Question

1. how many joules are there in a 255 calorie snack bar? a) ( 2.55 \times 10^5 ) b) ( 1.07 \times 10^6 ) c) ( 6.09 \times 10^4 ) d) ( 1.07 \times 10^3 ) e) none of the above

Explanation:

Step1: Recall the conversion factor

We know that 1 calorie (in the context of food, actually kilocalorie) is equal to 4184 joules. So first, we need to convert 255 calories (food calories, which are kilocalories) to joules. So the conversion factor is $1\ \text{calorie (food)} = 4184\ \text{J}$.

Step2: Set up the calculation

We have 255 food calories, so we multiply 255 by 4184 to get the number of joules.
$255\times4184$

Step3: Perform the multiplication

First, calculate $255\times4184$:
$255\times4184 = 255\times(4000 + 184)=255\times4000+255\times184$
$255\times4000 = 1020000$
$255\times184=(250 + 5)\times184=250\times184+5\times184=46000+920 = 46920$
Then add them together: $1020000+46920 = 1066920$

Step4: Express in scientific notation

Now, we express 1066920 in scientific notation. We move the decimal point 6 places to the left, so we get $1.06692\times10^{6}\approx1.07\times10^{6}$

Answer:

B) $1.07\times 10^{6}$