How many digits in a product?
Between 100 and 10,000.
Roxie’s claim
Roxie says: “The product of two 2-digit numbers can only be a 3-digit or a 4-digit number.”
Do you think she is right?
What this lesson covers
The idea
The product of two 2-digit numbers is a 3- or 4-digit number, because it is at least 10 × 10 = 100 and less than 100 × 100 = 10,000.
Roxie’s claim
Roxie says: “The product of two 2-digit numbers can only be a 3-digit or a 4-digit number.”
Do you think she is right?
- Yes, always 3 or 4 digits
- No, sometimes only 2 digits
- No, sometimes 5 digits
Hunt for the extremes
Slide the two numbers. Find the smallest and the biggest product you can make.
Why only 3 or 4 digits?
The smallest 2-digit number is 10, so the smallest product is 10 × 10 = 100. The smallest 3-digit number is 100, and every 2-digit number is less than that, so every product is less than 100 × 100 = 10,000.
The product of two 2-digit numbers is a 3- or 4-digit number, because it is at least 10 × 10 = 100 and less than 100 × 100 = 10,000.
Notes
The product of two 2-digit numbers is a 3- or 4-digit number, because it is at least 10 × 10 = 100 and less than 100 × 100 = 10,000.
Check yourself
Which number of digits is impossible for a product of two 2-digit numbers?
The biggest 2-digit number is 99. What is 99 × 99?
Answer: 9801
99 × 99 = 9801. It is just below 10,000.
The smallest 3-digit numbers are 100 and 100. How many digits does 100 × 100 have?
Answer: 5
100 × 100 = 10,000 has 5 digits. So a product of two 3-digit numbers has at least 5 digits.
- 3 digits. 10 × 12 = 120 has 3 digits. It is possible.
- 2 digits — correct. Yes! Even 10 × 10 = 100 has 3 digits.
- 4 digits. 50 × 50 = 2,500 has 4 digits. It is possible.