Explain patterns in the placement of the decimal point when multiplying 5 by 10^2, 10 ^1 and 10^0.
Please explain i'm not very good with math.
10^2 = 100
10^1 = 10
10^0 = 1
Multiply those values by 5.
Oh, you've come to the right place, my friend! Let's take a dive into the wacky world of decimal points.
When you multiply any number by 10 raised to the power of something (let's call it n), what you're essentially doing is moving the decimal point n places to the right. It's like giving the decimal point a little vacation!
So, when you multiply 5 by 10 raised to the power of 2 (or 10^2), you're moving the decimal point 2 places to the right. In this case, the number becomes 500 because the decimal point is now two places to the right of where it originally was.
When you multiply 5 by 10 raised to the power of 1 (or 10^1), you're moving the decimal point 1 place to the right. So, our decimal point goes on a short trip and lands after the 5, turning it into 50.
Finally, when you multiply 5 by 10 raised to the power of 0 (or 10^0), you don't have to move the decimal point at all. It just stays right where it is, making the result 5 (since 5 times 1 is still 5).
So, remember, when you multiply by 10 raised to the power of something, the decimal point likes to take a little vacation and move around to the right!
No problem, let's break it down step by step.
When multiplying a number by a power of 10, the decimal point is shifted to the right by the same number of places as the exponent of 10.
1. Multiplying by 10^2:
- Start with the number 5.
- Multiply it by 10^2, which is equal to 100.
- Since the exponent is 2 (10^2), we shift the decimal point two places to the right.
- The result is 500. So 5 multiplied by 10^2 is equal to 500.
2. Multiplying by 10^1:
- Start with the number 5.
- Multiply it by 10^1, which is equal to 10.
- Since the exponent is 1 (10^1), we shift the decimal point one place to the right.
- The result is 50. So 5 multiplied by 10^1 is equal to 50.
3. Multiplying by 10^0:
- Start with the number 5.
- Multiply it by 10^0, which is equal to 1.
- Since the exponent is 0 (10^0), there is no need to shift the decimal point.
- The result is 5. So 5 multiplied by 10^0 is equal to 5.
In summary, multiplying by powers of 10 moves the decimal point to the right by the same number of places as the exponent.
Of course! I'll be happy to explain this math concept to you.
When multiplying a number by powers of 10, such as 10^2, 10^1, and 10^0, the placement of the decimal point follows a specific pattern.
Let's start with multiplying 5 by 10^2. When we multiply a number by 10 raised to a positive power, it means moving the decimal point to the right by the number of places equal to the exponent.
In this case, 10^2 means moving the decimal point two places to the right. So, if we start with the number 5, moving the decimal point two places to the right gives us 500. Therefore, 5 multiplied by 10^2 is equal to 500.
Next, let's look at multiplying 5 by 10^1. Again, we move the decimal point to the right by the number of places equal to the exponent, which is 1 in this case. Starting with the number 5, moving the decimal point one place to the right gives us 50. Therefore, 5 multiplied by 10^1 is equal to 50.
Finally, let's consider multiplying 5 by 10^0. Any number raised to the power of 0 is equal to 1. So, when we multiply by 10^0, the decimal point doesn't move anywhere. Therefore, 5 multiplied by 10^0 is equal to 5.
To summarize:
- 5 multiplied by 10^2 is equal to 500.
- 5 multiplied by 10^1 is equal to 50.
- 5 multiplied by 10^0 is equal to 5.
I hope this explanation helps! Let me know if you have any more questions.