Question

at times it may be necessary to rewrite one of the expressions so that each has the same power of ten. in each pair of expressions below, practice rewriting one of the expressions to have the same power of ten as the other.
7.5 x 10³ and 2.6 x 10⁴ 1.32 x 10⁵ and 8 x 10⁻⁶
in 5 - 9, find the sum or difference. write all answers in scientific notation.

1. (9 x 10⁵)-(8 x 10⁴) 6. (4.7 x 10⁷)+(3.4 x 10⁵) 7. (7.2 x 10⁻³)-(6.8 x 10⁻⁴)
2. (6.4 x 10⁵)+320,000 9. 0.00054-(3.2 x 10⁻⁴)

apply your knowledge of adding and subtracting with powers of ten to answer 10 - 11.

1. summerville has a population of 430,000 people, while eagleton has a population of 5.7 x 10⁵ people. what is the difference in population between the two towns?
2. kristin is using paper for an art project that is 0.025 mm thick. if she glues a layer of the paper onto a construction board with a thickness of 7 x 10⁻² mm, what will the total thickness of the paper and the construction board be?

scientific:
standard:
scientific:
standard:

Explanation:

Step1: Rewrite numbers with same power of ten

For \(7.5\times 10^{3}\) and \(2.6\times 10^{4}\), rewrite \(7.5\times 10^{3}=0.75\times 10^{4}\). For \(1.32\times 10^{5}\) and \(8\times 10^{-6}\), rewrite \(1.32\times 10^{5} = 13200000000\times 10^{-6}\).

Step2: Solve problem 5

\((9\times 10^{5})-(8\times 10^{4})=(9\times 10^{5})-(0.8\times 10^{5})=(9 - 0.8)\times 10^{5}=8.2\times 10^{5}\)

Step3: Solve problem 6

\((4.7\times 10^{7})+(3.4\times 10^{5})=(4.7\times 10^{7})+(0.034\times 10^{7})=(4.7+ 0.034)\times 10^{7}=4.734\times 10^{7}\)

Step4: Solve problem 7

\((7.2\times 10^{-3})-(6.8\times 10^{-4})=(7.2\times 10^{-3})-(0.68\times 10^{-3})=(7.2 - 0.68)\times 10^{-3}=6.52\times 10^{-3}\)

Step5: Solve problem 8

Rewrite \(320000 = 3.2\times 10^{5}\), then \((6.4\times 10^{5})+320000=(6.4\times 10^{5})+(3.2\times 10^{5})=(6.4 + 3.2)\times 10^{5}=9.6\times 10^{5}\)

Step6: Solve problem 9

Rewrite \(0.00054=5.4\times 10^{-4}\), then \(0.00054-(3.2\times 10^{-4})=(5.4\times 10^{-4})-(3.2\times 10^{-4})=(5.4 - 3.2)\times 10^{-4}=2.2\times 10^{-4}\)

Step7: Solve problem 10

Rewrite \(430000 = 4.3\times 10^{5}\), then the difference is \((5.7\times 10^{5})-(4.3\times 10^{5})=(5.7 - 4.3)\times 10^{5}=1.4\times 10^{5}\) in scientific - notation and \(140000\) in standard form.

Step8: Solve problem 11

Rewrite \(0.025=2.5\times 10^{-2}\), then the total thickness is \((2.5\times 10^{-2})+(7\times 10^{-2})=(2.5 + 7)\times 10^{-2}=9.5\times 10^{-2}\) mm in scientific - notation and \(0.095\) mm in standard form.

Answer:

1. \(8.2\times 10^{5}\)
2. \(4.734\times 10^{7}\)
3. \(6.52\times 10^{-3}\)
4. \(9.6\times 10^{5}\)
5. \(2.2\times 10^{-4}\)
6. Scientific: \(1.4\times 10^{5}\), Standard: \(140000\)
7. Scientific: \(9.5\times 10^{-2}\), Standard: \(0.095\)