Question

circle the number with the greater value.

1. $(1.4×10^{5})·(3.1×10^{3})$ or $430,000,000$
2. $(4.5×10^{8})÷(2.5×10^{3})$ or $19,000$

solve and circle the answer that is different.
a. $(4.55×10^{5})·1,200$
b. $\frac{6.12×10^{8}}{1.2×10^{1}}$
c. $(6.552×10^{7})÷(1.2×10^{5})$

Explanation:

1. For \((1.4\times10^{5})\cdot(3.1\times10^{3})\) vs \(430,000,000\)

Step1: Calculate \((1.4\times10^{5})\cdot(3.1\times10^{3})\)

Use the rule \(a\times10^{m}\cdot b\times10^{n}=(a\cdot b)\times10^{m + n}\).
\((1.4\times3.1)\times10^{5 + 3}=4.34\times10^{8}=434000000\)

Step2: Compare \(434000000\) and \(430000000\)

Since \(434000000>430000000\)

2. For \((4.5\times10^{8})\div(2.5\times10^{3})\) vs \(19000\)

Step1: Calculate \((4.5\times10^{8})\div(2.5\times10^{3})\)

Use the rule \(\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}\).
\(\frac{4.5}{2.5}\times10^{8-3}=1.8\times10^{5}=180000\)

Step2: Compare \(180000\) and \(19000\)

Since \(180000>19000\)

3. For \(a.(4.55\times10^{5})\cdot1200\), \(b.\frac{6.12\times10^{8}}{1.2\times10^{1}}\), \(c.(6.552\times10^{7})\div(1.2\times10^{3})\)

Step1: Calculate \(a.(4.55\times10^{5})\cdot1200\)

\(1200 = 1.2\times10^{3}\), then \((4.55\times10^{5})\cdot(1.2\times10^{3})=(4.55\times1.2)\times10^{5 + 3}=5.46\times10^{8}\)

Step2: Calculate \(b.\frac{6.12\times10^{8}}{1.2\times10^{1}}\)

\(\frac{6.12}{1.2}\times10^{8 - 1}=5.1\times10^{7}\)

Step3: Calculate \(c.(6.552\times10^{7})\div(1.2\times10^{3})\)

\(\frac{6.552}{1.2}\times10^{7-3}=5.46\times10^{4}\)

Answer:

1. Circle \((1.4\times10^{5})\cdot(3.1\times10^{3})\)
2. Circle \((4.5\times10^{8})\div(2.5\times10^{3})\)
3. Circle \(b\)