Answer :
Sure! Let's solve each question one by one with clear explanations:
Question 12:
7 × 10^? = 7000
We start with the left-hand side, which is 7 multiplied by 10 raised to some power. On the right-hand side, we have 7000. We need to find what power will make the equation true.
- 7 is multiplied by a power of 10 to result in 7000.
- Notice that 7000 is the same as 7 followed by three zeros, which can be expressed as 7 times 1000.
- 1000 is the same as 10^3.
So, the missing number that makes this equation true is 3.
Question 13:
5.21 × 10^? = 521,000
In this case, we need 5.21 multiplied by 10 raised to some power to equal 521,000.
- We need to move the decimal point in 5.21 to the right until we reach 521,000.
- Starting at 5.21, moving the decimal point one place to the right gives 52.1, another place gives 521, the third place gives 5210, the fourth gives 52,100, and the fifth gives 521,000.
We moved the decimal point five places to get from 5.21 to 521,000. Therefore, the missing exponent is 5.
Question 14:
? × 10^4 = 25,000
We need to find the number that, when multiplied by 10 raised to the power of 4, results in 25,000.
- Start by recognizing that 10^4 is 10,000.
- We need a number that, when multiplied by 10,000, equals 25,000.
- Think of it as 25,000 divided by 10,000. This simplifies to 2.5.
So, the missing number is 2.5.
I hope this step-by-step explanation helps clarify how we determined the missing numbers!
Question 12:
7 × 10^? = 7000
We start with the left-hand side, which is 7 multiplied by 10 raised to some power. On the right-hand side, we have 7000. We need to find what power will make the equation true.
- 7 is multiplied by a power of 10 to result in 7000.
- Notice that 7000 is the same as 7 followed by three zeros, which can be expressed as 7 times 1000.
- 1000 is the same as 10^3.
So, the missing number that makes this equation true is 3.
Question 13:
5.21 × 10^? = 521,000
In this case, we need 5.21 multiplied by 10 raised to some power to equal 521,000.
- We need to move the decimal point in 5.21 to the right until we reach 521,000.
- Starting at 5.21, moving the decimal point one place to the right gives 52.1, another place gives 521, the third place gives 5210, the fourth gives 52,100, and the fifth gives 521,000.
We moved the decimal point five places to get from 5.21 to 521,000. Therefore, the missing exponent is 5.
Question 14:
? × 10^4 = 25,000
We need to find the number that, when multiplied by 10 raised to the power of 4, results in 25,000.
- Start by recognizing that 10^4 is 10,000.
- We need a number that, when multiplied by 10,000, equals 25,000.
- Think of it as 25,000 divided by 10,000. This simplifies to 2.5.
So, the missing number is 2.5.
I hope this step-by-step explanation helps clarify how we determined the missing numbers!
