Question

complete the addition using significant figures. note that the powers of 10 must be the same.
(8.88888×10^{22} dm)+(1.00×10^{21} dm)=
first, convert the exponent in 1.00×10^{21} dm to 10^{22} by 1 (multiplying or dividing) by 10^{1}, then 2 the 1.00 by 10^{1} (multiplying or dividing).
this gives and intermediate answer of 3 dm.
then, line up the decimals, complete the math, and use the rules of significant figures.
the final answer is 4.
a. multiplying b. dividing c. 0.100×10^{22} d. 0.1×10^{22}
e. 8.98888×10^{22} dm f. 8.9889×10^{22} dm g. 8.989×10^{22} dm
h. 8.99×10^{22} dm i. 9.00×10^{22} dm

Explanation:

Step1: Convert exponent

To change $1.00\times 10^{21}$ to the form with exponent $10^{22}$, we divide by $10^{1}$ (because $a^{m - n}=\frac{a^{m}}{a^{n}}$, here $m = 22,n = 1$), so the answer to the first - blank is dividing.

Step2: Adjust coefficient

When we divide the power of 10 by $10^{1}$, we multiply the coefficient 1.00 by $10^{1}$ to keep the value the same.

Step3: Get intermediate form

$1.00\times 10^{21}=\frac{1.00}{10}\times10^{21 + 1}=0.100\times 10^{22}$

Step4: Perform addition

$(8.88888\times 10^{22})+(0.100\times 10^{22})=(8.88888 + 0.100)\times10^{22}=8.98888\times 10^{22}$

Answer:

1. B. dividing
2. A. multiplying
3. C. $0.100\times 10^{22}$
4. E. $8.98888\times 10^{22}\text{ dm}$