Question

mark true or false for each statement.
①
t
when multiplying numbers in scientific notation, the exponents have to match.
f
②
t
when dividing numbers in scientific notation, you divide the decimal factors and subtract the exponents.
f
③
t
when multiplying or dividing in scientific notation, your answer should always have a decimal number of at least 1 but less than 10.
f
circle all the numbers that represent the same value.
$(9.63\times10^{14})\div(3\times10^{8})$ 963,000
$(1.07\times10^{4})\cdot(9\times10^{2})$
$(1.07\times10^{2})\cdot(3\times10^{4})$ $3.21\times10^{6}$

Explanation:

Step1: Calculate \((9.63\times10^{14})\div(3\times10^{8})\)

Use the rule \(a\times10^{m}\div(b\times10^{n})=(a\div b)\times10^{m - n}\).
So, \((9.63\div3)\times10^{14 - 8}=3.21\times10^{6}\)

Step2: Calculate \((1.07\times10^{4})\cdot(9\times10^{2})\)

Use the rule \((a\times10^{m})\cdot(b\times10^{n})=(a\cdot b)\times10^{m + n}\).
\((1.07\times9)\times10^{4 + 2}=9.63\times10^{6}\)

Step3: Calculate \((1.07\times10^{2})\cdot(3\times10^{4})\)

Use the rule \((a\times10^{m})\cdot(b\times10^{n})=(a\cdot b)\times10^{m + n}\).
\((1.07\times3)\times10^{2+4}=3.21\times10^{6}\)

Answer:

\((9.63\times10^{14})\div(3\times10^{8})\) and \((1.07\times10^{2})\cdot(3\times10^{4})\) and \(3.21\times10^{6}\) represent the same value.