Question

multiply. write your answer in scientific notation. 0.3·(1 × 10¹)

Explanation:

Step1: Multiply the coefficients

Multiply \( 0.3 \) and \( 1 \), we get \( 0.3\times1 = 0.3 \).

Step2: Keep the power of 10

The power of 10 is \( 10^{1} \), so we have \( 0.3\times10^{1} \).

Step3: Convert to scientific notation

Scientific notation requires the coefficient to be between \( 1 \) and \( 10 \). So we rewrite \( 0.3 \) as \( 3\times10^{-1} \). Then multiply by \( 10^{1} \): \( 3\times10^{-1}\times10^{1}=3\times10^{0} \) (since \( a^{m}\times a^{n}=a^{m + n} \), so \( - 1+1 = 0 \)). And \( 10^{0}=1 \), but in scientific notation, we can write it as \( 3\times10^{0} \) or simply \( 3\times10^{0} \) (but usually, if the exponent is 0, we can write the number as is, but following the scientific notation format, it's \( 3\times10^{0} \), but actually, \( 0.3\times10^{1}=3 \), and in scientific notation, \( 3 = 3\times10^{0} \)). Wait, actually, let's do it more simply: \( 0.3\times(1\times10^{1})=(0.3\times1)\times10^{1}=0.3\times10^{1} \). Now, to convert \( 0.3\times10^{1} \) to proper scientific notation, we move the decimal point in \( 0.3 \) one place to the right to get \( 3 \), and decrease the exponent of 10 by 1 (because we moved the decimal right, the exponent of 10 decreases by 1). So \( 0.3\times10^{1}=3\times10^{0} \). But \( 10^{0}=1 \), so \( 3\times1 = 3 \), and in scientific notation, that's \( 3\times10^{0} \), but also, since \( 3 \) is between \( 1 \) and \( 10 \), we can also write it as \( 3\times10^{0} \), or more straightforwardly, \( 0.3\times10^{1}=3 \), and \( 3 \) in scientific notation is \( 3\times10^{0} \). But maybe a better way: when multiplying a number in scientific notation (or a number and a number in scientific notation), we multiply the non - power - of - 10 parts and the power - of - 10 parts separately. So \( 0.3\times(1\times10^{1})=(0.3\times1)\times10^{1}=0.3\times10^{1} \). Now, \( 0.3 = 3\times10^{-1} \), so \( 3\times10^{-1}\times10^{1}=3\times10^{-1 + 1}=3\times10^{0}=3 \). And \( 3 \) in scientific notation is \( 3\times10^{0} \), but sometimes, if the exponent is 0, we can just write the number, but the problem says to write in scientific notation, so \( 3\times10^{0} \) or \( 3\times10^{0} \) (which is equivalent to 3, but in scientific notation form). Wait, maybe I overcomplicated. Let's do it step by step correctly:

1. Multiply the coefficients: \( 0.3\times1 = 0.3 \)
2. Multiply the powers of 10: \( 10^{0}\times10^{1}=10^{1} \) (wait, no, the second number is \( 1\times10^{1} \), so the power of 10 is \( 10^{1} \), and the first number is \( 0.3=0.3\times10^{0} \)). So \( (0.3\times10^{0})\times(1\times10^{1})=(0.3\times1)\times(10^{0}\times10^{1})=0.3\times10^{1} \)
3. Now, convert \( 0.3\times10^{1} \) to scientific notation. In scientific notation, the coefficient must be between 1 and 10. So we take \( 0.3 \) and move the decimal point one place to the right to get \( 3 \). When we move the decimal point one place to the right in \( 0.3 \), we are multiplying by 10, so to keep the value the same, we must divide by 10 (or multiply by \( 10^{-1} \)) the power of 10. So \( 0.3\times10^{1}=3\times10^{-1}\times10^{1}=3\times10^{-1 + 1}=3\times10^{0} \)

Answer:

\( 3\times10^{0} \) (or simply \( 3\times10^{0} \), and since \( 10^{0}=1 \), it can also be written as \( 3 \), but in scientific notation, \( 3\times10^{0} \) is correct)