Counting decimal places in a product

The idea

To multiply two decimals, multiply the numbers obtained by removing the decimal points; the number of digits after the decimal point in the product is the total number in the multiplier and multiplicand.

596 × 248

Suppose we know that 596 × 248 = 147808. Now look at 5.96 × 24.8. The number 5.96 is a little less than 6 and 24.8 is a little less than 25. And 6 × 25 = 150.

Can you write 5.96 × 24.8 straight away?

• 14.7808
• 147.808
• 1478.08

Move the points

The digits of both numbers stay the same. Move the decimal point in each factor. The product follows, and the toy counts the decimal places.

Add the places

A factor with 2 places after the point is hundredths; one with 1 place is tenths. Hundredths × tenths make thousandths: 3 places. The places just add up.

To multiply two decimals, multiply the numbers with the decimal points removed. The product has as many digits after the decimal point as the multiplier and multiplicand together.

• Multiply | Whole numbers, then places
• 5.96 × 24.8 | 596 × 248 = 147808. 2 + 1 = 3 places: 147.808
• 5.8 × 1.24 | 58 × 124 = 7192. 1 + 2 = 3 places: 7.192
• 1.64 × 6 | 164 × 6 = 984. 2 + 0 = 2 places: 9.84
• 5.7 × 13.35 | 57 × 1335 = 76095. 1 + 2 = 3 places: 76.095

Notes

Remove the points and multiply as whole numbers. Then put as many digits after the point in the product as the two numbers have together.

Check yourself

You know 18 × 12 = 216. What is 1.8 × 1.2?

Answer: 2.16

1 + 1 = 2 places: 216 becomes 2.16.

Using 18 × 12 = 216, what is 0.18 × 0.12?

Answer: 0.0216

4 places: 216 → 0216 → 0.0216.

25 × 4 = 100. What is 2.5 × 4?

Does 56.50 × 2.250 give the same product as 56.5 × 2.25?

You know 596 × 248 = 147808. What is 0.596 × 24.8?

Answer: 14.7808

3 + 1 = 4 places: 147808 becomes 14.7808. (Check by size: 0.596 is about 0.6 and 0.6 × 24.8 is about 15.)

• 1. That puts 2 places in the product. 2.5 has one place and 4 has none: 1 place only.
• 10 — correct. 1 + 0 = 1 place: 100 becomes 10.0 and the 0 after the point can be dropped. The product is a counting number.
• 100. The point has to move: 2.5 has one place after the point.
• No. 56.50 is bigger than 56.5, so the product is bigger.. Zero at the end of the decimal part adds nothing: 56.50 = 56.5.
• No. The first product has 5 places and the second only 3, so they differ.. The 5 places give 127.12500. The last two are zeroes, so the value is 127.125.
• Yes, the same. The extra zeroes at the end change nothing. — correct. 5650 × 2250 = 12712500 and 2 + 3 = 5 places: 127.12500, which is 127.125. A zero at the end of the decimal part changes nothing.