Which number is greater, 23×103 or 11×104 ? How do you know? Show your work and explain your steps.
To compare the two numbers, we need to simplify each expression.
23 × 10^3 = 23,000
11 × 10^4 = 110,000
Comparing these two value, we can see that 110,000 is greater than 23,000.
Therefore, 11 × 10^4 is greater than 23 × 10^3.
Which number is greater, 23×103 or 11×104 ? How do you know? Show your work and explain your steps.
To compare the two numbers, we need to simplify each expression.
23 × 10^3 = 23,000
11 × 10^4 = 110,000
Comparing these two values, we can see that 110,000 is greater than 23,000.
Therefore, 11 × 10^4 is greater than 23 × 10^3.
Can you explain it
Certainly! To compare the two numbers, we look at the coefficients and the exponents.
For 23 × 10^3:
- The coefficient is 23, which is a smaller number compared to 11 in the other expression.
- The exponent is 3. Since 10^3 means multiplying by 10 three times, we can write it as 10 × 10 × 10, which equals 1,000.
So, 23 × 10^3 can be written as 23 × 1,000 = 23,000.
Now, let's look at 11 × 10^4:
- The coefficient is 11, which is greater than 23 in the previous expression.
- The exponent is 4. Similarly, 10^4 means multiplying by 10 four times, which can be written as 10 × 10 × 10 × 10, equal to 10,000.
So, 11 × 10^4 can be written as 11 × 10,000 = 110,000.
Comparing the two values, we see that 110,000 is greater than 23,000.
Therefore, 11 × 10^4 is greater than 23 × 10^3.
To determine which number is greater, we can compare the two numbers by calculating their values.
Let's calculate the value of 23×10^3:
23 × 10^3 = 23 × 1000 = 23,000
Now let's calculate the value of 11×10^4:
11 × 10^4 = 11 × 10,000 = 110,000
Comparing the two values, we can see that 110,000 is greater than 23,000.
Therefore, 11×10^4 is greater than 23×10^3.
To compare the two numbers, let's first write them in standard form:
23 × 10^3 = 23,000
11 × 10^4 = 110,000
Now we can clearly see that the second number, 11 × 10^4, is greater than the first number, 23 × 10^3. This is because 110,000 is greater than 23,000.
So, the answer is that 11 × 10^4 is the greater number.
Here are the steps to determine this:
1. Convert both numbers to standard form by multiplying the coefficient by the power of 10.
- For the first number, 23 × 10^3, multiply 23 by 10 raised to the power of 3, which equals 23,000.
- For the second number, 11 × 10^4, multiply 11 by 10 raised to the power of 4, which equals 110,000.
2. Compare the two standard form numbers.
- 23,000 is less than 110,000.
3. Determine which number is greater.
- Since 110,000 is greater than 23,000, we conclude that 11 × 10^4 is the greater number.