L2 · Multiplying decimals

Learning goal

“I can multiply decimals by whole numbers and by 1- or 2-digit decimals, placing the decimal point by counting decimal places - and I can use estimation to prove my point is in the right place.”

Factor — a number being multiplied: in 3.4 x 6, the factors are 3.4 and 6.

Product — the result of a multiplication.

Decimal places — the number of digits after the decimal point: 2.35 has 2 decimal places; 0.7 has 1.

Estimate — a rough calculation with rounded numbers (from L1), the referee for decimal-point placement.

Worked example

3.4 x 6. Step 1 (estimate): 3.4 is about 3, so the product is near 3 x 6 = 18 - the answer is a two-digit-ish number, NOT 2.04 or 204. Step 2 (ignore the point, multiply): 34 x 6 = 204. Step 3 (place the point): 3.4 has 1 decimal place, so the product has 1 decimal place: 20.4. Step 4: Estimate said about 18-20. 20.4 checks out. (The other candidates, 2.04 and 204, fail the estimate - that is what the estimate is FOR.) Say it plainly: multiply as whole numbers, then let the total count of decimal places tell you where the point lands - and let the estimate referee.

Check yourself — explain it

In 3.4 x 6, the product has exactly 1 decimal place because...

Paired problem — example still visible

12.6 x 3 -> 126 x 3 = 378, 1 decimal place -> 37.8

Faded completion — last step is yours

"4.25 x 8: 425 x 8 = 3,400; decimal places = 2, so the product is ___" -> 34.00 (= 34)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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