Jerome and Shannon used other paper-and-pencil methods to solve 8.5 7.5.
“I think my rule will work here,” exclaimed Lee Yah. “Let's see if the sum of the number of digits after the decimal points in the factors equals the number of digits after the decimal point in the product. “
Lee Yah went on to explain, “In this problem, there is one digit after the decimal point in 8.5 and one digit after the decimal point in the other factor, 7.5. That's a total of two digits after the decimal points in the factors, so there should be two digits after the decimal point in the product, 63.75. My rule works!”
Jessie wanted to try Lee Yah's rule. She used all-partials to multiply 2.6 5.1.
“Your answer is 1326! That can't be right!” exclaimed Shannon. “I'll estimate to check. First round 2.6 to 3 and 5.1 to 5. 3 5 = 15. The answer should be close to 15.”
“Oh! I forgot to put the decimal point in my answer,” said Jessie. I think the decimal point should go between the 3 and the 2 to make 13.26.”
Jessie also noticed, “There is one digit after the decimal point in 2.6 and one digit after the decimal point in 5.1. That's a total of two digits after the decimal points in the factors, and there are two digits after the decimal point in my product, 13.26. Lee Yah's rule works!”