Question

evaluate. express your answer in scientific notation.
$930,000 - 6.6 \times 10^4$
answer
attempt 1 out of 3
answer: $\square \times 10^{\square}$
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Explanation:

Step1: Convert 930,000 to scientific notation

To convert 930,000 to scientific notation, we move the decimal point 5 places to the left, so \( 930,000 = 9.3\times10^{5} \). We can also rewrite it with the same exponent as \( 6.6\times10^{4} \) by adjusting the coefficient. Since \( 10^{5}=10\times10^{4} \), we have \( 930,000 = 93\times10^{4} \) (because \( 9.3\times10^{5}=9.3\times10\times10^{4}=93\times10^{4} \)).

Step2: Perform the subtraction

Now we subtract \( 6.6\times10^{4} \) from \( 93\times10^{4} \). Using the distributive property of multiplication over subtraction, \( (93 - 6.6)\times10^{4} \). Calculating \( 93 - 6.6 = 86.4 \), so we have \( 86.4\times10^{4} \).

Step3: Convert to proper scientific notation

In scientific notation, the coefficient must be between 1 and 10. So we rewrite \( 86.4\times10^{4} \) as \( 8.64\times10^{5} \) (because \( 86.4 = 8.64\times10^{1} \), so \( 86.4\times10^{4}=8.64\times10^{1}\times10^{4}=8.64\times10^{5} \) by the rule of exponents \( a^{m}\times a^{n}=a^{m + n} \)).

Answer:

\( 8.64 \times 10^{5} \)