HSPT: Decimals: multiply and place the point
Learn to multiply decimals by working with whole numbers first and then placing the decimal point by counting.
How do you know where the decimal point goes when you multiply two decimals?
Short answer
Multiply the digits as whole numbers. Then count the decimal places in both factors together, and give the answer that many places.
Know first: Multiplying whole numbers, Place value to the thousandths
Step 1 of 5
Multiply as whole numbers, then count places
To multiply decimals, you don't need to line up the decimal points. Ignore them at first and multiply the digits as whole numbers.
Then count the decimal places, the digits to the right of each decimal point, in both factors together. Your answer gets that many decimal places.
| Problem | Whole-number product | Places in factors | Answer |
|---|---|---|---|
| 3 × 0.2 | 6 | 0 + 1 = 1 | 0.6 |
| 0.07 × 0.9 | 63 | 2 + 1 = 3 | 0.063 |
| 1.5 × 0.04 | 60 | 1 + 2 = 3 | 0.060 = 0.06 |
Count the places before you drop any zeros at the end.
Step 2 of 5
Place the decimal point by counting
Worked example: A decimal times a decimal
What is 2.6 × 0.4?
- A10.4
- B1.04
- C0.104
- D3
- 1
Multiply the digits
26 × 4 = 104.
- 2
Count the places
2.6 has one decimal place and 0.4 has one, so the answer needs two.
- 3
Place the point
104 with two decimal places is 1.04.
- 4
Estimate
0.4 is a bit less than half, and half of 2.6 is 1.3. 1.04 is a little under 1.3, so it fits.
- 5
See why the other choices are there
10.4 uses only one decimal place. 0.104 uses three. 3 adds the numbers instead of multiplying them.
Answer
1.04
Find the wrong step
A student multiplies 0.5 × 0.8.
- 1
Multiplies the digits: 5 × 8 = 40.
- 2
Drops the zero to get 4, then counts two places back and writes 0.04.
What went wrong
The places must be counted on the full product, 40. Dropping the zero first loses a digit.
- 3
Answers 0.04.
The fix
40 with two decimal places is 0.40, which equals 0.4. Check: half of 0.8 is 0.4.
Step 3 of 5
Count the places every time
Check yourself · Question 1
What is 3.1 × 0.7?
Answer: C
31 × 7 = 217. The factors have two decimal places in all, so the answer is 2.17. Estimate: 0.7 of about 3 is about 2.1.
Trap answer: 21.7
Too few decimal places
- Why it looks right
- 21.7 keeps one decimal place, like 3.1 and 0.7, so it looks consistent.
- Why it's wrong
- Decimal places add up: one from 3.1 plus one from 0.7 makes two. Also, multiplying by a number less than 1 must give less than 3.1.
- The right answer
- 2.17
Check yourself · Question 2
What is 0.25 × 0.08?
Answer: B
25 × 8 = 200. There are four decimal places in all (two in each factor), so the answer is 0.0200, which is 0.02.
Common mistake
"I line up the decimal points, like when I add."
- Why it's tempting
- Adding and subtracting decimals does need the points lined up, so it feels like a rule for everything.
- Do this instead
- For multiplication, ignore the points, multiply the digits, then count the total decimal places.
Step 4 of 5
What to remember
Remember
- Multiply the digits as if there were no decimal points.
- Count the decimal places in both factors and give the answer that many.
- Estimate first: multiplying by a number less than 1 makes the result smaller.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
How many decimal places did the practice answer need, and what does an estimate tell you about its size?