Question

the table shows 93.7 multiplied by different powers of 10.

multiplication	product
$93.7 \times 10^3$	93,700
$93.7 \times 10^4$	937,000
$93.7 \times 10^5$	?
$93.7 \times 10^6$	?

Explanation:

Step1: Analyze the pattern of multiplying by powers of 10

When multiplying a number by \(10^n\), we move the decimal point \(n\) places to the right. For \(93.7\times10^2 = 9370\) (moved 2 places right), \(93.7\times10^3=93700\) (moved 3 places right), \(93.7\times10^4 = 937000\) (moved 4 places right).

Step2: Calculate \(93.7\times10^5\)

For \(10^5\), we move the decimal point 5 places to the right. \(93.7\) with decimal moved 5 places right: \(93.7\times10^5=9370000\) (since \(93.7\) → \(9370000\) when moving decimal 5 places right: \(93.7\) → \(937.\) (1), \(9370.\) (2), \(93700.\) (3), \(937000.\) (4), \(9370000\) (5)).

Step3: Calculate \(93.7\times10^6\)

For \(10^6\), we move the decimal point 6 places to the right. \(93.7\times10^6 = 93700000\) (moving decimal 6 places right: \(93.7\) → \(937.\) (1), \(9370.\) (2), \(93700.\) (3), \(937000.\) (4), \(9370000\) (5), \(93700000\) (6)).

Answer:

For \(93.7\times10^5\), the product is \(9370000\); for \(93.7\times10^6\), the product is \(93700000\).