Which exponent is missing from this equation?
[tex]$5.6 \times 10^{\square}=56,000$[/tex]
A. 5
B. 4
C. 3
D. 2
Answer (2)
Divide 56,000 by 5.6 to find the value that 1 0 □ should equal.
Calculate 5.6 56 , 000 = 10 , 000 .
Express 10,000 as a power of 10: 10 , 000 = 1 0 4 .
Conclude that the missing exponent is 4 .
Explanation
Understanding the Problem We are given the equation 5.6 × 1 0 □ = 56 , 000 and asked to find the missing exponent.
Isolating the Power of 10 We can rewrite the number 56,000 as a product of 5.6 and a power of 10. To do this, we divide 56,000 by 5.6: 5.6 56 , 000 = 10 , 000
Expressing 10,000 as a Power of 10 Now we express 10,000 as a power of 10. Since 10 , 000 = 10 × 10 × 10 × 10 = 1 0 4 , we have 5.6 × 1 0 □ = 5.6 × 10 , 000 = 5.6 × 1 0 4
Finding the Missing Exponent From the equation 5.6 × 1 0 □ = 5.6 × 1 0 4 , we can see that the missing exponent is 4.
Final Answer Therefore, the missing exponent is 4.
Examples
Exponents are used to represent very large or very small numbers in a compact form. For instance, the distance to a star can be expressed using exponents. If a star is 56,000,000,000 km away, we can write this as 5.6 × 1 0 10 km. This makes it easier to work with and understand such large numbers.
The missing exponent in the equation 5.6 × 1 0 □ = 56 , 000 is 4. This is determined by dividing 56,000 by 5.6 to find that 1 0 □ = 10 , 000 , which can be expressed as 1 0 4 . Therefore, the correct answer is option B, 4.
;
