5 Problems - SHOW ALL WORK!
In 2012, the population of NY was about 2.4 x 10^7 and the population of Oregon was 4 x 10^5.
How many more people live in NY than in Oregon? = (2.4 x 10^7) - (4 x 10^5) = 2.36 x 10^6 more people in NY than Oregon.
4.29 x 10^6 - 1.68 x 10^6=
5.08 x 10^-4 - 3.12 x 10^-5=
A. 6 x 10^4 - 8 x 10^2=
B. 6 x 10^4 - 0.08 x 10^4=
In problem 4, what do you notice between the two answers?
For the first two problems, we are subtracting numbers in scientific notation.
For 4.29 x 10^6 - 1.68 x 10^6:
= (4.29 - 1.68) x 10^6
= 2.61 x 10^6
For 5.08 x 10^-4 - 3.12 x 10^-5:
= (5.08 - 0.312) x 10^-4
= 4.768 x 10^-4
For problem A, 6 x 10^4 - 8 x 10^2:
= (6 - 0.8) x 10^4
= 5.2 x 10^4
For problem B, 6 x 10^4 - 0.08 x 10^4:
= (6 - 0.08) x 10^4
= 5.92 x 10^4
In problem 4, we see that for the first two problems, when subtracting numbers in scientific notation, we simply subtract the coefficients and keep the same exponent. This is illustrated by how we solved problems 1 and 2.
For problems A and B, we notice that both involve subtracting numbers with the same exponent (10^4 in this case), but in problem B, one of the coefficients is not in scientific notation. To subtract, we first need to convert this to scientific notation, which is illustrated by the solving of problem B.