Question

6200.07 = 6.2 × 10^c + 7 × 10^d
Work out the values of c and d.

Answer 1

b = 3, c = -2

Explanation:

Given the standard form of the expression with unknown value

6200.07 = 6.2 × 10^c + 7 × 10^d

Step 1:

We will write 6200.07 as a sum of whole number and a decimal.

6200.07 = 6200+0.07

Step 2:

Expressing each term in it standard form.

6200 = 6.2×10³ ((it has a positive power because it is a value greater than zero)

0.07 = 7×10^-2 (it has a negative power because it is less than zero)

6200.07 = 6.2 × 10^3 + 7 × 10^-2

Comparing with the question, it can be seen that b = 3, c = -2

Answer 2

Answer: We have c = 3 and d = -2

Explanation:

We want to solve the equation:

6200.07 = 6.2x10^c + 7x10^d

First, we can separate the left number into two pieces:

6200.07 = 6200 + 0.07 = 6.2x10^c + 7x10^d

Now we can solve it as:

6200 = 6.2x10^c

6200/6.2 = 10^c

1000 = 10^c

now we can use that if y = a^x, then ln(y)/ln(a) = x

here we have:

c = ln(1000)/ln(10) = 3

and

0.07 = 7x10^d

0.07/7 = 10^d

0.01 = 10^d

d = ln(0.01)/ln(10) = -2