Answer:
- 6.02 x 10⁵ = 602000.
- 3.12 x 10⁻⁶ = 0.00000312.
- 5 x 10³ = 5000.
- -4.73 x10⁷ = -47300000.
- 5.436 x 10² = 543.6.
- 5 x 10⁻⁶ = 0.000005.
- 3.41 x 10¹ = 34.1.
Step-by-step explanation:
Measurements => Scientific Notation.
As we already know, to write numbers in scientific notation we have to write a coefficient greater or equal to 1 and less than 10 multiplied by 10 raised to a power. In this case, we have to write the long form of a number by a given number in scientific notation, so let's analyze each case:
- 6.02 x 10⁵: You can see that we 10⁵ equals 100000. This means that this number has in total 6 digits (if we count the first digit of the coefficient. Remember that this condition applies if we have less number of decimals than the exponent of ten), so 6.02 x 10⁵ = 602000.
- 3.12 x 10⁻⁶: You can note that this is a very small number because the exponent of ten is a negative number. One way to write the long form by a number in scientific notation when we have negative exponents is to write the number of zeros that has the power of ten, in this case, six zeros remembering that we have one zero as coefficient and the other digits are written as decimals, so 3.12 x 10⁻⁶ = 0.00000312.
- 5 x 10³: We apply the same steps that we followed in the first number. We have in total 4 digits numbers. 5 x 10³ = 5000.
- -4.73 x10⁷: We apply the same steps that we followed in the first number; the only difference is that this number is negative. We have in total 8 digits, so -4.73 x10⁷ = -47300000.
- 5.436 x 10²: We apply the same steps that we followed in the first number; the only difference is that this number will not result as an integer because it has a decimal, so 5.436 x 10² = 543.6.
- 5 x 10⁻⁶: We have to follow the same steps that we followed in the second number. We will have that 5 x 10⁻⁶ = 0.000005.
- 3.41 x 10¹: We apply the same steps that we followed in the first number; the only difference is that this number will not result as an integer because it has a decimal, so 3.41 x 10¹ = 34.1.