decimal places can decrease.
Why can I remove a final zero from 0.360?
It names zero thousandths, so removing it leaves the same value, 0.36. Removing a zero inside 0.306 would change the value.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Decimal place value: tenths and hundredths. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Ask what fraction of the original amount the multiplier represents. A size prediction is more informative than asking only how many decimal places to count.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Multiply decimals with place-value reasoning”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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