Multiplying Decimals: Homework

Multiply as if the decimal points are not there, then count the places and put the point back.

Part A — Multiply / 10

Multiply, then count the decimal places. Use the margin for your work.

Each of these has a trap. Count the places and ask whether your answer is reasonable.

1.
0.3 × 0.2. Is it 0.6, 0.06 or 0.006?Answer
2.
8 × 0.5. Is the product more or less than 8?Answer
3.
A student multiplies 25 × 4 = 100 and then writes 2.5 × 4 = 100 with no point. Where does the point go?Answer
4.
0.04 × 0.5. The digits give 20. How many places should the product have, and what is it?Answer
5.
Without multiplying, which is greater, 6.8 × 1.1 or 6.8 × 0.9? Why?Answer

Real numbers from the U.S. Mint. Multiply to find the weight or the height.

Think it through, then write your answer and one sentence about how you knew.

1.
Two decimals with two places each should make a product with four places. Write two such decimals whose product shows only THREE places, and show the product.Answer
2.
0.6 times what number equals 0.18? Use a multiplication fact to help.Answer

Write your own, then work it.

1.
Write a multiplication of two decimals whose product is smaller than BOTH of the numbers you multiplied. Show it and explain why it works.Answer

Total / 24

Graded by

Notes

Part A — the products.

Part B — the answer.

0.06. One place plus one place makes two places.
4, which is less than 8. Taking half of something makes less.
10. 2.5 has one decimal place, so 100 becomes 10.0, or 10.
0.02. Two places plus one place is three places, 0.020, and the zero on the end can be dropped.
6.8 × 1.1. Times more than 1 makes it bigger than 6.8, and times less than 1 makes it smaller. (7.48 against 6.12.)

Part C — the answers.

Part D — one correct answer, and what a good explanation says.

Answers vary. One that works is 0.25 × 0.14 = 0.0350, written 0.035. The product has four places, but its last digit is a zero, so it shows only three.
0.3, because 6 × 3 = 18, and 0.6 × 0.3 has two places, 0.18.

Part E — what a good problem looks like.

Answers vary. A good one uses two numbers less than 1, such as 0.5 × 0.4 = 0.2. Taking part of a part leaves less than either one.