Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Entry Level Assessment - Multiple Choice - Page XXXIV: 8


H) $237,000$

Work Step by Step

Step 1: 10 to the 4th has a positive 4, meaning the decimal point will move to the right 4 places (see below why). Step 2: Find the decimal point; 23.7 has a decimal point between 3.7. Step 3: Move it to the right 4 places (23.7 --> 237 --> 2370 --> 23700 --> 237000) Step 4: Add units and state answer; the Final answer is 237,000 dollars. Word Explanation: For this equation of 23.7 x 10^{4}, the decimal point has to move forward because the exponent, 4, is positive. Therefore, by moving to the right, the number gets bigger, which would be expected when multiplying by a positive integer. One way to solve this would be to find out 10 to the 4th power is 10,000. Multiplying this by 23.7 would mean counting the number of zeros, which is 4, and moving it from its position in between the 3.7 in 23.7 to the right 4 places, which was already established before. Therefore, the final answer would be 237,000 dollars. However, a simpler way to do this would just be simply to look at the exponent of 10, and see if it's positive or negative. The number would signify how much places the decimal would move, and the sign would indicate which direction. Since 10 to the 4th is positive and 4, the decimal point in 23.7 would move 4 spots to the right, and every spot where there is no place or number, add a 0 there. By doing so, you also get $237,000. Detailed Explanation of Why: This is because multiplying by a positive integer would mean the decimal point would go to the right; increasing the value of the number. So, if the exponent is positive, it would go to the right "n" number of values, where n is the exponent number itself. If the exponent was a negative "n", then the decimal point would move to the left "n" places; multiplying by a negative number would make the number smaller; therefore moving it to the left would make it closer to becoming a decimal <1.
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