Neft Teacher · Learn It

Unit 2 · Standard 6.NOS.3

Multiply Decimals

Lesson 2-12 · Learn It — how the math works

Why we're learning this

The station needs 4.5 meters of heat shielding that costs $12.60 per meter. Commander Diaz needs to calculate the total cost before submitting the supply order. What is the total cost of the shielding?

✱ Math Workbench

Learn It

How do you multiply decimals?

To multiply decimals, you multiply the numbers as if there were no decimal points. Then you count the decimal places and put the point back in the answer.

Picture itSee what the math looks like before you read about it

The station needs 4.5 meters of heat shielding. The shielding costs $12.60 per meter.
Where you see this in real lifeThe station needs 4.5 meters of heat shielding. The shielding costs $12.60 per meter.

Watch me solve itI do — read one step at a time

The problem looks like this
Table of steps: 45 × 1260 is 56,700; 1 + 2 is 3 decimal places; the point goes 3 places in, giving 56.700, or $56.70.StepMultiply 45 × 1260Decimal places: 1 + 2Point 3 places inResult56,700356.700 = $56.70
  1. I want 4.5 × 12.60, the cost of 4.5 meters at $12.60 each.4.5 × 12.60
  2. First I multiply without points, like whole numbers:45 × 1260 = 56,700
  3. Now I count : 4.5 has 1, and 12.60 has 2, so 1 + 2 = 3 decimal places.1 + 2 = 3
  4. I put the point 3 places from the right in 56,700: that gives 56.700, or $56.70.
  5. I check with an : 5 × $13 = $65, and $56.70 is close, so my answer is reasonable.5 × $13 = $65

Watch out — mistakes students make here

  • Recompute 46 × 23 first, then place the decimal point.
  • Count decimal places: one plus one equals two places.
  • The digits are right, but where is the decimal point?

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Let's multiply 0.4 × 0.7. First multiply like whole numbers: what is 4 × 7?0.4 × 0.7
    Check this step
    (28.)
  2. Now count : 0.4 has 1 and 0.7 has 1, so that is 2 places total.
  3. Put the point 2 places from the right in 28: 0.28. So 0.4 × 0.7 = 0.28.0.4 × 0.7 = 0.28

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: count the in both factors and add them to place the point.

Solve: A car travels 55.5 miles per hour for 2.4 hours. How far does it go?

My answer

Stuck? Open one hint at a time.

Hint 1

Distance = speed × time, so this is 55.5 × 2.4. Estimate 55 × 2 first so you know roughly how big the answer must be.

Hint 2

Multiply 555 × 24 as whole numbers, then count the decimal places: one from 55.5 plus one from 2.4.

Hint 3

Split it up: 555 × 24 = 555 × 20 + 555 × 4. Add those two pieces, then shift the decimal point two places left.

Check my answer
✅ Answer: 133.2 miles
555 × 24 = 13,320. Total decimal places: 1 + 1 = 2. Answer: 133.20 = 133.2 miles.

Turn & TalkSay it out loud with a partner

The station needs 4.5 meters of heat shielding at $12.60 per meter. About how much will it cost, and how did you before multiplying?

Try starting with:

  • I estimate about $___ because 4.5 is close to ___ and $12.60 is close to ___.Estimo unos $___ porque 4.5 está cerca de ___ y $12.60 está cerca de ___.
  • So the real answer should be near ___.Entonces la respuesta real debe estar cerca de ___.
Use these wordsproductdecimal pointestimateplace valuedecimal places