Question

9. Calculate 5.3 * 10 ^ - 3 - 6.7 * 10^-6. Express the answer in scientific notation rounding to 2 decimal places.

Answer 1

To subtract two numbers written in scientific notation, the exponents of the powers of ten must be the same.

Given:

5.3 * 10^-3 - 6.7 * 10^-6

Let's change the first number so that the exponent becomes -6 instead of -3. This can be done by multiplying it by 10^(-3 + 6) = 10^3:

5.3 * 10^-3 - 6.7 * 10^-6 = 5.3 * (10^-3 * 10^3) - 6.7 * 10^-6
= 5.3 * 10^(3-3) - 6.7 * 10^-6
= 5.3 * 10^0 - 6.7 * 10^-6

Since 10^0 = 1, we can simplify to:

5.3 * 10^0 - 6.7 * 10^-6 = 5.3 - 6.7 * 10^-6

To express the answer in scientific notation rounded to 2 decimal places, we can convert it back into scientific notation:

5.3 - 6.7 * 10^-6 = 5.3 - 0.0000067
= 5.2999933

Rounded to 2 decimal places, the answer is approximately 5.30.

Therefore, 5.3 * 10^ - 3 - 6.7 * 10^-6 = 5.30 * 10^0 in scientific notation.